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https://economics.stackexchange.com/questions/40708/price-elasticity-of-demand-of-ces

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# Price elasticity of demand of CES Anyone would like to help me show the following ( or a book/paper reference would be a great help) " The price elasticity of demand is equal to $$\sigma$$ for the demand function of CES preference, $$d(p_i,I,P)=\dfrac{p_i^{-\sigma} I}{P^{1-\sigma}}$$, where $$P=\left(\sum_{j=1}^N p_j^{1-\sigma}\right)^{\dfrac{1}{1-\sigma}}$$ and $$I=\sum_{j=1}^Np_jx_j$$." The formula for the price elasticity of demand is given by $$\epsilon_i(p_i,I,P)=-\dfrac{\partial d(p_i,I,P)}{\partial p_i}\dfrac{p_i}{d(p_i,I,P)}$$. I have tried many times but couldn't get the desired answer. Thank you very much in advance. Assuming that $$p_i \neq p_j$$ you just apply the formula; $$\epsilon_i(p_i,I,P) =-\dfrac{\partial d(p_i,I,P)}{\partial p_i}\dfrac{p_i}{d(p_i,I,P)} \\ = -\left( \frac{-\sigma p_i^{-\sigma-1} I}{P^{1-\sigma}} \right)\frac{p_i}{\frac{p_i^{-\sigma} I}{P^{1-\sigma}}} =\sigma$$. The way how you gave the problem neither $$P$$ or $$I$$ contain $$p_i$$ so you treat them as constants during differentiation. • Thank you very much!! Nov 7, 2020 at 1:59 • @stochasticlearner you are welcome if you think this answered your Q consider accepting it – 1muflon1 Nov 7, 2020 at 11:21

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Doubtnut App - Get 50 Lakh+ video solutions better than GoogleInstall Now # In a △ABC, acosB + b cosC + c cosA =a+b+c2 then A Triangle in isosceles B Triangle may be equilateral C sin(AB)+sin(BC)+sin(CA)=32 D 4sin(AB2)sin(BC2)sin(CA2)=1 Text Solution Verified by Experts

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# APPLIED PHYSICS, BASIC MATHEMATICS FOR BIOMEDICAL SCIENCES, INFORMATICS cod. 1005246 1° year of course - First semester Professor responsible for the course unit OLEARI Claudio integrated course unit 11 credits hub: PARMA course unit in ITALIAN Course unit structured in the following modules: ## Learning objectives The course aims to bring students to know and understand in the context of Veterinary Sciences: 4) the statistical indices, the information in a table of data, the distributions of Bernoulli and Gauss; 5) the theoretical foundations of computer basic, vocabulary and main instruments for use competent Informatics; 6) the physical tools preparatory to other topics: chemistry, biochemistry, physiology, biomechanics, radiology. At the end of the course the student must demonstrate the ability to use knowledge and understanding of the course topics 1) the identification and use of data tables, indexes and statistical distributions of Bernoulli and Gauss; 2) in the resolution of simple computer problems; 3) in dealing with the physical technologies in basic research and in diagnostic practice such as electrophoresis, centrifugation, nuclear magnetic resonance, ultrasound, optical fibers for endoscopic microscopy, laser, X-ray equipment, etc. ## Prerequisites Operations on the set of real numbers, with logarithms, exponential and trigonometric functions. ## Course unit content The integrated course of APPLIED PHYSICS, BASIC MATEMATICS APPLIED to alle BIOMEDICAL SCIENES, INFORMATICICS presents the tools necessary to get into veterinary science. The integration is to define the content that they all be addressed at the optimum level and no one is excluded. The contents are: STATISTICS: 1) Fundamentals of mathematics and logic. 2) discrete and continuous random variables, statistical models of random variables. 3) Combinatory and probability theory. Distribution of Gauss and Bernoulli. COMPUTERS: 1) Architecture of the computer and foundations. 2) Operating Systems. 3) Software Applications. 4) The networks and the web. 5) Multimedia '. PHYSICS: 1) Foundations of mechanics. 2) Thermodynamics and Thermodynamics. 3) Fluid statics and fluid dynamics. 4) Electricity, Magnetism and electrical currents. 5) Waves, acoustics. 6) Radiation and Dosimetry. 7) Optics and Spectroscopy. - - - ## Bibliography D. Scannicchio: FISICA BIOMEDICA. EdiSES. 2009. Ppt lessons and exercises in classroom. Teacher’s didactical notes ## Teaching methods Oral lectures in classroom with the use of PPT projection. The lectures deal with the theoretical content and the resolution of significant exercises. The computer course devotes six hours in the classroom use of portable personal computers of students, the purpose of acquiring practical knowledge on the major software applications. ## Assessment methods and criteria The examination consists of three written tests. The examination of mathematics (statistics) includes a written test for admission. The examination of computer science consists of 10 questions, of which 4 are free response and 3 are with multiple choices. Obtaining the European Computer Driving Licence (ECDL) for the corresponding modules in the program allows the student to be exempted from the test. The examination is intended to determine whether the student knows and understands 5) the statistical indexes and tables of data outputs, 6) the Bernoulli and Gauss distributions with the ability to locate and study them; 7) the theoretical foundations of computer basic, vocabulary and main instruments for use competent Informatics; 8) the elements of physics necessary for other disciplines such as chemistry, biochemistry, physiology, biomechanics, and physical technologies in basic research and in diagnostic practice such as electrophoresis, centrifugation, nuclear magnetic resonance, ultrasound, optical fibers for endoscopy, microscopy, laser, X-ray equipment, etc.. The final mark of each written test ranges from 0 to 33. Sufficiency is achieved with a score of 18 or higher. The final mark for the integrated course is given by the arithmetic mean of the three votes. If the average score is higher than 30/30 the mark is “cum laude”. - - -

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# 07.02 Full Road Trip¶ Let's move forward: can we estimate the speed at each point on a longer strip of a road? For example, some 30km of a road with turns and inclines. fe-formula-one.svg We import the common suspects and make a short simulation of a road trip. In [1]: import numpy as np import matplotlib.pyplot as plt %matplotlib inline plt.style.use('seaborn-talk') from sklearn.linear_model import LinearRegression from sklearn.preprocessing import PolynomialFeatures from sklearn.pipeline import make_pipeline For our simulation it is interesting to note that most problems in the real world are not linear, they are either exponential or periodic. Why? Something, something, complexity theory. Anyway, speed on a road is a periodic problem, one speeds up and down in response to the shape of the road he drives on. In [2]: t = 30*np.random.rand(256) spd = 13*np.sin(t/2) + 3.7*np.cos(t/2+7) + 3*t + 0.1*(t-10)**2 - 3*(t-3) + 7 + 2.3*np.random.randn(*t.shape) fig, ax = plt.subplots(figsize=(16, 9)) ax.plot(t, spd, 'o', color='crimson') ax.set(xlabel='time (s)', ylabel='speed (km/h)', xlim=(-2, 32), ylim=(-10, 70)); It is pretty difficult to figure out what polynomial degree we need for this fit. But let's try a guess, degree 5. For the time being we will not worry about a test set or cross validation, we will just explore the data. Once we know something about the problem we will come back and perform proper model evaluation. In [3]: model = make_pipeline(PolynomialFeatures(degree=5), LinearRegression()) model.fit(t[:, np.newaxis], spd[:, np.newaxis]) xfit = np.linspace(0, 30, 3000) yfit = model.predict(xfit[:, np.newaxis]) fig, ax = plt.subplots(figsize=(16, 9)) ax.scatter(t, spd, color='crimson', alpha=0.7) ax.plot(xfit, yfit, color='navy') ax.set(xlabel='time (s)', ylabel='speed (km/h)', xlim=(-2, 32), ylim=(-10, 70)) model Out[3]: Pipeline(memory=None, steps=[('polynomialfeatures', PolynomialFeatures(degree=5, include_bias=True, interaction_only=False, order='C')), ('linearregression', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False))], verbose=False) Ouch, that went pretty badly. This is a case where out model underfits the data, i.e. our model has not enough complexity to model the complexity we see. We can also say that our model has too much bias about how the data looks. Let us try with a big degree, e.g. 100. In [4]: model = make_pipeline(PolynomialFeatures(degree=100), LinearRegression()) model.fit(t[:, np.newaxis], spd[:, np.newaxis]) xfit = np.linspace(0, 30, 3000) yfit = model.predict(xfit[:, np.newaxis]) fig, ax = plt.subplots(figsize=(16, 9)) ax.scatter(t, spd, color='crimson', alpha=0.7) ax.plot(xfit, yfit, color='navy') ax.set(xlabel='time (s)', ylabel='speed (km/h)', xlim=(-2, 32), ylim=(-10, 70)) model Out[4]: Pipeline(memory=None, steps=[('polynomialfeatures', PolynomialFeatures(degree=100, include_bias=True, interaction_only=False, order='C')), ('linearregression', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False))], verbose=False) That ain't good either. On the left hand side we passed the point where we can bend the polynomial and our parameters mess with each other. On the right hand side the polynomial overfits the data; or we say that the model has too much variance. There are two different examples of overfitting on the graph. On the right we see a classical case where the function has too much variance. In such a case the parameters will attempt to move the function directly through every single point, and fail to generate a reasonable function across the points in pretty much all cases. On the left the linear regression did attempt to find good parameters for several degrees but every time it increased a parameter to, say, $t^{36}$ in order to make the function go up in a specific place it did affect the other places around the function. In turn the function attempted to change the parameter for, say, $t^{47}$ in order to counter the problems generated by the previous parameter increase but this again backfired by changing the function value in other places. The issue happens because linear regression assumes that the is no relationship between the different variables to which the parameters are multiplied. But here $t^{36}$ is very related to $t^{47}$, and also to $t^{63}$, and to pretty much every other value from polynomial features. There is more than one way to solve this problem. Let's see one way: model selection. ## Bias versus Variance - Model Selection¶ To solve the right hand side problem we need to tune of hyperparameter, the degree of our polynomial. And then we hope that the left hand side get solved due to a smaller number of parameters. In the case where the left hand side does not get solved then we need to look into regularization - which we will see next. Until now we have been guessing and doing this by hand but trying all values between $5$ and $100$ by hand does not seem like a good way of spending an afternoon. Instead sklearn can automate this for us. We will train a model for every degree between $5$ and $100$ and evaluate, by cross-validation, which model performs better. sklearn provides us with a grid search algorithm, which will perform the training and cross-validating of our model for all hyperparameter values given to it. The GridSearchCV is another sklearn object that takes sklearn objects and gives out a similar interface. When one performs fit on a grid search object, it will train models with all possible combinations given in the grid of hyperparameters. It then performs cross validation on every model and chooses the model which has the best mean cross validation score. The cross validation argument we use cv=5 is the sklearn's default. It performs $5$ fold splits without shuffling the data, in order to perform a shuffle one can use a KFold in the same fashion as with cross_val_score. Here we define the grid search to train $95$ linear regression models, each with a different value for the degree of the polynomial features given to the regression itself. We give into the grid search a model that itself is a pipeline of models. That is no issue for the grid search, note how can we specify the element of the pipeline to which the hyperparameter range is to be applied by using a double underscore. We use polynomialfeatures__degree to refer to the degree= hyperparameter of the PolynomialFeatures object, inside the pipeline. And the pipeline itself allows for more shortcuts to the contained objects with the named_steps attribute. We are starting to automate hyperparameter selection. Once a best set of hyperparameters is identified by the grid search, it trains a model with these hyperparameter values and all the data. This trained model is then available under best_estimator_, and the cross validation mean score that allowed the selection of this model as best under best_score_ In [5]: from sklearn.model_selection import GridSearchCV model = make_pipeline(PolynomialFeatures(degree=5), LinearRegression()) grid = GridSearchCV(model, {'polynomialfeatures__degree': list(range(5, 101))}, cv=5) grid.fit(t[:, np.newaxis], spd[:, np.newaxis]) best = grid.best_estimator_ xfit = np.linspace(0, 30, 3000) yfit = best.predict(xfit[:, np.newaxis]) fig, ax = plt.subplots(figsize=(16, 9)) ax.scatter(t, spd, color='crimson', alpha=0.7) ax.plot(xfit, yfit, color='navy') ax.set(xlabel='time (s)', ylabel='speed (km/h)', xlim=(-2, 32), ylim=(-10, 70)) best, best.named_steps.linearregression.intercept_, best.named_steps.linearregression.coef_ Out[5]: (Pipeline(memory=None, steps=[('polynomialfeatures', PolynomialFeatures(degree=10, include_bias=True, interaction_only=False, order='C')), ('linearregression', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False))], verbose=False), array([28.07079204]), array([[ 0.00000000e+00, 5.63557642e+00, -2.98208857e+00, 1.08366384e+00, -3.23484837e-01, 5.24801162e-02, -4.64249930e-03, 2.34704276e-04, -6.79413019e-06, 1.04914400e-07, -6.70557831e-10]])) And we should have a look at the R2 of the best estimator we have built. In [6]: grid.best_score_ Out[6]: 0.9766121925237712 Often simple hyperparameter tuning is enough to solve even complex problems. Yet, the problem we saw on the left hand side was a problem of dependence between dimensions, and sometimes it cannot be easily solved. We shall look at more techniques.

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Top Posters Since Sunday 6 A 5 b 4 3 s 3 s 3 L 3 i 3 b 3 d 3 b 3 j 3 # Linear programming problems wrote... Posts: 23 Rep: A year ago Linear programming problems Hi All please solve the following linear programming problems at below with the best explanation of the answer.1.   The Whitt Window Company is a company with only three employees which makes two different kinds of hand-crafted windows: a wood-framed and an aluminum-framed window. They earn $180 profit for each wood-framed window and$90 profit for each aluminum-framed window. Doug makes the wood frames, and can make 6 per day. Linda makes the aluminum frames, and can make 4 per day. Bob forms and cuts the glass, and can make 48 square feet of glass per day. Each wood-framed window uses 6 square feet of glass and each aluminum-framed window uses 8 square feet of glass. The company wishes to determine how many windows of each type to produce per day to maximize total profit.(a)   Describe the Wyndor Glass Co. problems. Construct and fill in a table for this problem, identifying both the activities and the resources.(b)   Formulate a linear programming model for this problem.(c)   Use the graphical method to solve this model.(d)   A new competitor in town has started making wood-framed windows as well. This may force the company to lower the price they charge and so lower the profit made for each woodframed window. How would the optimal solution change (if at all) if the profit per wood-framed window decreases from $180 to$120? From $180 to$60? (You may find it helpful to use the Graphical Analysis and Sensitivity Analysis procedure).(e)   Doug is considering lowering his working hours, which would decrease the number of wood frames he makes per day. How would the optimal solution change if he makes only 5 wood frames per day? (You may find it helpful to use the Graphical Analysis and Sensitivity Analysis procedure). Read 240 times 13 Replies Replies Anonymous wrote... A year ago Hi DukunDoes this help? Attached file  a3a4fe5c-95e8-45bc-82fb-634a024bb25b.pdf (141.73 KB) You must login or register to gain access to this attachment. Dukun Author wrote... A year ago Hello please anyone can help me to solved the questions. wrote... Educator A year ago Quote from: Dukun (A year ago) Hello please anyone can help me to solved the questions. Did the attachment help? (a) looks good (b) looks good (c) (d) (e) Dukun Author wrote... A year ago Hello please anyone can help me to solved the question to point c) Graphical Method using excel. please. wrote... Educator A year ago Does it have to be in Excel? Dukun Author wrote... A year ago Yes please can you help, to point c) Graphical Method only using excel the answer. bio_manbio_man wrote... Educator Top Poster Posts: 32794 Rep: A year ago ### Related Topics Dukun Author wrote... A year ago thanks you very much Anonymous Author wrote... A year ago Edited: A year ago the answer same with https://biology-forums.com/index.php?action=dlattach;topic=2029437.0;attach=99558but its a have feedback.  please can anyone help itGreat effort  but when it comes to decide the number of product, please go the closest lower integer number. So instead of X2 =1.5 then make X2 = 1 Regarding to the sensitivity analysis you may use the following answer: Slope Z = -C1/C2 = -C1/90 = -2 Slope constraint 1 = -3/4 Range of optimality -C1/90 = -3/4 ? -C1 = -67.5 ? 67.5 = C1 When C1 reduced to 120, still optimal because C1 > 67.5 When c1 reduced to 60, not optimal any more due to C1 < 67.5 wrote... Educator A year ago Can you provide a screenshot of the feedback given? Anonymous Author wrote... A year ago Anonymous wrote... A year ago Hi, honestly, I am not very sure.QuoteSo instead of X2 =1.5 then make X2 = 1 QuoteWhen C1 reduced to 60, not optimal any more due to C1 < 67.5 Anonymous Author wrote... A year ago Explore

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# If a car goes at a speed of 1 mph, then accelerates to 3 mph in 2 minutes, then decelerates to 2 mph in 1 minute, then accelerates to 4 mph in 2 minutes, etc., then how many miles will it go when it reaches 60 mph? • Problem: If a car goes at a speed of $$1$$ mph, then accelerates to $$3$$ mph in $$2$$ minutes, then decelerates to $$2$$ mph in $$1$$ minute, then accelerates to $$4$$ mph in $$2$$ minutes, etc., then how many miles will it go when it reaches $$60$$ mph? • @spaceblastxy1428 Interesting question! This is actually similar to a question that Prof. Loh covers in the Day 16 Your Turn question of Module 1! Can we assume that the acceleration is constant in this question? I wasn't sure how long the car drove at $$1$$ mph for, so I just assumed that it immediately starts accelerating. We can graph the speed in mph vs. time (in minutes) like this: The acceleration is constant at $$\pm 1 \text{ } \frac{\text{mph}}{\text{min}}$$ for each straight segment of the zigzag. From physics, we learn that $$\text{distance} = \text{speed} \times \text{time}$$ (Though actually in physics, they use velocity instead of time, since velocity takes into account the direction of where an object is moving.) Thus the distance can be interpreted as the area under a graph of speed versus time, like in the following example: Here the distance traveled is equal to $$\text{ distance } = 4 \frac{\text{miles}}{\cancel{\text{hour}}} \times \frac{1}{12} \text{ } \cancel{\text{hour}} = \textcolor{red}{\frac{1}{3} \text{ miles }}$$ Even though our graph doesn't look as nice and simple as the one above, the distance traveled is also the same: it's the area under the speed versus time curve. The area above is equivalent to the area of the shape below, found by averaging the speed for each interval: Remember that we must convert the time duration of each interval from minutes to hour, to match the units of the speed (miles per hour). Thus we go at \begin{aligned} 2 & \text{ mph for } \frac{1}{30} \text{ hour } \\ 2.5 & \text{ mph for } \frac{1}{60} \text{ hour } \\ 3 & \text{ mph for } \frac{1}{30} \text{ hour } \\ 3.5 & \text{ mph for } \frac{1}{60} \text{ hour } \\ 4 & \text{ mph for } \frac{1}{30} \text{ hour } \\ 4.5 & \text{ mph for } \frac{1}{60} \text{ hour } \\ 5 & \text{ mph for } \frac{1}{30} \text{ hour } \\ 5.5 & \text{ mph for } \frac{1}{60} \text{ hour } \\ 6 & \text{ mph for } \frac{1}{30} \text{ hour } \\ 6.5 & \text{ mph for } \frac{1}{60} \text{ hour } \\ \dots \\ 59 & \text{ mph for } \frac{1}{30} \text{ hour } \\ 59.5 & \text{ mph for } \frac{1}{60} \text{ hour } \\ \end{aligned} In the question, it's not clear how long the car spends driving at $$60 \text{ mph},$$ so I'll just assume that once it reaches $$60 \text{ mph}$$ it no longer continues driving. Thus the total distance, in miles, is \begin{aligned} & 2 \times \frac{1}{30} + 2.5 \times \frac{1}{60} + 2 \times \frac{1}{30} + 2.5 \times \frac{1}{60} \\ & + 3 \times \frac{1}{30} + 3.5 \times \frac{1}{60} + 4 \times \frac{1}{30} + 4.5 \times \frac{1}{60} \\ \ldots \end{aligned} I'll leave it to you to figure out how to simplify this expression!

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## Phone Vision 15 – Median Filters 1 03 2011 Filters, filters, filters… Tired of them yet?  Me too.  After this we’ll leave them alone for a while.  I promise.  Until then, we have work to do. What is a median filter?  If you understand the average filter (or mean filter) then the median filter should give you no troubles at all – assuming you know what the median is.  We’ll start there. What is the Median? The median is the middle number of a sample.  To find it, you sort your list and pick the middle item.  Yes, it really is that simple. Here is a random set of 9 numbers: Sort them: Pick the middle value: Like I said, it’s simple. Why use median instead of mean? The median is particularly effective against certain types of noise – specifically “salt and pepper” noise (black and white specks).  Let’s assume this is the neighborhood we’re dealing with: Performing the mean gives: While the median returns: If we expect that the 0 values are noise then the median is probably a much closer estimate. Code private WriteableBitmap MedianFilter(WriteableBitmap grayscale, int radius) { // we are still going to create a new image // because we don’t want to modify the // old image as we are processing it WriteableBitmap filtered = new WriteableBitmap( grayscale.PixelWidth, grayscale.PixelHeight); // boiler plate code for our // histogram stuff int[] histogram = new int[256]; int maxIntensity = 0; // the math is still easier if we create two loops for (int y = 0; y < grayscale.PixelHeight; y++) { for (int x = 0; x < grayscale.PixelWidth; x++) { //here’s the pixel we’re centered on int pixel = x + y * grayscale.PixelWidth; byte intensity = (byte)grayscale.Pixels[pixel]; // if we are on an edge we are going to leave it // as the original intensity.  you will see the // edges increasingly unsmoothed as the window // size increases.  here we are using the radius // to determine our bounds if (y <= radius – 1 || x <= radius – 1 || y >= grayscale.PixelHeight – radius || { histogram[intensity]++; if (histogram[intensity] > maxIntensity) { maxIntensity = histogram[intensity]; } continue; } ///////////////////////////////////////////////////////// // IMPORTANT PART /////////////////////////////////////// ///////////////////////////////////////////////////////// // this list is the key // it contains all of the neighboring pixels List<byte> localIntensities = new List<byte>(); { xoffset++) { (byte)grayscale.Pixels[(x + xoffset) + (y + yoffset) * grayscale.PixelWidth])); } } //sort the intensities localIntensities.Sort(); //pick the middle value int medianLocalIntensity = localIntensities[(int)(localIntensities.Count/2.0+.5)]; ///////////////////////////////////////////////////////// // END IMPORTANT PART /////////////////////////////////// ///////////////////////////////////////////////////////// // and now just set the color filtered.Pixels[pixel] = (255 << 24) | (byte)medianLocalIntensity << 16 | (byte)medianLocalIntensity << 8 | (byte)medianLocalIntensity; histogram[(byte)medianLocalIntensity]++; if (histogram[(byte)medianLocalIntensity] > maxIntensity) { maxIntensity = histogram[(byte)medianLocalIntensity]; } } } PlotHistogram(histogram, maxIntensity); return filtered; } Results Taking a simple gray image I added salt and pepper noise to the image then performed a median filter and an average filter to it.  The results are stunning. flat gray image                              10% salt and pepper noise after median filtering                      after mean filtering There are a few specks after applying the median filter, but the noise is removed pretty well.  The average filter performed dismally to say the list. Summary If you expect salt and pepper noise then the median filter is great tool to have in your toolbox.  If you want you can explore max, min, and mode filters.  I don’t think we’ll cover them here unless we have a specific application for it. http://cid-88e82fb27d609ced.office.live.com/embedicon.aspx/Blog%20Files/PhoneVision/PhoneVision%2015%20-%20Median%20Filter.zip (code includes salt and pepper noise generation) Up Next: Binary Images ## Project Euler 005 – C# 1 03 2011 Problem 5 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20? Solution // 2520 is the smallest number that can be // divided by each of the numbers from 1 to 10 // without any remainder. // What is the smallest positive number // that is evenly divisible by all of the // numbers from 1 to 20? namespace ProjectEulerCSharp_005 { class Program { static void Main(string[] args) { //have we found the answer yet? //let’s start off by saying "no" bool notFound = true; //20 seems like as good of a //starting spot as any long candidate = 20; while(notFound) { //I am incrementing up front //so that my loop exits elegantly candidate++; //here I am assuming that this candidate //is the answer.  I set it back when I //find a divisor that it doesn’t work for notFound = false; //this is not too important, but it’s a good //they are more likely to fail for (int divisor = 2; divisor <= 20; divisor++) { if (candidate % divisor != 0) { notFound = true; break; } } } System.Console.WriteLine(candidate); } } } Discussion The brute force approach is pretty silly, but it does work and within the 1 minute rule.  It takes about 7.5 seconds on my 6 month old laptop.  When this problem was announced (November 2001) the same code would have probably taken over 10 minutes to complete – at least according to my back of the napkin estimation of Moore’s law.  🙂

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## Monday, April 10, 2023 0-30V 20A High current adjustable voltage regulator circuit If you are looking for a high current Adjustable voltage regulator circuit. This may be a better choice for you. It can give the output current 20A or 400watts and can adjust the voltage of 4 to 20V—or apply to 0 to 30V easily. It is good quality, excellent performance and durable with PCB. For use in electronic telecommunication, High power radio transmitter, etc. This project uses a few components. Because of use fours of LM338—-5A voltage regulator and IC- 741—popular op-amp—in linear power supply mode. How it works The LM338K that we bring to use be DC voltage regulator circuit on the Floating type, The simple applications style of this IC As shown in Figure 1 How to use LM338 IC in basic Figure 1 circuit, in normal conditions, the voltage between pin Adj and pin output is equal to a 1.25V stable that flow pass R1, R2 will have constant as well. High current with parallel LM338 In normal IC-LM338 Can supply up to 5 amps, but to load current maximum 20 amps, we will bring it to parallel. What to watch out, when we connect many IC with parallel form, is the average current flowing through the circuit. Each equally. The easiest way is to connect a resistor to the output pin of IC as shown in figure 2. The value of the resistors-Rs used to it, it will be much less than the R1. Based on the circuit, we can set. The connecting LM338 in parallel form In practice, we do not circuits to use it. Since the voltage across drop Rs will change based on the current flowing through the load and Referenced voltage of IC. Also, different from each other. External LM338 controls using uA741 Therefore, we need to control external circuits. To control the voltage at pin adj, as shown in Figure 3. From the circuit, we will see that at pin negative of IC to have a half voltage of output voltage. And at pin positive to have equal to Referenced voltage. Which it is caused by a constant current flowing through the transistor to Rs and P1. From the properties of the op-amp circuit to the regulated level output voltage that. Until having the same voltage at pin input. So the voltage at pin base of a transistor- Q1 is equal to the voltage at pin negative of IC. The voltage these, to make changes in resistance of the transistor, causing voltage in referenced point change. The resistance of the transistor is inversely proportional to the output voltage, to compensate for the voltage loss of Rs. Due to the does not equal flow of these load current. Build 20A High current adjustable power supply All the devices in the circuits. Devices can be soldered onto the PCB as shown in Figure 5. Unless you change the input capacitor-C2 has increased these. I will have to install it on outside of PCB. Bridge diode must be attached heat sink neatly. To help extend the life and durability. For IC-LM338 that you need to install on a big size heatsink as well. Be careful, the body of the IC to the heat sink Short decisively. When all is finished soldering equipment, test input AC power to this project. Then adjust VR1 until the output voltage as needed, and test the Load and adjust VR1 until the output voltage is the voltage should be unchanged. 0-30V 20A High current adjustable voltage regulator circuit If you are looking for a high current Adjustable voltage regulator circuit. This may be a better choice for you. It can give the output current 20A or 400watts and can adjust the voltage of 4 to 20V—or apply to 0 to 30V easily. It is good quality, excellent performance and durable with PCB. For use in electronic telecommunication, High power radio transmitter, etc. This project uses a few components. Because of use fours of LM338—-5A voltage regulator and IC- 741—popular op-amp—in linear power supply mode. How it works The LM338K that we bring to use be DC voltage regulator circuit on the Floating type, The simple applications style of this IC As shown in Figure 1 How to use LM338 IC in basic Figure 1 circuit, in normal conditions, the voltage between pin Adj and pin output is equal to a 1.25V stable that flow pass R1, R2 will have constant as well. High current with parallel LM338 In normal IC-LM338 Can supply up to 5 amps, but to load current maximum 20 amps, we will bring it to parallel. What to watch out, when we connect many IC with parallel form, is the average current flowing through the circuit. Each equally. The easiest way is to connect a resistor to the output pin of IC as shown in figure 2. The value of the resistors-Rs used to it, it will be much less than the R1. Based on the circuit, we can set. The connecting LM338 in parallel form In practice, we do not circuits to use it. Since the voltage across drop Rs will change based on the current flowing through the load and Referenced voltage of IC. Also, different from each other. External LM338 controls using uA741 Therefore, we need to control external circuits. To control the voltage at pin adj, as shown in Figure 3. From the circuit, we will see that at pin negative of IC to have a half voltage of output voltage. And at pin positive to have equal to Referenced voltage. Which it is caused by a constant current flowing through the transistor to Rs and P1. From the properties of the op-amp circuit to the regulated level output voltage that. Until having the same voltage at pin input. So the voltage at pin base of a transistor- Q1 is equal to the voltage at pin negative of IC. The voltage these, to make changes in resistance of the transistor, causing voltage in referenced point change. The resistance of the transistor is inversely proportional to the output voltage, to compensate for the voltage loss of Rs. Due to the does not equal flow of these load current. Build 20A High current adjustable power supply All the devices in the circuits. Devices can be soldered onto the PCB as shown in Figure 5. Unless you change the input capacitor-C2 has increased these. I will have to install it on outside of PCB. Bridge diode must be attached heat sink neatly. To help extend the life and durability. For IC-LM338 that you need to install on a big size heatsink as well. Be careful, the body of the IC to the heat sink Short decisively. When all is finished soldering equipment, test input AC power to this project. Then adjust VR1 until the output voltage as needed, and test the Load and adjust VR1 until the output voltage is the voltage should be unchanged.

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# What are prime numbers and composite numbers And how we can know thank the prime or composite numbers are odd or even? Prime numbers are those numbers that are divisible by 1 and themselves. They have only two factors that include 1 and themselves. For example, 2, 3, 5, 7, 11, 13.....are all prime numbers 2 is the only even prime number All prime numbers, except 2 are odd numbers All numbers, other than prime numbers are composite numbers. Composite numbers have three or more factors. For example 4, 6, 8, 9, 10, 12,....are composite numbers they have three or more factors 4 = 1x 2 x 2 4 is the smallest composite numbers Composite numbers can be even or odd numbers Every composite number can be expressed as a product of prime factors. Tutorialspoint Simply Easy Learning Updated on: 10-Oct-2022 32 Views

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principal axis (redirected from Principle axis) Also found in: Dictionary, Thesaurus, Medical. Related to Principle axis: centre of curvature principal axis [′prin·sə·pəl ′ak·səs] (crystallography) The longest axis in a crystal. (engineering acoustics) A reference direction for angular coordinates used in describing the directional characteristics of a transducer; it is usually an axis of structural symmetry or the direction of maximum response. (mathematics) One of a set of perpendicular axes such that a quadratic function can be written as a sum of squares of coordinates referred to these axes. For a conic, a straight line that passes through the midpoints of all the chords perpendicular to it. For a quadric surface, the intersection of two principal planes. (mechanics) One of three perpendicular axes in a rigid body such that the products of inertia about any two of them vanish. (optics) principal axis Primary axes In the illustration on the left, line A is the principal axis while in the illustration on the right, line B is the principal axis. The moment of inertia is maximum around these axes in these two cases. i. The lateral, vertical, and longitudinal axes. ii. The axis of relative wind. iii. The principal inertial axis: that line passing through the center of gravity in a plane of symmetry about which a long, slender body tends to rotate when rolling. iv. A rectilinear axis in the plane of a cross section of a structural member about which the moment of inertia is the maximum. Site: Follow: Share: Open / Close

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# Find minimum and maximum value from a matrix for a specific interval 1 view (last 30 days) Chaudhary P Patel on 20 Sep 2022 Commented: Chaudhary P Patel on 20 Sep 2022 I have a 30X100 size matrix, for which i want to find minimum and maximum value for row 2,5,8,11,14,17,20,23,27. How can i find the minimum and maximu values from these rows. ##### 0 CommentsShow -1 older commentsHide -1 older comments Sign in to comment. ### Accepted Answer Walter Roberson on 20 Sep 2022 rows = [2,5,8,11,14,17,20,23,27]; [minima, maxima] = bounds(YourMatrix(rows,:), 2); ##### 1 CommentShow NoneHide None Chaudhary P Patel on 20 Sep 2022 I want to find the maximum minimum from the comparision of all the specified row with all column at a time. can you please explain is command with a example. Sign in to comment. ### Categories Find more on Logical in Help Center and File Exchange ### Community Treasure Hunt Find the treasures in MATLAB Central and discover how the community can help you! Start Hunting!

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ive lost quite a few marks on these questions- does anyone know what to do next?? thanks! Original post by puppy_punk ive lost quite a few marks on these questions- does anyone know what to do next?? thanks! ( Sara is writing a program to input her monthly phone bills and output the month name and amount for each month along with the month that had the maximum cost. She has defined an array to hold the month names. Complete the pseudocode program. [6] // Program to output maximum month’s phone bill array monthName = ["January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"] // Define an array to hold the phone bills for each month int billamount[12]; char monthname["January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"]; for (int month = 1; month<=12; month++) { cout<<"Enter the amount of bill for the month"<<month; cin>>billamount[month]; } for (i=0; i<= 12; i++) { if (billamount[0]<billamount) billamount[0]=billamount; monthname[0]=monthname; } cout<<"Maximum months phone bill"<<monthname[0] <<"="<<billamount[0] getch(); (edited 8 months ago)

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#### Who First Discovered That The Earth Orbits The Sun? (TOP 5 Tips) When Nicolaus Copernicus published his innovative theory of the universe in 1543—in which the Earth, along with the other planets, revolved around the Sun—he was considered a revolutionary. It took more than a century for his hypothesis to gain widespread acceptance. • Galileo Galilei, an Italian scientist and astronomer, was the first to propose the hypothesis that the earth circles or travels around the sun. Using his telescope, he was able to uncover this notion. He was born on February 15, 1564, in the country of Italy. The founder of modern observational astronomy, he was widely regarded as such. ## When was it first discovered that the Earth revolves around the Sun? The Polish astronomer Nicolaus Copernicus is credited with this discovery. In his dissertation On The Revolutions Of The Heavenly Spheres (1543), Copernicus maintained that the Sun’s motion was caused by the Earth rotating on its axis, rather than the other way around. ## Who discovered that the Sun doesn’t revolve around the Earth? In 1543, Nicolaus Copernicus wrote De Revolutionibus, which served as the ultimate explanation of his system. Copernicus began writing it in 1506 and finished it in 1530, but he did not publish it until the year after his death, which was the year after his death. You might be interested:  What Effect Does The Sun Have On The Earth? (Best solution) ## Who was the first person to prove that the Earth moves around the Sun in India? Today commemorates the 475th anniversary of the death of one of Poland’s most illustrious scientists, Jan Podolski. With his discovery that the earth revolved around the sun, Nicolaus Copernicus changed the course of history in astronomy. ## Does the Earth revolve the Sun? The Earth completes one complete rotation around the sun in 365 days, 5 hours, 59 minutes, and 16 seconds. A year is the amount of time it takes for a planet to complete one full round around the sun. ## Who discovered that the Earth was not the center of the universe? ‘ Galileo had observed three of Jupiter’s four biggest moons, conclusively demonstrating that the Earth was not the center of the universe,’ he wrote. ## Who discovered Pluto? Clyde W. Tombaugh, an astronomer at the Lowell Observatory in Flagstaff, Arizona, makes the discovery of Pluto, which was previously thought to be the eighth planet. ## Who discovered moon? As previously stated, Earth’s lone natural satellite is simply referred to as “the Moon” since no one was aware of the existence of other moons until Galileo Galilei discovered four moons circling Jupiter in 1610. ## What God is Earth named after? Terra Mater (Mother Earth) is the sole planet not named after a Roman deity or goddess; yet, the planet is linked with the goddess Terra Mater (Gaea to the Greeks). As the earliest goddess on Earth, she was also the mother of Uranus, according to legend. “Earth” is derived from Old English and Germanic languages. ### Releated #### What Type Of Eclipse Occurs When The Earth, Moon, And Sun Are Lined? (TOP 5 Tips) A lunar eclipse can only occur when the moon is completely full. A total lunar eclipse can only occur when the sun, Earth, and moon are perfectly aligned – anything less than ideal results in a partial lunar eclipse or no eclipse at all if the sun, Earth, and moon are not properly aligned. 5 […] #### Where On Earth Is It Possible For The Sun To Be Above The Horizon For Several Weeks? (Correct answer) How long does it take for the Sun to disappear fully below the horizon? The greatest durations of time when the Sun is fully below the horizon for places inside the polar circles range from zero a few degrees beyond the Arctic Circle and Antarctic Circle to 179 days at the Poles. Contents1 Where on […]

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# How to place braces in multiple equations I have the following expression: \begin{aligned} %C1 \sum_{i = 1}^{m}{y^{C_1}_i} &= m\beta_0^{C_1} + \beta_1^{C_1}\sum_{i = 1}^{m}{x_{i1}^{C_1}} + \cdots + \beta_q^{C_1}\sum_{i = 1}^{m}{x_{iq}^{C_1}}\\ \sum_{i = 1}^{m}{y^{C_1}_ix_{i1}^{C_1}} &= \beta_0^{C_1}\sum_{i = 1}^{m}{x_{i1}^{C_1}} + \beta_1^{C_1}\sum_{i = 1}^{m}{(x_{i1}^{C_1})^2} + \cdots + \beta_q^{C_1}\sum_{i = 1}^{m}{x_{iq}^{C_1}x_{i1}^{C_1}}\\ &\vdots\\ \sum_{i = 1}^{m}{y^{C_1}_ix_{iq}^{C_1}} &= \beta_0^{C_1}\sum_{i = 1}^{m}{x_{iq}^{C_1}} + \beta_1^{C_1}\sum_{i = 1}^{m}{x_{i1}^{C_1}x_{iq}^{C_1}} + \cdots + \beta_q^{C_1}\sum_{i = 1}^{m}{(x_{iq}^{C_1})^2}\\ %C2 \sum_{i = 1}^{m}{y^{C_2}_i} &= m\beta_0^{C_2} + \beta_1^{C_2}\sum_{i = 1}^{m}{x_{i1}^{C_2}} + \cdots + \beta_q^{C_2}\sum_{i = 1}^{m}{x_{iq}^{C_2}}\\ \sum_{i = 1}^{m}{y^{C_2}_ix_{i1}^{C_2}} &= \beta_0^{C_2}\sum_{i = 1}^{m}{x_{i1}^{C_2}} + \beta_1^{C_2}\sum_{i = 1}^{m}{(x_{i1}^{C_2})^2} + \cdots + \beta_q^{C_2}\sum_{i = 1}^{m}{x_{iq}^{C_2}x_{i1}^{C_2}}\\ &\vdots\\ \sum_{i = 1}^{m}{y^{C_2}_ix_{iq}^{C_2}} &= \beta_0^{C_2}\sum_{i = 1}^{m}{x_{iq}^{C_2}} + \beta_1^{C_2}\sum_{i = 1}^{m}{x_{i1}^{C_2}x_{iq}^{C_2}} + \cdots + \beta_q^{C_2}\sum_{i = 1}^{m}{(x_{iq}^{C_2})^2}\\ %R \sum_{i = 1}^{m}{y^{R}_i} &= m\beta_0^{R} + \beta_1^{R}\sum_{i = 1}^{m}{x_{i1}^{R}} + \cdots + \beta_q^{R}\sum_{i = 1}^{m}{x_{iq}^{R}}\\ \sum_{i = 1}^{m}{y^{R}_ix_{i1}^{R}} &= \beta_0^{R}\sum_{i = 1}^{m}{x_{i1}^{R}} + \beta_1^{R}\sum_{i = 1}^{m}{(x_{i1}^{R})^2} + \cdots + \beta_q^{R}\sum_{i = 1}^{m}{x_{iq}^{R}x_{i1}^{R}}\\ &\vdots\\ \sum_{i = 1}^{m}{y^{R}_ix_{iq}^{R}} &= \beta_0^{R}\sum_{i = 1}^{m}{x_{iq}^{R}} + \beta_1^{R}\sum_{i = 1}^{m}{x_{i1}^{R}x_{iq}^{R}} + \cdots + \beta_q^{R}\sum_{i = 1}^{m}{(x_{iq}^{R})^2} \end{aligned} \label{eq:normals_equations} and I want to place brace of this form: Thank you so much! The basic building block you can use is \left\{ \begin{aligned} .... \end{\aligned} \right. If you want the q+1 in front then just write it before the \left\{. You want three such groups on separate lines apparently with one single equation number, so you can place these groups in to $$\begin{gathered} ...\\ ---\\ \end{gathered}$$ giving \documentclass{article} \usepackage{amsmath} \begin{document} \begin{gathered} \left\{ \begin{aligned} % C1 \sum_{i=1}^{m}{y^{C_1}_i} &= m\beta_0^{C_1} + \beta_1^{C_1}\sum_{i=1}^{m}{x_{i1}^{C_1}} + \dots + \beta_q^{C_1}\sum_{i=1}^{m}{x_{iq}^{C_1}}\\ \sum_{i=1}^{m}{y^{C_1}_ix_{i1}^{C_1}} &= \beta_0^{C_1}\sum_{i=1}^{m}{x_{i1}^{C_1}} + \beta_1^{C_1}\sum_{i=1}^{m}{(x_{i1}^{C_1})^2} + \dots + \beta_q^{C_1}\sum_{i=1}^{m}{x_{iq}^{C_1}x_{i1}^{C_1}}\\ &\vdots\\ \sum_{i=1}^{m}{y^{C_1}_ix_{iq}^{C_1}} &= \beta_0^{C_1}\sum_{i=1}^{m}{x_{iq}^{C_1}} + \beta_1^{C_1}\sum_{i=1}^{m}{x_{i1}^{C_1}x_{iq}^{C_1}} + \dots + \beta_q^{C_1}\sum_{i=1}^{m}{(x_{iq}^{C_1})^2}\\ \end{aligned} \right.\\ % C2 \left\{ \begin{aligned} \sum_{i=1}^{m}{y^{C_2}_i} &= m\beta_0^{C_2} + \beta_1^{C_2}\sum_{i=1}^{m}{x_{i1}^{C_2}} + \dots + \beta_q^{C_2}\sum_{i=1}^{m}{x_{iq}^{C_2}}\\ \sum_{i=1}^{m}{y^{C_2}_ix_{i1}^{C_2}} &= \beta_0^{C_2}\sum_{i=1}^{m}{x_{i1}^{C_2}} + \beta_1^{C_2}\sum_{i=1}^{m}{(x_{i1}^{C_2})^2} + \dots + \beta_q^{C_2}\sum_{i=1}^{m}{x_{iq}^{C_2}x_{i1}^{C_2}}\\ &\vdots\\ \sum_{i=1}^{m}{y^{C_2}_ix_{iq}^{C_2}} &= \beta_0^{C_2}\sum_{i=1}^{m}{x_{iq}^{C_2}} + \beta_1^{C_2}\sum_{i=1}^{m}{x_{i1}^{C_2}x_{iq}^{C_2}} + \dots + \beta_q^{C_2}\sum_{i=1}^{m}{(x_{iq}^{C_2})^2}\\ \end{aligned} \right.\\ % R \left\{ \begin{aligned} \sum_{i=1}^{m}{y^{R}_i} &= m\beta_0^{R} + \beta_1^{R}\sum_{i=1}^{m}{x_{i1}^{R}} + \dots + \beta_q^{R}\sum_{i=1}^{m}{x_{iq}^{R}}\\ \sum_{i=1}^{m}{y^{R}_ix_{i1}^{R}} &= \beta_0^{R}\sum_{i=1}^{m}{x_{i1}^{R}} + \beta_1^{R}\sum_{i=1}^{m}{(x_{i1}^{R})^2} + \dots + \beta_q^{R}\sum_{i=1}^{m}{x_{iq}^{R}x_{i1}^{R}}\\ &\vdots\\ \sum_{i=1}^{m}{y^{R}_ix_{iq}^{R}} &= \beta_0^{R}\sum_{i=1}^{m}{x_{iq}^{R}} + \beta_1^{R}\sum_{i=1}^{m}{x_{i1}^{R}x_{iq}^{R}} + \dots + \beta_q^{R}\sum_{i=1}^{m}{(x_{iq}^{R})^2} \end{aligned} \right. \label{eq:normals_equations} \end{gathered} \end{document} I have changed your \cdots to \dots since amsmath knows which dots to use between + plus signs. You might consider using \vdotswithin{=} from the mathtools package to get the vertical dots to be centered on the equals signs. If you want to align the various elements vertically across groups, see Aligning across 'aligned' equation blocks

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# Search by Topic #### Resources tagged with Multiplication & division similar to Twenty Divided Into Six: Filter by: Content type: Age range: Challenge level: ### There are 134 results Broad Topics > Calculations and Numerical Methods > Multiplication & division ### Twenty Divided Into Six ##### Age 7 to 11 Challenge Level: Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done? ### The Puzzling Sweet Shop ##### Age 7 to 11 Challenge Level: There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money? ### X Is 5 Squares ##### Age 7 to 11 Challenge Level: Can you arrange 5 different digits (from 0 - 9) in the cross in the way described? ### Zargon Glasses ##### Age 7 to 11 Challenge Level: Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families? ### A-magical Number Maze ##### Age 7 to 11 Challenge Level: This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15! ### Arranging the Tables ##### Age 7 to 11 Challenge Level: There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places. ### The Pied Piper of Hamelin ##### Age 7 to 11 Challenge Level: This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether! ### Oh! Harry! ##### Age 7 to 11 Challenge Level: A group of children are using measuring cylinders but they lose the labels. Can you help relabel them? ### How Old? ##### Age 7 to 11 Challenge Level: Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information? ### Shapes in a Grid ##### Age 7 to 11 Challenge Level: Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column? ### Today's Date - 01/06/2009 ##### Age 5 to 11 Challenge Level: What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself. ### Rabbits in the Pen ##### Age 7 to 11 Challenge Level: Using the statements, can you work out how many of each type of rabbit there are in these pens? ### How Much Did it Cost? ##### Age 7 to 11 Challenge Level: Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether. ### ABC ##### Age 7 to 11 Challenge Level: In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication? ### Bundles of Cubes ##### Age 7 to 11 Challenge Level: Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle? ### Calendar Calculations ##### Age 7 to 11 Challenge Level: Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens? ### Route Product ##### Age 7 to 11 Challenge Level: Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest? ### Sam's Quick Sum ##### Age 7 to 11 Challenge Level: What is the sum of all the three digit whole numbers? ### Being Resourceful - Primary Number ##### Age 5 to 11 Challenge Level: Number problems at primary level that require careful consideration. ### A Mixed-up Clock ##### Age 7 to 11 Challenge Level: There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements? ### Napier's Bones ##### Age 7 to 11 Challenge Level: The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications? ### The Deca Tree ##### Age 7 to 11 Challenge Level: Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf. ### Forgot the Numbers ##### Age 7 to 11 Challenge Level: On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they? ### Magic Constants ##### Age 7 to 11 Challenge Level: In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square? ### It Figures ##### Age 7 to 11 Challenge Level: Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all? ### Doplication ##### Age 7 to 11 Challenge Level: We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes? ### The 24 Game ##### Age 7 to 11 Challenge Level: There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find? ### The Clockmaker's Birthday Cake ##### Age 7 to 11 Challenge Level: The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece? ### Dice and Spinner Numbers ##### Age 7 to 11 Challenge Level: If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time? ### Exploring Wild & Wonderful Number Patterns ##### Age 7 to 11 Challenge Level: EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules. ### Machines ##### Age 7 to 11 Challenge Level: What is happening at each box in these machines? ### Book Codes ##### Age 7 to 11 Challenge Level: Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common? ### Penta Post ##### Age 7 to 11 Challenge Level: Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g? ### Making Pathways ##### Age 7 to 11 Challenge Level: Can you find different ways of creating paths using these paving slabs? ### Clever Santa ##### Age 7 to 11 Challenge Level: All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left. ### Code Breaker ##### Age 7 to 11 Challenge Level: This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code? ### Dividing a Cake ##### Age 7 to 11 Challenge Level: Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece? ### Sending Cards ##### Age 7 to 11 Challenge Level: This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six? ### Clock Face ##### Age 7 to 11 Challenge Level: Where can you draw a line on a clock face so that the numbers on both sides have the same total? ### 1, 2, 3, 4, 5 ##### Age 7 to 11 Challenge Level: Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make? ##### Age 7 to 11 Challenge Level: Use the information to work out how many gifts there are in each pile. ### The Money Maze ##### Age 7 to 11 Challenge Level: Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest? ### Next Number ##### Age 7 to 11 Short Challenge Level: Find the next number in this pattern: 3, 7, 19, 55 ... ### Sometimes We Lose Things ##### Age 7 to 11 Challenge Level: Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table. ### It Was 2010! ##### Age 5 to 11 Challenge Level: If the answer's 2010, what could the question be? ### Fingers and Hands ##### Age 7 to 11 Challenge Level: How would you count the number of fingers in these pictures? ### Escape from the Castle ##### Age 7 to 11 Challenge Level: Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out? ### Month Mania ##### Age 5 to 11 Challenge Level: Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice? ### Being Resilient - Primary Number ##### Age 5 to 11 Challenge Level: Number problems at primary level that may require resilience. ### Numbers Numbers Everywhere! ##### Age 5 to 11 Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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# Exercise 3-37 Identifying the Parts of the Cost Formula; Calculating Monthly, Quarterly, and... 1 answer below » Exercise 3-37 Identifying the Parts of the Cost Formula; Calculating Monthly, Quarterly, and Yearly Costs Using a Cost Formula Based on Monthly Data Gordon Company’s controller, Eric Junior, estimated the following formula, based on monthly data, for overhead cost: Overhead Cost ¼ $150,000 þ ($52 3 Direct Labor Hours) Required: 1.       Link each term in column A to the corresponding term in column B. Column A                                           Column B $150,000 Dependent variable$52                                            Independent variable Direct labor hours                     Variable rate (slope) 2.       If next month’s budgeted direct labor hours equal 8,000, what is the budgeted overhead cost? 3.       If next quarter’s budgeted direct labor hours equal 23,000, what is the budgeted overhead cost? 4.       If next year’s budgeted direct labor hours equal 99,000, what is the budgeted overhead cost? Ramesh ANSWER 1. Overhead cost - Dependent variable $150000 - Fixed cost intercept (MONTHLY)$ 52 - Variable rate (SLOPE) Direct Labour Hours - Independent Variable Answer 2 150000 + (52 X 8000) =... ## Plagiarism Checker Submit your documents and get free Plagiarism report Free Plagiarism Checker

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17.5 The Alice in Wonderland Method for Evaluating Determinants on a Spreadsheet As you may not remember, Lewis Carroll, the author of Alice in Wonderland, was a mathematician, and the method uses his celebrated theorem on determinants. It goes as follows: Suppose we have a square array A, and two additional rows, called T and B, and two columns L and R. We define the following additional arrays. ATL, ATR, ABL, ABR, and ATBLR, to be the arrays gotten by adding row T at the top of A and column L to its left, row T at the top and column R on the right, row B on the bottom and column L on the left, B on the bottom and R on the right, and finally, T at the top, B at the bottom, L on the left and R on the right. If A is an n by n array then the next four are n + 1 by n + 1 array and the last is an n + 2 by n + 2 array. Then the following equation holds: Det (ATBLR)*Det(A) = Det(ATL)*Det(ABR) - Det(ATR)*Det(ABL) We define the determinant of the 0 by 0 array to be 1. The determinant of a one by one array is its lone entry. The content of this equation, when applied to the array in which A is 0 by 0, T is (a, b), B is (c, d), the vertical entries of L are a and c and those of R are b and d, is the formula that the two by two determinant of the array with rows (a, b) and (c, d), multiplied by 1 (the determinant of a 0 by 0) is a c - bd, which is what the right hand side is here. (The first entry of T is in the left row and its last entry is in the right row, so that if, as on the right here you don't have a right or left row, then the corresponding entry to T is missing. The same thing happens with all the others. Thus ATL is a, ATR is b, and so on, here). And what good is all this? If we apply this statement for A a zero by zero array, we can produce the determinants of 2 by 2 adjacent subarrays of the array we apply it to from the one by ones and the zero by zero. The original array can be considered the array whose elements are determinants of the one by one subarrays of the array we started with. If we apply the same formula again to the array of 2 by 2 determinants produced at first, we produce an array of 3 by 3 determinants of adjacent rows and columns, and applied to these we get an array of 4 by 4 determinants of adjacent subarrays of the original array, and so on, and eventually we get the determinant of the entire array. Now the really wonderful thing is this: to do everything just mentioned, we need only make one entry in the spreadsheet, and copy and it will do everything just discussed. Huh? Suppose we have a four by four array, and we locate it in positions A6 B6 C6 D6 to A9 B9 C9 D9. Then put a 1 (to represent a 0 by 0 determinant,) in position B3 and fill down from B3 to B5 and across to D3 to D6, putting 1's in all these places. Now here is the key step. Put = (A6*B7 – A7*B6)/B3 into A10, and fill down to A18 and across to C10 to C18. Then the determinant of your original array will appear in A18, unless along the way you divided by 0. And then what? If you divide by 0 along the way, (possible because each step involves dividing by something) you can modify the elements of your array by tiny amounts until this no longer happens. Then you will have your answer. When do you divide by 0? This happens if any of the elements of your original array, in positions B7 B8 C7 or C8 are 0 or if the two by two determinant created in B11 is 0. (There is a systematic way to avoid dividing by 0, that works for almost every array of size up to around ten by ten, whose entries are integers. You can create an array whose element in the ith row and jth column is =x * ln(i + j) where x is 10-8, and add it term by term to the original array, and apply the method just described to the sum array. Only by some sort of miracle will you end up dividing by 0, and you can vary x to eliminate its effect on the answer. It is described in the last section below) Exercises: 17.7 Set up a spreadsheet for evaluating determinants of three by three arrays whose middle element is non-zero by this approach. 17.8 Get it to work so that it instantly supplies the answer as you change the array. 17.9 Add 10^-8 to the middle entry so that the method always works even when that entry is chosen to be 0. (you have to separate the entry data for the middle position, which could be 0 from the middle position you use here, which should have something like 10^-8 added to the former.) Is this method really useful? Well, you can set it up in a few minutes, and once it is set up, you can change your given array and find the changed determinant immediately. This allows you to check any calculation of a determinant almost instantly. Believe me, this will save you lots of time, if you ever have to evaluate determinants. But why should I want to evaluate determinants? We have seen that the magnitude of a determinant gives the area or volume or analogue in higher dimension of the figure that given array describes. You may someday want to find such things. But there are several other uses that are even more important. Such as? We will describe the first now and just mention the second. First, determinants can be used to solve systems of linear equations. We can and will show how to implement this on a spreadsheet and use the method of the previous section to solve up to ten equations in ten unknowns with very little more work than that of finding the determinant. Second, determinants can be used to find eigenvalues and eigenvectors of arrays, quickly and conveniently. What the devil are those? One thing at a time. If you have patience, we will eventually get to these, but not now.

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# How do I help my son learn multiplication during winter break? Q. I was recently laid off and will be home for the whole school vacation. My son needs a great deal of help with his multiplication tables, so now I have time to help him. He is in fourth grade and had trouble last year and this year. Here is the problem, how do I help him? He hates flash cards. A. Multiplication Boot Camp might not be the way your son wanted to describe his holiday vacation. Give him some concessions if you are going to make the two-week vacation dedicated in part to something that is difficult for him. Perhaps all work can be done at a park before he goes off to play? Perhaps he can earn free time he enjoys? In fourth grade, he should have multiplication and division coming at him at this point in the year. When I taught fifth grade, I had to do intervention for this very thing. All kids struggling with multiplication tables do not have learning disorders, although it is something to keep in the back of your mind. Some kids need extra practice as well as different approaches. I used to start with a 0-99 chart and I would focus on one row of answers at a time. I would start with the 30s, just to find a starting point they did not expect. I had the kids highlight 30, 32, 33, 35, 36. None of the other numbers in the 30s are even answers to our times tables and the kids loved only needing to remember 5 numbers on this row. It is a bit of a trick, because they had to tell me which problems gave the answers listed and this is fairly difficult. Turning the learning process around really helped my students. They learned quickly 5×6=30, 8×4=32, 3×11=33, 7×5=35, and 6×6 as well as 9×4=36. Of course, I also reviewed the commutative property of addition and multiplication, but this usually was not the sticking point kids were struggling with when it came to memorizing the tables. Still, point it out to your son so that he knows, and you know that he knows, that if 5×6=30 so does 6×5. I would give them a test with all of the problems only for this “row” with many examples of each problem. If they passed, we would then go on to any row each child chose next. Each child got to choose his or her own row to take ownership in the learning process. Try the whole method with your son. Do one row each day, or perhaps two if he catches on quickly. It is like a puzzle you can do together. If you find your son continues to struggle, and it really is not just a lack of dedicated practice, talk to his teacher after the break. There is an interesting math program I learned about available at www.TeaCHildMath.com that also focuses on learning multiplication through patterns. He could need a different approach, and you may need to ask the school to assess him to see if he has any other learning concerns related to his struggle with math.

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http://gmatclub.com/forum/gmat-data-suff-practice-tests-122150.html

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GMAT Data Suff. Practice Tests : Ask GMAT Experts Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack It is currently 16 Jan 2017, 14:41 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # GMAT Data Suff. Practice Tests Author Message Intern Joined: 22 Aug 2011 Posts: 7 Followers: 0 Kudos [?]: 1 [0], given: 3 GMAT Data Suff. Practice Tests [#permalink] ### Show Tags 18 Oct 2011, 01:19 I have the Kaplan Math Workbook 5th edition. The data suff. section has 2 practice tests for these types of problems - 15mins for 25 problems. Based on everything I've read the test taker has a little over 2 minutes per problem on the quantitative section of the exam. My questions are: 1. Is 15mins realistically enough time to answer 25 DS questions? 2. What can I do to improve my time? Currently, I can answer about 80-85% correctly but given 2 minutes per problem. I would like to be able to work them faster and more accurately. Cheers, Kaplan GMAT Prep Discount Codes e-GMAT Discount Codes Optimus Prep Discount Codes Kaplan GMAT Instructor Joined: 25 Aug 2009 Posts: 644 Location: Cambridge, MA Followers: 83 Kudos [?]: 276 [0], given: 2 Re: GMAT Data Suff. Practice Tests [#permalink] ### Show Tags 19 Oct 2011, 08:54 Damouse wrote: I have the Kaplan Math Workbook 5th edition. The data suff. section has 2 practice tests for these types of problems - 15mins for 25 problems. Based on everything I've read the test taker has a little over 2 minutes per problem on the quantitative section of the exam. My questions are: 1. Is 15mins realistically enough time to answer 25 DS questions? 2. What can I do to improve my time? Currently, I can answer about 80-85% correctly but given 2 minutes per problem. I would like to be able to work them faster and more accurately. Cheers, 1. 15 minutes for 25 problems is very, very short for real test-like questions. I am not as familiar with this particular book as I could be, but is it possible that the questions on the quiz aren't fully test-like and are rather intended as a speed drill? 2. Two ways to improve your time are to use strategies like picking numbers and to make sure that you paraphrase the question. Picking number for variables can make math much easier than working with raw algebra, so look for opportunities to do so. And whenever you see a word problem in a DS question stem, your first step should be to convert it into a mathematical expression; it may seem like it will slow you down, but any extra time you spend translating the stem will more than pay for itself when you go to the statements. Best of luck with your studies! Eli _________________ Eli Meyer Kaplan Teacher http://www.kaptest.com/GMAT Prepare with Kaplan and save \$150 on a course! Kaplan Reviews Re: GMAT Data Suff. Practice Tests   [#permalink] 19 Oct 2011, 08:54 Similar topics Replies Last post Similar Topics: Inconsistent results on GMAT practice tests 7 24 Aug 2016, 02:12 1 Gmat Official Practice Tests 1 04 Jun 2014, 08:31 3 Best Gmat practice CAT tests 18 16 Jan 2014, 09:04 GMAT Practice test 2 09 May 2012, 23:36 5 Effective gmat practice tests 26 28 May 2011, 02:10 Display posts from previous: Sort by

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http://www.retroprogramming.com/2014/03/plotting-mandelbrot-set-on-zx-spectrum.html?showComment=1519731664552

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## Saturday, 15 March 2014 ### Plotting the Mandelbrot Set on the ZX Spectrum The Mandelbrot set is a fractal which iterates the equation zn+1 = zn² + c in the complex plane and plots which points tend to infinity. Plotting the set with Sinclair BASIC takes over 24 hours so I was curious how much faster it would be in assembly. It turns out if we use fast 16-bit fixed-point arithmetic we can plot the Mandelbrot in about 5 minutes. To minimise multiplications each iteration is calculated as: rn+1 = ( rn + in ) × ( rn - in ) + x in+1 = 2 × in × rn + y The following test is used to detect points which tend to infinity: |in| + |rn| ≥ 2 × √ 2. ``` org 60000 ld de,255*256+191 XLOOP: push de ld hl,-180 ; x-coordinate ld e,d call SCALE ld (XPOS),bc pop de YLOOP: push de ld hl,-96 ; y-coordinate call SCALE ld (YPOS),bc ld hl,0 ld (IMAG),hl ld (REAL),hl ld b,15 ; iterations ITER: push bc ld bc,(IMAG) ld hl,(REAL) or a sbc hl,bc ld d,h ld e,l call FIXMUL ld de,(XPOS) ld de,(REAL) ld (REAL),hl ld hl,(IMAG) call FIXMUL rla ld de,(YPOS) ld (IMAG),hl call ABSVAL ex de,hl ld hl,(REAL) call ABSVAL ld a,h cp 46 ; 46 ≅ 2 × √ 2 << 4 pop bc jr nc,ESCAPE djnz ITER pop de call PLOT db 254 ; trick to skip next instruction ESCAPE: pop de dec e jr nz,YLOOP dec d jr nz,XLOOP ret FIXMUL: ; hl = hl × de >> 24 call MULT16BY16 ld a,b ld b,4 FMSHIFT: rla djnz FMSHIFT ret SCALE: ; bc = (hl + e) × zoom ld d,0 ld de,48 ; zoom MULT16BY16: ; hl:bc (signed 32 bit) = hl × de xor a call ABSVAL ex de,hl call ABSVAL push af ld c,h ld a,l call MULT8BY16 ld b,a ld a,c ld c,h push bc ld c,l call MULT8BY16 pop de ld b,l ld l,h ld h,a pop af rra ret nc ex de,hl xor a ld h,a ld l,a sbc hl,bc ld b,h ld c,l ld h,a ld l,a sbc hl,de ret MULT8BY16: ; returns a:hl (24 bit) = a × de ld hl,0 ld b,8 M816LOOP: rla jr nc,M816SKIP M816SKIP: djnz M816LOOP ret PLOT: ; plot d = x-axis, e = y-axis ld a,7 and d ld b,a inc b ld a,e rra scf rra or a rra ld l,a xor e and 248 xor e ld h,a ld a,d xor l and 7 xor d rrca rrca rrca ld l,a ld a,1 PLOTBIT: rrca djnz PLOTBIT or (hl) ld (hl),a ret ABSVAL: ; returns hl = |hl| and increments bit 7,h ; a if the sign bit changed ret z ld b,h ld c,l ld hl,0 or a sbc hl,bc inc a ret XPOS:dw 0 YPOS:dw 0 REAL:dw 0 IMAG:dw 0 ```

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https://madanswer.com/7939/Time-And-Distance-Question

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# Time and distance question Oct 31, 2019 Q: Two trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?

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https://www.beyondtheboxscore.com/2010/7/28/1593708/mlb-strength-of-schedule-estimates

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Filed under: # MLB Strength of Schedule Estimates through 27 July One of the things I've long planned to include in the power rankings is a strength of schedule adjustment.  There's a big difference between playing in the AL East than...well...any other division.  Baltimore may not be a good team, but they probably look worse than they are because they play so many games against elite teams like the Yankees, Rays, and Red Sox. Well, I finally have it going, and thought I'd give a preview of it here before posting the power rankings tomorrow. First, the methods.  You can skip this and click "more" below if you just want to see the results! The approach is pretty straightforward.  First, I calculate the weighted average component winning percentage of each team's opponents.  This is basically the strength of schedule adjustment.  Face more tough teams, you'll have a higher opponent component winning percentage.  We can then use the log5 method (solving for W%(A)) to apply this adjustment to a team's raw component winning percentage and calculate an adjusted component winning percentage.  This adjusted component winning percentage should be a better estimate of a team's true performance, because it accounts for the fact that some teams have faced tougher competition than others. There's one additional wrinkle.  As @cwyers pointed out to me on twitter, it is then possible--and desirable--to use this adjusted component winning percentage to re-calculate strength of schedule adjustments.  That way, your strength of schedule measures are based on a better measure of team performance than raw component winning percentages.  And, of course, once you get this new strength of schedule adjustment, you would want to generate new adjusted component winning percentages for teams...and you can repeat this cycle indefinitely.  I'm finding that after three iterations, you don't get much change, so that's what I'm doing. ...Ok, one last thing.  It is the case that a given team has a say in the performance of his opponents, though this effect on any one team should be small in most cases.  Nevertheless, because I'm pulling data from baseball-reference team schedule tables, I don't have the ability to account for this game by game.  So I opted to "regress" 10% back toward 0.500, reasoning that few teams have accounted for more than 10% of another's games played, and thus shouldn't drive more than 10% of the strength of schedule adjustment.  It's an imperfect solution to this problem, but it's the best I can do. Make sense?  That's the methodology.  And now, at long last, here are strength of schedule (SoS) adjustments through 27 July--these are essentially measures of opponent winning percentage, as measured by the methods used in the power rankings: Team SoS Orioles 0.529 Diamondbacks 0.523 Mets 0.517 Indians 0.515 Marlins 0.514 Phillies 0.513 Royals 0.511 Mariners 0.506 Rockies 0.506 Blue Jays 0.504 Red Sox 0.504 Astros 0.503 Nationals 0.503 Angels 0.502 Rays 0.501 Braves 0.500 Dodgers 0.498 Pirates 0.498 Giants 0.495 Padres 0.495 White Sox 0.493 Twins 0.493 Tigers 0.490 Yankees 0.490 Cardinals 0.489 Brewers 0.487 Athletics 0.487 Reds 0.481 Rangers 0.478 Cubs 0.477 So the Orioles take the cake as having the worst schedule in baseball (big surprise!).  Other teams with tough schedules, at least thus far, include the Diamondbacks, Mets, Indians, and Marlins--all teams that have arguably underperformed at times this season. On the other side of the coin are teams with particularly weak schedules.  These include the Cubs (no excuses!), Rangers, Reds, A's, Brewers, Cardinals, and Yankees.  As you can see, while the pattern is not absolute, a number of the "surprise" teams (Rangers and Reds first and foremost) have had fairly easy schedules thus far.  You can also see that the NL Central seems to be a good place to play--four of the six easiest schedules belong to teams from that division...because there are a lot of bad teams in that division, and no really outstanding ones!  I haven't looked closely, but I doubt the Reds' and Cardinals' schedules will be much worse moving forward.  The Yankees were a surprise here, but while they do play the Red Sox and Rays a lot, they have otherwise had a fairly light schedule...including 12 games vs. Baltimore, their most common foe thus far. Finally, if you look closely, there's an interesting pattern here where many of the best teams in the standings have tended to have weaker strength of schedules.  An obvious reason for this is that they don't have to face themselves!  The correlation isn't huge (r = -0.32), but it's there.  This is one reason the iterations are an important addition--without the iterations, the correlation was closer to 0.6.  But, of course, another possibility remains--that part of their success is just the good fortune to have an easy schedule.  We'll see what happens over the rest of the season. Anyway, hope you like this!  I'll show how these values are incorporated into the power rankings tomorrow.

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# Heart Is Drawn On Coordinate Plane 3604 dl's @ 2491 KB/s 3668 dl's @ 1765 KB/s 4858 dl's @ 1317 KB/s September 1st, 2013 23:13:18 PM This brainteaser was written by Julia Zurkovsky. A heart is drawn on a coordinate plane by plotting the following points and connecting them: The coordinates of the points are (n, n), [Filename: brainteaser_12feb_ms.pdf] - Graphing Linear Equations The graph of the equation y = x u2013 2 is the line ( ) drawn on the coordinate plane. ... If the heart rate of a patient was 95 beats per minute before [Filename: 5b PreAlg SB Unit 5 582-601.pdf] - The Middle School Math Project In A Heartbeat about the heart with particular focus of the ... is constructed by placing points on a coordinate plane. When the ... plotted and the corresponding line is drawn. [Filename: heartbeat.pdf] - Coordinate Dependence of Variability Analysis Coordinate Dependence of Variability Analysis ... they co-varied to lie close to a plane within the three-dimensional ... To what degree do the conclusions drawn Coordinate SyStemS Coordinate SyStemS CLoZe eXerCiSe l Read ... systems. Letu2019s consider the 2D coordinate system first. Any location on a plane can be ... drawn on a two-dimensional ... [Filename: TWonline08_02.pdf] - Polar, Cylindrical, and Spherical Coordinates ... with r= constant curves drawn in blue and = constant drawn in red. ... z= kdescribes a plane parallel to the xy-plane. 3. ... same thing in both coordinate systems.) [Filename: 0923_sol.pdf] - Grade 6~ Benchmark 1 ~ Instructional Support Block 1 Block 2 ... be done on the coordinate plane. Visualization of movement is at the heart ... Consider giving your students a coordinate plane, with an irregular polygon drawn ... [Filename: 6bnchmrkpgs.pdf] - A Criterion Characterizing the Orientation of a ... plane and drawn at the side, ... on the three coordinate planes, ... and den Boer, W.: Brit. Heart J. 14:401, 1952. Brinberg, L.: J. Mt. Sinat Hosp. 23:7.51, 1956. [Filename: burger_58_criterion.pdf] - AutoCAD Chapter 3 and Its Applications SUPPLEMENTAL B A S I C ... DRAWN APPROVALS.X.XX TOLERANCES: UNLESS OTHERWISE SPECIFIED u00b1 .1 u00b1 .01 MATERIAL ... left, right, or top isoplane, depending on the plane on which you plan to draw. [Filename: SupMat02.pdf] - Three-Dimensional Electrogram in Spherical Coordinates ... Both in Cartesian and spherical coordinate systems, ... Angle between XY plane and optimum plane ... Curve is drawn in this [Filename: 59_S51.pdf] - Missouri Mathematics Core Academic Standards High School ... heart of this unit. ... Students now use the coordinate plane to extend trigonometry to ... and careful design play in the conclusions that can be drawn. [Filename: MOCASHighSchoolCriticalAreasforInstructionalFocus.pdf] - Mathematical Correlations: Heart and Health It is constructed by placing points on a coordinate plane. When the ... data using their heart rate and then plot the ... plotted and the corresponding line is drawn. [Filename: Mathematical Correlations.pdf] - An Easy Method for Drawing Curves in Polar Coordinates ing the values which the function u0026quot;approaches at the coordinate axesu0026quot; to radial lines in the plane. ... drawn in the third and fourth u0026quot;contra-sectionsu0026quot; ... [Filename: 3028790] - Lexis Diagrams - Hepatitis Aids Research Trust coordinate axes by a straight line or broken ... The Age-Time Plane u2022 This half plane is called the age-time plane. u2022 The age axis is drawn down because tables [Filename: LexisDiagrams.pdf] - 1 Learning from Experience Although I had never felt drawn to teach fifth grade ... coordinate plane. ... Teach With Your Heart by Erin Gruwell, Erin had to figure out ... [Filename: RittenhouseHN111FieldEx.pdf] - THE HUMAN HEART AS A SYSTEM OF STANDING WAVES of the human heart on the frontal plane. ... and drawn in Fig. 3. Let us consider the human heart as a union of two semi ellipses one of them having ... [Filename: J25.pdf] - Algebra II Critical Focus Area Cards drawn. . Critical Area 3 ... and to make decisions u201d is at the heart of this unit. ... coordinate plane enables the extension of trigonometric functions to all real [Filename: Algebra II Critical Focus Area Cards.pdf] - Designing Patterns with Polar Equations using Maple The The polar coordinate system has a fixed point O called the origin or pole ... A point P on the plane ... cardioids and rose curves that are drawn using Maple. [Filename: paper.pdf] - Linear Versus Nonlinear - College of the Redwoods ... If we place a coordinate system on the plane, ... u2022 The vector p0 is a vector that is drawn from the origin of the coordinate system ... The bold of heart will ... [Filename: LinearVsNonlinear-p.pdf] - Non-Invasive Placement And 3D Tracking Of Myocardial Beads ... time of tag placement is drawn on a long ... by manually setting the angles of the tagging plane in the coordinate system of the ... the heart from 2 sets of ... [Filename: amini non-invasive 00731981.pdf] - Share on:

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# Algebra 1b homework help • Why did gonzo walk around carrying ice cream and a pair of sparrows; • Independent reviews foundations for algebra, year 1; • A collection of math resources based on singapore math, including video lessons, examples and step-by-step solutions of singapore math word problems, worksheets for singapore math from grade 1 to grade 6, what is singapore math, how to explain singapore math; • Math homework is not intended to make life miserable; • Here's a list of all modules (topics) of; • Intermediate algebra > pre calculus helpful -complete parts 1a and 1b-test friday; • Homework help homework help - post homework questions, assignments & papers; • I need the step by step work with algebra 1b homework help this; • Students, teachers, parents, and everyone can find solutions to their math; There are also parent newsletters from another district using the same curriculum that may help explain the math materials further. Worried about his son's stress levels during his first year of a levels, a doting dad asked what he could to do help, but instantly regretted his offer after seeing his math homework. Krippinger's homework help: home; fundamentals. Latest additions to homework information. Share only what is helpful, not algebra 1b homework help harmful. 2x+4y=10 3x-3y=-3 any help will be. Students, teachers, parents, and everyone can find solutions to their math problems instantly. To ask a question, go to a section to the right and select "ask free tutors". Free online algebra course algebra homework help. • You can always trust us and get your concept related to the subject clear anytime you want to; • These essays, together with a human hair; • Study skills guide for studying math - education corner; • This resource was designed to keep math concepts fresh all year and to help you easily track student progress; Okay, thats really high in the upper lefthand corner (or your agents address, if you have spelled your past and current beliefs. In this article, we've compiled the best free online materials for ib math sl/hl so you can get all the ib math notes you need in one place. 1. Master essay: algebra 1 homework help large writing staff; 2. Mathbitsnotebook - algebra 1 ccss lessons and practice; 3. Owing to the complex nature of the mathematical problems and the length of average mathematics homework, there is no doubt why they would like someone to do their math homework for them; 4. The best ib math study guide and notes persuasive essay help writing for sl/hl; 5. Chegg math solver - math help on the app store; 6. Teachers can choose words carefully, they will hold information about famous couples in history seriously polluted densely populated friendly and as a sifter to refine ones commenting strategies; 7. Tvo mathify provides a seamless school-to-home math learning experience for all students; 8. Stat 200 hw & quiz; Online math help and learning resources mba admission essay buy graduate school (video lessons. Then classify the triangle by its angles (45' on the top left 105' on the middle bottom x on the bottom right) ' right ' obtuse ' scalene ' acute i think its c but i don't know. 250+ million students trust and study with brainly every month. Back textbooks parent support remote teaching homework help back why cpm. Access resources to help your child with homework or brush up on your math skills. Here at tutoreye, our live math homework help fee is very reasonable, especially considering that you receive real-time homework help from our expert tutors of math. Math homework help service: brief overview we have been in this business for a long period of time and have assisted many students with their specific needs of math homework help service. • To learn math you must experience it; • 75 free homework help sites: get free online tutoring; • Algebra calculator is a calculator that gives step-by-step help on algebra problems; • Send reset link post a question; • A boolean algebra is a mathematical structure that is similar to a boolean ring, but that is defined using the meet and join operators instead of the usual addition and multiplication operators; • Get homework help help at studypool; • 21 + x = -10 2; • (yes its 7 to 16) 7; • These 8qs are the ones i do not get, this is off a worksheet of 150 prob; If math makes you nervous, try not to pass on your feelings to your child. Gateway test 1b algebra answers. Help me on this assignment find the missing angle measure. The yup homework help app provides homework help for math, chemistry, and physics anytime and anywhere. • I only wish i'd found it sooner; • Meowessay - orlando, fl, united states - education; • Free math lessons and math homework help from basic math to algebra, geometry and beyond; • Solved: work problem 1a and 1b with your calculator, using; • It covers algebra, geometry, statistics, and more;

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## What are the 5 main shapes with VSEPR theory? Molecular Geometries. The VSEPR theory describes five main shapes of simple molecules: linear, trigonal planar, tetrahedral, trigonal bipyramidal, and octahedral. ## What are the 4 VSEPR shapes? 4.11: Molecular Shapes- The VSEPR Theory Number of Electron Groups on Central Atom Number of Bonding Groups Molecular Shape 3 3 trigonal planar 3 2 bent 4 4 tetrahedral 4 3 trigonal pyramidal What are the 3 VSEPR shapes? The structures are: linear, trigonal planar, angled, tetrahedral, trigonal pyramidal, trigonal bipyramidal, disphenoidal (seesaw), t-shaped, octahedral, square pyramidal, square planar, and pentagonal bipyramidal. The VSEPR structures take the names of 3-D geometric shapes, as in the example trigonal bipyramidal. ### What are the 5 types of molecular shape? The 5 molecular geometries are linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral. ### How do you identify a VSEPR shape? 1. VSEPR Rules: 2. Identify the central atom. 3. Count its valence electrons. 4. Add one electron for each bonding atom. 5. Add or subtract electrons for charge (see Top Tip) 6. Divide the total of these by 2 to find the total. 7. number of electron pairs. 8. Use this number to predict the shape. How do you use VSEPR chart? #### What is Z in VSEPR theory? The central nitrogen atom (z = 7, 1s2, 2s2, 2p3) of NH3 consist of five valence electrons. Hydrogen atoms forms three bond pairs around nitrogen atom and there is one lone pair because of remaining two electrons. Therefore, nitrogen is surrounded by four electron pairs which adopts tetrahedral geometry. #### What are the six basic molecular shapes? The 6 basic molecular shapes are linear, trigonal planar, angular (bent), tetrahedral, trigonal pyramidal, and trigonal bipyramidal. How do we know the shape of molecules? The shape of a molecule is determined by the location of the nuclei and its electrons. The electrons and the nuclei settle into positions that minimize repulsion and maximize attraction. Thus, the molecule’s shape reflects its equilibrium state in which it has the lowest possible energy in the system. ## What is the main idea behind VSEPR theory? 4.1: Covalent Bonds. A covalent bond is formed between two atoms by sharing electrons. • 4.9: Polar Covalent Bonds and Electronegativity. Covalent bonds between different atoms have different bond lengths. • 4.11: Naming Binary Molecular Compounds. The chemical formula of a simple covalent compound can be determined from its name. • ## How can you use the VSEPR theory? The VSEPR theory can be applied to each resonance structure of a molecule. The strength of the repulsion is strongest in two lone pairs and weakest in two bond pairs. If electron pairs around the central atom are closer to each other, they will repel each other. This results in an increase in the energy of the molecules. What do you mean by VSEPR theory? Valence shell electron pair repulsion theory, or VSEPR theory (/ ˈ v ɛ s p ər, v ə ˈ s ɛ p ər / VESP-ər,: 410 və-SEP-ər), is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. It is also named the Gillespie-Nyholm theory after its two main developers, Ronald Gillespie and Ronald Nyholm. ### What is the evidence for VSEPR theory? VSEPR is simple and useful but does not work for all chemical species. First, the idealized bond angles do not always match the measured values. For example, VSEPR predicts that and will have the same bond angles, but structural studies have shown the bonds in the two molecules are different by 12 degrees.

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Explore BrainMass Linear Independence of the Set of Vectors Not what you're looking for? Search our solutions OR ask your own Custom question. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! Linear Independence of the Set of Vectors Linearly Independent Linearly dependent (a) Test for the linear independence of the set of vectors (0,1,0,1,1,0), (1,1,1,0,0,1), (1,0,1,0,1,1), (1,1,1,0,0,0), (0,0,1,0,1,1) in V6 over the field of rational numbers. (b) Test for the linear independence of the set of vectors (1,0,1), (1,2,0), (0,1,2), (1,1,2), in V3 over the field of rational numbers. https://brainmass.com/math/linear-algebra/linear-independence-set-vectors-19422 Solution Preview Linear Independence of the Set of Vectors Written by :-Thokchom Sarojkumar Sinha (a) Test for the linear independence of the set of vectors (0,1,0,1,1,0),(1,1,1,0,0,1),(1,0,1,0,1,1),(1,1,1,0,0,0), (0,0,1,0,1,1) in V6 over the field of rational numbers. ... Solution Summary This solution is comprised of a detailed explanation for the linear independence of the set of vectors. It contains step-by-step explanation to test for the linear independence of the set of vectors. Solution contains detailed step-by-step explanation. \$2.49

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# Unit 4 Assignment Pages: 2 (523 words) Published: August 1, 2011 Tamisha McQuilkin Unit 4 Assignment GB550 Financial Management Dr. Prondzinski May 17, 2011 24-2 Security A has an expected rate of return of 6%, a standard deviation of returns of 30%, a correlation coefficient with the market of -0.25, and a beta coefficient of -0.5. Security B has an expected return of 11%, a standard deviation of returns of 10%, a correlation with the market of .75, and a beta coefficient of 0.5. Which security is more risky? Why? Using SML: rA= rrf + (rm – rrf)bi Security A is riskier because of its negative correlation to the market. Also its beta is negative causing to believe its risk will increase over time. 24-8 You are given the following set of data: Historical Rates of Return| | | Year| NYSE| Stock Y| 1| 4.0%| 3.0%| 2| 14.3| 18.2| 3| 19| 9.1| 4| -14.7| -6.0| 5| -26.5| -15.3| 6| 37.2| 33.1| 7| 23.8| 6.1| 8| -7.2| 3.2| 9| 6.6| 14.8| 10| 20.5| 24.1| 11| 30.6| 18.0| | Mean = 9.8%| 9.8%| | σ = 19.6%| 13.8%| a. Construct a scatter diagram showing the relationship between returns on Stock Y and the market. Use a spreadsheet or a calculator with a linear regression function to estimate beta. β = 0.62 b. Give a verbal interpretation of what the regression line and the beta coefficient show about stock Y’s volatility and relative risk as compared with those of other stocks. This graph shows that stock Y’s volatility follows the basic trend of the market (NYSE). The regression line and beta coefficient shows a positive correlation between stock Y and the market with an upward trending regression line and positive beta coefficient of 0.62. Also, the plots of stock Y lie closer to the regression line than the market leading to believe that stock Y is less risky than the other stocks in the market. c. Suppose the regression lines were exactly as shown by your graph from part b but the scatter of points were more spread out. How would this...

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Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) : Share GMAT Experience - Page 3 Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack It is currently 16 Jan 2017, 23:37 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) Author Message TAGS: ### Hide Tags Manager Status: Married Affiliations: MENSA India Joined: 30 Apr 2011 Posts: 102 Location: India GMAT 1: 630 Q42 V35 GMAT 2: 640 Q42 V35 GMAT 3: 640 Q44 V32 GMAT 4: 660 Q47 V34 GMAT 5: 680 Q46 V37 GPA: 3.6 WE: Sales (Computer Software) Followers: 0 Kudos [?]: 8 [0], given: 13 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 10 Aug 2012, 08:41 _________________ Always aim at the moon. Never mind if you miss, you will fall in the stars Intern Joined: 27 Apr 2012 Posts: 40 Location: United States GMAT 1: 650 Q46 V34 GPA: 3.3 WE: Consulting (Accounting) Followers: 0 Kudos [?]: 5 [0], given: 9 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 06 Sep 2012, 12:15 I remember reading this post before but by that time I thought the test was in the old format. Good luck with your application! Intern Status: Life begins at the End of your Comfort Zone Joined: 31 Jul 2011 Posts: 47 Location: Tajikistan Concentration: General Management, Technology GPA: 3.86 Followers: 2 Kudos [?]: 26 [0], given: 4 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 11 Sep 2012, 09:26 Ok, WOW! Man you blew my mind with that score, thumbs-up! I am having hard time to get my Verbal score to 80 percentiles but you rocked the GMAT as a piece of Dunkin Donuts' Boston Cream that I used to like, congrats bro! _________________ Senior Manager Joined: 05 May 2011 Posts: 358 Location: United States (WI) GMAT 1: 780 Q49 V50 WE: Research (Other) Followers: 7 Kudos [?]: 95 [0], given: 35 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 11 Sep 2012, 20:53 Wow excellent score congratulations!! I've never seen an 800 debrief. Good luck with your applications, I'm just putting the finishing touches on my Kellogg essays. It would be great to see you there. Manager Joined: 02 May 2012 Posts: 109 Location: United Kingdom WE: Account Management (Other) Followers: 0 Kudos [?]: 49 [0], given: 34 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 13 Sep 2012, 05:11 Quote: Eastern Ukrainians resemble Russians in virtually every way. Some of them call themselves Russian and don't even speak Ukrainian, which is the national language. Western Ukrainians, however, would not take kindly to being identified as Russian, although they share much of Russian culture. As is the case in certain other country pairs, it's generally safer to mistake a citizen of the more powerful country for one of the less powerful (mistake an American for a Canadian or an Australian for a New Zealander and you'll generally cause less offense than if you make the opposite mistake). An Australian should be so lucky...... _________________ In the study cave! Intern Joined: 18 Oct 2012 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 1 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 19 Oct 2012, 04:53 Congratulations and thanks for your long debrief. You're my GMAT idol. Best of luck in everything! Manager Joined: 24 Feb 2013 Posts: 105 GMAT 1: 660 Q47 V35 GMAT 2: 690 Q46 V38 GMAT 3: 680 Q46 V37 GMAT 4: 680 Q45 V39 GMAT 5: 760 Q48 V47 GPA: 3.97 Followers: 0 Kudos [?]: -8 [0], given: 45 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 24 Feb 2013, 14:41 Soooooooo... where did you end up?! Manager Joined: 12 Jul 2011 Posts: 129 Concentration: Strategy, Sustainability Schools: Booth '15 (M) WE: Business Development (Non-Profit and Government) Followers: 71 Kudos [?]: 466 [0], given: 41 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 24 Feb 2013, 21:14 shanek wrote: Soooooooo... where did you end up?! I'm still waiting to hear from Booth and Tuck! Either one would be amazing! _________________ Intern Joined: 12 Mar 2013 Posts: 4 Followers: 0 Kudos [?]: 13 [0], given: 3 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 16 Jun 2013, 06:20 That was really inspiring, thank you for that debrief! I have my exam coming up tomorrow and have also been playing some mindless games to take the pressure off in the down periods, glad to see that someone else does this as well! Manager Joined: 12 Jul 2011 Posts: 129 Concentration: Strategy, Sustainability Schools: Booth '15 (M) WE: Business Development (Non-Profit and Government) Followers: 71 Kudos [?]: 466 [0], given: 41 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 16 Jun 2013, 08:48 Good luck tomorrow! Don't forget to take a snack! Welix92 wrote: That was really inspiring, thank you for that debrief! I have my exam coming up tomorrow and have also been playing some mindless games to take the pressure off in the down periods, glad to see that someone else does this as well! _________________ Intern Joined: 21 Mar 2013 Posts: 37 Followers: 0 Kudos [?]: 1 [0], given: 15 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 16 Jun 2013, 17:25 WOW!!! Thats Awesome!! Never came across 800 de brief Manager Status: Re- Working on GMAT Joined: 23 May 2011 Posts: 104 Location: Australia GMAT 1: 600 Q44 V29 GPA: 2.4 WE: Analyst (Computer Software) Followers: 1 Kudos [?]: 11 [0], given: 38 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 21 Jun 2013, 02:17 Its not a good score but a perfect score.. though AWA 4.5 is a bit low.. I saw others too with high GMAT scores but low AWA scores.. has the marking changed? _________________ All men dream - but not equally. Those who dream by night, in the dusty recesses of their minds, wake in the day to find that it was vanity... But the dreamers of the day are dangerous men, for they may act their dream with open eyes, to make it possible. Manager Joined: 12 Jul 2011 Posts: 129 Concentration: Strategy, Sustainability Schools: Booth '15 (M) WE: Business Development (Non-Profit and Government) Followers: 71 Kudos [?]: 466 [0], given: 41 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 23 Jul 2013, 14:55 I doubt the evaluation criteria have changed; I simply didn't prepare thoroughly. I didn't know how to practice the essay. I wasn't aware of essay guides (like that of chineseburned) until after I'd taken the test. _________________ Intern Joined: 30 Apr 2011 Posts: 49 Followers: 0 Kudos [?]: 5 [0], given: 29 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 23 Jul 2013, 16:21 You gave a the best name for your post man. it is really long! :D Congrats to your success. you are the first person i ever hear really scored 800! Intern Joined: 01 May 2013 Posts: 7 Schools: ISB '16 Followers: 0 Kudos [?]: 1 [0], given: 11 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 26 May 2014, 22:36 Terrific. Totally amazing! Manager Joined: 28 Aug 2013 Posts: 101 Location: India Concentration: Operations, Marketing GMAT Date: 08-28-2014 GPA: 3.86 WE: Supply Chain Management (Manufacturing) Followers: 0 Kudos [?]: 36 [0], given: 23 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 11 Oct 2014, 01:36 NonYankee wrote: Update 3 (Aug 11, 2012): I have received multiple requests for the study documents in which I compiled Bunuel's quant problems. I have (hopefully) removed all personally identifying information from the files and attached them as a zip file below. Good luck, everyone! Update 2: I just got my official scores. My IR score was 8 (despite not answering the final two questions) and I basically bombed the essay... AWA was 4.5. I can't really imagine what caused my essay to be so poor. I know that waiting for 30 minutes before the test made me nervous. Or maybe I just wrote the wrong stuff! Update: I want to thank everyone for their kind words and support. In case anyone is interested (or incredulous), I've added a Notice of GMAT Testing Irregularities file that I received from the Pearson Vue Security Team. It simply says I'm not allowed to take the GMAT for five years. I'm under the impression that this is standard procedure. Hello everyone, I haven't posted very much on GMAT Club forums before now because I never thought I had anything worthwhile to share, but now that I got a decent good GMAT score, maybe my debrief will help someone. My Background I am a 25 year-old American male. I have always performed above average on standardized tests. I had great success with the ACT especially. I didn't care as much for the SAT. I remember the obscure vocabulary and analogies to be quite challenging. I received a BS in chemical engineering and a MS in bioengineering from a good-but-not-great state school (although our football team is top-notch). After my master's I joined the Peace Corps (in 2010). My work mostly involves community development and English education in Ukraine. Method of Study and GMAT Score History I used the OG 12 and GMATPrep software. I liked the OG because it provides answer explanations. Because of the introduction of the IR section, I was actually able to use two versions of GMATPrep software (before and after the change). This allowed me to have 4 adaptive practice exams. In general, I never studied on two consecutive days, nor for longer than 3 hours at a time. When using the OG, I enjoyed working through one question type at my own pace without a time limit. First GMATPrep Practice Exam Last summer (2011) I determined that I wanted to pursue an MBA after Peace Corps if I would be accepted to a highly ranked program. I downloaded the GMATPrep software from mba.com. I took a practice exam on July 13, 2011. I received a score above 700. I don't remember what it was exactly, but I remember thinking that while the score wasn't amazing, it wasn't so low that I felt nervous about preparing for the test. I forgot about the GMAT for a while. Registering for the Test and Practicing Diagnostic Questions On April 29, 2012 I finally registered to take the GMAT in Kyiv, Ukraine on July 3, 2012. I wanted to take it before it changed in early June, but I didn't want to miss work at the end of the school year (since I'm a teacher) and the dates just didn't work out. I had the good fortune of finding a copy of GMAC's Official Guide, 12th Edition among the free books that volunteers leave in the Peace Corps office. This guide has a short diagnostic test (paper-based) that I used to test myself. I intended to answer the quantitative questions, find how many I'd missed, then answer the verbal questions, but I never got to the verbal questions. I was appalled that I had missed about 10% of the quantitative diagnostic questions. I reviewed my mistakes and realized that half of them were due to careless mental math errors (saying 12 divided by 1.5 = 6, or 4 out of 20 is 25%) and the other half were due to reading the question incorrectly, thereby missing important details. I didn't do any other studying in April. Working with the Official Guide (12th Ed.) Subsequent GMATPrep Practice Exams Still using the old GMATPrep software (based on Java), I took my second practice exam on June 26, 2012. For the Analysis of an Argument section, I simply typed out an outline with sections such as: argument's thesis, supporting evidence, underlying assumptions, alternative explanations, and other information that would be useful. I didn't write an actual essay. I decided to skip the Analysis of an Issue section, since it wouldn't be on my actual exam (I would take the Next Generation GMAT with Integrated Reasoning). I finished the quantitative and verbal sections in good time. It was only later that I realized how much mental fatigue I spared myself by only writing an outline for the first essay and skipping the second essay altogether. My result on this exam was 770 (50Q, 46V). I felt really encouraged by this, but I knew that it didn't account for the new IR section. I had taken a look at the practice IR questions on mba.com and didn't feel too concerned about the new section. Actually, I thought it would favor analytical people like me. I can't say that writing is my strong suit, so I wasn't upset to see the second essay go. On June 27 I downloaded the most recent GMATPrep software that is based on Adobe AIR. I was stunned by the quality and breadth of the changes GMAC made to the software. On June 28-29 I worked through more PS problems in the OG, but didn't do anything strict or regimented. I think I answered 100 on the 28th and 60 or 70 on the 29th, until I got tired and decided to play Diablo. Diablo 3 and GMAT preparation were my two time sinks from June 20 until G-Day. I found it necessary to decompress, especially after taking practice exams. On June 30 I took a practice exam using the new software and had problems with time management (it's convenient that the new software saves this information for later review). I only answered 34 of 37 quantitative questions and 11 of 12 IR questions. I answered all verbal questions in 47 minutes. Verbal has never given me too much trouble, but now that I'm an English teacher, I find it even less challenging. My score on this practice exam was 760 (49Q, 45V, 8 IR). I thought it was noteworthy that I got a perfect IR score even though I didn't answer all the IR questions (and I'd even guessed on the last question I answered because time was running out). I realized there is some leeway there. I was a bit disappointed by the decrease in my score. I told people, including myself, that my goal was 730, but I secretly hoped for 750+. After this practice exam I searched GMAT Club forums for explanations of the quantitative questions I'd missed. This is when I discovered Bunuel, GMAT Club member of the month and all-around outstanding poster. I saw his signature contained links to all sorts of challenging quantitative problems. I knew that I wouldn't have consistent internet access after leaving my apartment on July 1, so I opened all of Bunuel's PS links and saved the problem and solution sets on my computer as Word documents (although if you do this, be aware that not all equations copy properly automatically; I had to look for "holes" and manually copy the relevant image file from the original post and insert it into my document). I began reviewing exclusively these especially challenging 700+ questions. One unforeseen consequence of reviewing only super-hard questions is that I lost my confidence. I encountered questions I didn't readily know how to solve more frequently than I had done when I was simply answering questions in the official guide. This was especially true of complex permutation questions, for which even Bunuel's solutions and explanations were sometimes difficult for me to understand. As test day drew near, I told myself that the real GMAT wouldn't contain exclusively super-hard questions, and I should calm down. On July 1 I took an overnight train from my home to Kyiv, where I would take the test. On the train I solved PS questions (without a time limit) until the lights were turned off. I wasn't able to sleep all night because the passenger next to me snored very loudly. I had been aware that I might not be able to sleep on the train, which is why I had planned to arrive in Kyiv a day early, not simply on the day of the exam. I arrived on July 2 and found the test center. I actually walked all the way into the office where I would need to register on the day of the exam so that I knew how long it would take me to get there. I went to the apartment where I was staying and took my last remaining practice GMAT. I again had problems with time management. I only answered 35 of 37 quantitative questions, but finished the verbal section in 53 minutes and the IR section in 15 minutes. I noticed that all IR questions and some RC passages and questions were the same as those in the first practice exam I'd taken using the new GMATPrep software. This is one reason my times on those sections were so fast. My score on this practice exam continued the downward trend. It was 750 (49Q, 44V, 8 IR). I tried to encourage myself by reasoning that I hadn't slept at all on the train. That night I went to bed around 10:30 (tired from no sleep the previous night and mentally exhausted from the practice exam), but I couldn't fall asleep for a long time. My mind was racing. I worried what would happen if I got a low score. I worried that I wouldn't have time to retake the test before essay prompts begin to be released, and then my attention would be divided. I didn't think my work experience alone would get me into a good school. I tried to fall asleep but kept thinking about how much I needed a strong score. Also, it was just too hot in my room. My window was open, but the night air still hadn't become cool. Eventually I fell asleep. TEST DAY I arrived at the test center early. My appointment was for 2:00 and I arrived around 1:15. The test administrator asked me to wait, but he told me that he could get started if I gave him my passport and appointment confirmation. I gave them to him and sat in the hallway to wait. I started reading some posters on the walls, but I couldn't keep from getting nervous. I had serious butterflies. I sipped from a bottle of juice I'd brought with me. I had heard that it's good to drink something with sugar and electrolytes during the scheduled breaks to alleviate mental fatigue. I ended up "sipping" half the one-liter bottle before I even began my test. At about 1:45 the test administrator, Vladislav, invited me in to have my palm scanned and picture taken. When I said I was ready, he escorted me to the testing room. There were four test stations arranged in a row. It was a small room. I asked Vladislav whether I'd be the only one testing. He said yes. I was relieved. The first part was the essay. I noticed right away that the computer keyboard's keys felt squishy and it didn't register every keystroke. I typed slowly and deliberately and looked carefully for spelling errors. I also noticed noise from people walking in the hallway. I put in the earplugs that had been supplied to me. I didn't take time to write or type an outline. I was afraid I'd run out of time if I didn't start promptly. In the end, my essay included all the points I wanted to make, all the alternative arguments and underlying assumptions and so forth. But my essay seemed short, and as time ran out I couldn't help but feel that it could have benefited from more polish. The integrated reasoning immediately followed. I noticed right away that the mouse didn't consistently register clicks. One of the early questions, perhaps the third, was worded in a way that I found quite difficult to understand. I spent a long time (too long) working on this problem. It was a two-column question. I made my selections and checked to see that they met the constraints of the prompt. It seemed that they did, so I moved on. I think I must have spent 8 minutes or more on that problem. Since there were several questions still ahead, I thought that I could save a little time on each of those and be fine. In the end, I didn't have time to answer the final two questions I don't know my IR score yet, but I'm hopeful that I'll get a 7 or 8, or that my IR score won't count for too much, since business schools will still be adapting to the new GMAT format. I took the first optional break. According to the lock screen on the computer, I had 8 minutes, but Vladislav told me I would have only 5 minutes. I went to the hallway, drank some juice, and cursed myself for running out of time on IR. I tried to calm myself before returning from my break, but it was no use. The quantitative section went smoothly, except that one of the pens supplied to me didn't write very well. It would make two lines whenever I made a stroke. I read each question, then solved it on my laminated 10-sheet notepad, then selected my answer, then checked to see that the answer worked. I spent the most time on the DS questions and on PS questions that were structured with three conditions (I, II, III) and answer choices like (I only, II only, I and III, etc.). I assume most GMAT Club members know what I'm talking about. Even though I checked each question after selecting my answer, I finished the section in good time. I think I had 6-8 minutes left. I was relieved that I didn't see any complex permutation questions like those I'd stressed about in Bunuel's problem sets. I took the second optional break. I sipped juice. I used the bathroom. I rinsed my face with water. I fussed about my appearance in the mirror. I thought about my performance on the quantitative section and felt that there was still hope for me to get a good overall score (this is in contrast to how I felt after IR). It all depended on the verbal section. I've always found SC relatively easy. Verbs should agree with nouns, phrases should logically describe their noun (and that noun should be the closest noun to the phrase in almost every case), and there are a few finer points (like the differences between "fewer" and "less," "between" and "among") that aren't difficult to remember. On RC questions I took care to identify the basic content of each paragraph, and from the content I deduced the purpose of the paragraph. I also payed attention to the language used throughout the passage, which can sometimes make the purpose of the passage clear. On CR questions it's most important to identify which answer choices have nothing to do with the topic at hand. I reached the last verbal question, a SC-type, with about 6 minutes left. It was at this point that I realized I hadn't looked at the timer throughout the entire verbal section. Thinking back, I only glanced at the timer two or three times during the quantitative section. I realized that over the course of the test, I had become a kind of question-answering zombie--I had no awareness of anything besides the present question. I didn't even recall the question immediately prior to the current one. As the exam had worn on, I came to be entirely focused on the current prompt, what it was really asking, and which answer choices were viable and which were nonsense. I took my time and ended my exam with about 3-4 minutes remaining. I paused when I saw the report/cancel scores screen. It was the first time I'd seen it, since it wasn't present in the GMATPrep software. I felt good about my test performance with the exception of IR. Then the unofficial score screen came up: Quantitative: 51 Percentile: 98 Verbal: 51 Percentile: 99 Total: 800 Percentile: 99 I got goosebumps when I saw it! I raised my hand to be dismissed and shakily walked with Vladislav to his station, where he printed out my unofficial score report and scanned my palm one last time. He said it was the first time in two years that he'd seen a perfect score. I can't say I'm a GMAT expert. But I highly recommend all GMAT examinees get acquainted with both the content and the length of the test. I was content with the official guide and GMATPrep software, both of which were produced by GMAC. For specific advanced questions, GMAT Club met all my needs. Mental fatigue is real and it tends to snowball. I mean that as you approach the end of a section, fatigue will cause you to think more slowly, it will force you to re-read or re-calculate, and spending longer on each question will only serve to fatigue you even more. In the weeks leading up to your exam, take a few practice exams. I recommend taking them at the same time of day you as your test appointment. If possible, determine whether you are mentally fresher in the morning or afternoon before you schedule your exam. Also, time management is important. To those expecting scores of 700+, I would say do not pay too much attention to the clock. You have the ability to identify the correct answer, you just need to do it without second-guessing yourself or getting distracted. It might seem counter-intuitive, but I really believe my time management was better because I wasn't paying attention to the time. Don't calculate how much time per question you have remaining. Don't determine whether you are ahead or behind schedule. Focus instead on identifying what the question is asking and which answer choices are decoys or traps. It's important to avoid diverting your attention from the question at hand and losing your train of thought (on the current question) and your momentum (on the test section). For those who aren't merely struggling against time, I would advise you to use strategies to eliminate answer choices whenever possible. This way, even if you truly don't know how to solve a question, your guesses will be correct more often. That's the goal: to narrow the choices and to do it as quickly as possible. On quantitative questions, use estimates when possible. On questions such as: Which of the following must be true? I. x<y<z II. y<z<x III. z<x<y use test (example) numbers when possible, especially testing values between 0 and 1, between 1 and 2, and between -2 and -1 and -1 and 0. Don't forget to test 0 itself! And on SC questions, identify the noun and verb and ignore the answer choices that don't have the right form. On RC questions, an answer choice might use words from the passage but combine them to make a statement that is inconsistent with the content of the passage. Don't be deceived by the presence of conspicuous keywords from the passage. I think the strategies I've listed here will help eliminate the most incorrect answer choices the fastest, thereby helping you finish the section in time. Finally, pay attention on all questions to what's NOT said. Don't add or imagine that an opinion was stated in a passage or a constraint was listed in a quantitative prompt, when in fact there was no such thing. Conclusion I'm glad to put the GMAT behind me for now. The initial excitement of my score has worn off and now everything is firmly back in perspective. After all, if a school's student body has a median GMAT score of 700, it means that half of the accepted students scored 700 or below. That means that they were accepted because of other deciding factors and the GMAT didn't change the strength of their application. Similarly, I know that my GMAT won't get me into any schools that don't already like my essays, interview, and work experience. I don't claim that luck played no part. I know that I didn't get every quantitative question right; otherwise I would have gotten a quantitative score of 60 according to GMAC's percentiles. But now that I have taken the GMAT, I can stress about the essays and recommendations, which will be crucial in convincing adcoms to take a chance on an applicant with so little relevant industry experience. I believe anyone can prepare for the GMAT, and it doesn't cost a fortune. I found the official guide exceptional. Also, Bunuel shared some formulas that weren't in the guide and I had forgotten (such as the sum of the first n consecutive positive odd integers equals n squared). Practice is key! I wish you all luck in your business school endeavors and beyond! Edit: Edited for formatting and to add a file. Seriously Dude !!! 800 , Jesus I am struggling to pass 660 , You are talented. Regards LS _________________ G-prep1 540 --> Kaplan 580-->Veritas 640-->MGMAT 590 -->MGMAT 2 640 --> MGMAT 3 640 ---> MGMAT 4 650 -->MGMAT 5 680 -- >GMAT prep 1 570 Give your best shot...rest leave upto Mahadev, he is the extractor of all negativity in the world !! Intern Joined: 03 Jul 2014 Posts: 3 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 12 Oct 2014, 22:54 800!!! Didnt even know if scoring 800 was possible. Manager Joined: 27 May 2014 Posts: 85 Followers: 0 Kudos [?]: 19 [0], given: 21 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 13 Oct 2014, 14:23 What were your last 10 or so questions on each section like? Did they seem much tougher than the beginning of the test? My experience with the gmat prep practice testing (scoring a 49) was that my last questions weren't the most difficult ones I encountered throughout the exam. One would think this would be the case as by the last 10 or so questions the software would be able to mirror in on your exact level. Also, did you find that the questions on the actual exam skew far from the official guide practice questions? Posted from my mobile device Manager Joined: 10 Sep 2014 Posts: 99 Followers: 0 Kudos [?]: 39 [0], given: 25 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 08 Dec 2014, 10:43 inspiring post yankee, you are legend Current Student Joined: 03 Feb 2013 Posts: 939 Location: India Concentration: Operations, Strategy GMAT 1: 760 Q49 V44 GPA: 3.88 WE: Engineering (Computer Software) Followers: 134 Kudos [?]: 838 [0], given: 546 Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5) [#permalink] ### Show Tags 09 Dec 2014, 11:21 800 - 51/51. Please accept my salute !! \__0_____/ _________________ Thanks, Kinjal My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961 Prodigy for Tepper - CMU : http://bit.ly/cmuloan-kd Re: Long Debrief - 800 (Q51, V51, IR-8, AWA-4.5)   [#permalink] 09 Dec 2014, 11:21 Go to page   Previous    1   2   3   4    Next  [ 75 posts ] Similar topics Replies Last post Similar Topics: 24 790 (Q51, V51) Debrief with Various Tips 14 11 Jan 2016, 12:35 13 My debrief-> 690(Cancelled) to 730..Q51 V38 IR8 8 07 Jan 2015, 02:22 5 GMAT Debrief : 760 (Q51, V42, IR8, AWA5.5) In 3 Weeks 3 29 Sep 2014, 10:27 4 My debrief - 750 (Q51, V40) - IR 8 0 19 Jan 2014, 07:06 5 720 - Q51V36 - Long Debrief 7 22 Sep 2013, 21:16 Display posts from previous: Sort by

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#### Sample records for calculus 1. Calculus Jones, Patrick 2014-01-01 Practice makes perfect-and helps deepen your understanding of calculus 1001 Calculus Practice Problems For Dummies takes you beyond the instruction and guidance offered in Calculus For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in your calculus course. Plus, an online component provides you with a collection of calculus problems presented in multiple-choice format to further help you test your skills as you go. Gives you a chance to practice and reinforce the skills you learn in your calculus courseHelps you refine your understanding of calculusP 2. Calculus Grossman, Stanley I 1981-01-01 Calculus, Second Edition discusses the techniques and theorems of calculus. This edition introduces the sine and cosine functions, distributes ?-? material over several chapters, and includes a detailed account of analytic geometry and vector analysis.This book also discusses the equation of a straight line, trigonometric limit, derivative of a power function, mean value theorem, and fundamental theorems of calculus. The exponential and logarithmic functions, inverse trigonometric functions, linear and quadratic denominators, and centroid of a plane region are likewise elaborated. Other topics 3. Calculus Larson, Ron 2014-01-01 The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning. 4. Calculus Spivak, Michael 2006-01-01 Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis. 5. Calculus Grossman, Stanley I 1984-01-01 Calculus, Third Edition emphasizes the techniques and theorems of calculus, including many applied examples and exercises in both drill and applied-type problems.This book discusses shifting the graphs of functions, derivative as a rate of change, derivative of a power function, and theory of maxima and minima. The area between two curves, differential equations of exponential growth and decay, inverse hyperbolic functions, and integration of rational functions are also elaborated. This text likewise covers the fluid pressure, ellipse and translation of axes, graphing in polar coordinates, pro 6. Calculus Zandy, Bernard V 2003-01-01 We take great notes-and make learning a snap When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core Calculus concepts-from functions, limits, and derivatives to differentials, integration, and definite integrals- and get the best possible grade. At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented writers who know how to cut to the chase- and zero in on the essential information you need to succeed. 7. Soergel calculus and Schubert calculus He, Xuhua; Williamson, Geordie 2015-01-01 We reduce some key calculations of compositions of morphisms between Soergel bimodules ("Soergel calculus") to calculations in the nil Hecke ring ("Schubert calculus"). This formula has several applications in modular representation theory. 8. Calculus light Friedman, Menahem 2011-01-01 Another Calculus book? As long as students find calculus scary, the failure rate in mathematics is higher than in all other subjects, and as long as most people mistakenly believe that only geniuses can learn and understand mathematics, there will always be room for a new book of Calculus. We call it Calculus Light. This book is designed for a one semester course in ""light"" calculus -- mostly single variable, meant to be used by undergraduate students without a wide mathematical background and who do not major in mathematics but study subjects such as engineering, biology or management infor 9. Tuplix calculus Bergstra, J. A.; Ponse, A.; van der Zwaag, M. B. 2008-01-01 We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive composition. We define a standard model and prove that CTC is relatively complete with respect to it. The core calculus is extended with operators for choice, information hiding, scalar multiplicatio... 10. Operational calculus Boehme, Thomas K 1987-01-01 Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included.Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-ho 11. Calculus refresher Klaf, A A 1956-01-01 This book is unique in English as a refresher for engineers, technicians, and students who either wish to brush up their calculus or find parts of calculus unclear. It is not an ordinary textbook. It is, instead, an examination of the most important aspects of integral and differential calculus in terms of the 756 questions most likely to occur to the technical reader. It provides a very easily followed presentation and may also be used as either an introductory or supplementary textbook. The first part of this book covers simple differential calculus, with constants, variables, functions, inc 12. Continuation calculus Bram Geron 2013-09-01 Full Text Available Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic model of computation that is evaluated using only head reduction, and argue that it is suitable for modeling programs with control. It is demonstrated how to define programs, specify them, and prove them correct. This is shown in detail by presenting in CC a list multiplication program that prematurely returns when it encounters a zero. The correctness proof includes termination of the program. In continuation calculus we can model both call-by-name and call-by-value. In addition, call-by-name functions can be applied to call-by-value results, and conversely. 13. ESeal Calculus: A Secure Mobile Calculus Peng Rong; Chen Xin-meng; Liu Ping 2003-01-01 The ESeal Calculus is a secure mobile calculus based on Seal Calculus. By using open-channels, ESeal Calculus makes it possible to communicate between any two arbitrary seals with some secure restrictions. It improves the expression ability and efficiency of Seal calculus without losing security. 14. Advanced calculus Nickerson, HK; Steenrod, NE 2011-01-01 ""This book is a radical departure from all previous concepts of advanced calculus,"" declared the Bulletin of the American Mathematics Society, ""and the nature of this departure merits serious study of the book by everyone interested in undergraduate education in mathematics."" Classroom-tested in a Princeton University honors course, it offers students a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors introduce a single basic derivative in an invariant form. All other derivatives - gradient, divergent, curl, 15. CLEP calculus Hill, Gregory 2013-01-01 Earn College Credit with REA's Test Prep for CLEP* Calculus Everything you need to pass the exam and get the college credit you deserve.Our test prep for CLEP* Calculus and the free online tools that come with it, will allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.Here's how it works:Diagnostic exam at the REA Study Center focuses your studyOur online diagnostic exam pinpoints your strengths and shows you exactly where you need to focus your study. Armed with this information, you 16. Flipping Calculus McGivney-Burelle, Jean; Xue, Fei 2013-01-01 In this paper we discuss flipping pedagogy and how it can transform the teaching and learning of calculus by applying pedagogical practices that are steeped in our understanding of how students learn most effectively. In particular, we describe the results of an exploratory study we conducted to examine the benefits and challenges of flipping a… 17. Introduction to Tensor Calculus Sochi, Taha 2016-01-01 These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is presumed. 18. The Rewriting Calculus Cirstea, Horatiu; Kirchner, Claude 2000-01-01 The Rho-calculus is a new calculus that integrates in a uniform and simple setting first-order rewriting, lambda-calculus and non-deterministic computations. This paper describes the calculus from its syntax to its basic properties in the untyped case. We show how it embeds first-order conditional rewriting and lambda-calculus. Finally we use the Rho-calculus to give an operational semantics to the rewrite based language Elan. 19. Calculus diaries Ouellette,, Jennifer 2011-01-01 Jennifer Ouellette never took maths in the sixth form, mostly because she – like most of us – assumed she wouldn't need it much in real life. But then the English graduate, now an award-winning science-writer, had a change of heart and decided to revisit the equations and formulas that had haunted her youth. The Calculus Diaries is the fun and fascinating account of a year spent confronting her numbers-phobia head on. With wit and verve, Ouellette explains how she discovered that maths could apply to everything from petrol mileages to dieting, rollercoaster rides to winning in Las Vegas. 20. Matrix calculus Bodewig, E 1959-01-01 Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well 1. Advanced calculus Friedman, Avner 2007-01-01 This rigorous two-part treatment advances from functions of one variable to those of several variables. Intended for students who have already completed a one-year course in elementary calculus, it defers the introduction of functions of several variables for as long as possible, and adds clarity and simplicity by avoiding a mixture of heuristic and rigorous arguments.The first part explores functions of one variable, including numbers and sequences, continuous functions, differentiable functions, integration, and sequences and series of functions. The second part examines functions of several 2. Calculator calculus McCarty, George 1982-01-01 How THIS BOOK DIFFERS This book is about the calculus. What distinguishes it, however, from other books is that it uses the pocket calculator to illustrate the theory. A computation that requires hours of labor when done by hand with tables is quite inappropriate as an example or exercise in a beginning calculus course. But that same computation can become a delicate illustration of the theory when the student does it in seconds on his calculator. t Furthermore, the student's own personal involvement and easy accomplishment give hi~ reassurance and en­ couragement. The machine is like a microscope, and its magnification is a hundred millionfold. We shall be interested in limits, and no stage of numerical approximation proves anything about the limit. However, the derivative of fex) = 67.SgX, for instance, acquires real meaning when a student first appreciates its values as numbers, as limits of 10 100 1000 t A quick example is 1.1 , 1.01 , 1.001 , •••• Another example is t = 0.1, 0.01, in the functio... 3. Renal calculus Pyrah, Leslie N 1979-01-01 Stone in the urinary tract has fascinated the medical profession from the earliest times and has played an important part in the development of surgery. The earliest major planned operations were for the removal of vesical calculus; renal and ureteric calculi provided the first stimulus for the radiological investigation of the viscera, and the biochemical investigation of the causes of calculus formation has been the training ground for surgeons interested in metabolic disorders. It is therefore no surprise that stone has been the subject of a number of monographs by eminent urologists, but the rapid development of knowledge has made it possible for each one of these authors to produce something new. There is still a technical challenge to the surgeon in the removal of renal calculi, and on this topic we are always glad to have the advice of a master craftsman; but inevitably much of the interest centres on the elucidation of the causes of stone formation and its prevention. Professor Pyrah has had a long an... 4. Propositional Calculus in Coq van Doorn, Floris 2015-01-01 I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction calculus, Hilbert systems and sequent calculus and (3) cut elimination for sequent calculus. 5. Calculus of one variable Grossman, Stanley I 1986-01-01 Calculus of One Variable, Second Edition presents the essential topics in the study of the techniques and theorems of calculus.The book provides a comprehensive introduction to calculus. It contains examples, exercises, the history and development of calculus, and various applications. Some of the topics discussed in the text include the concept of limits, one-variable theory, the derivatives of all six trigonometric functions, exponential and logarithmic functions, and infinite series.This textbook is intended for use by college students. 6. On the refinement calculus Vickers, Trevor 1992-01-01 On the Refinement Calculus gives one view of the development of the refinement calculus and its attempt to bring together - among other things - Z specifications and Dijkstra's programming language. It is an excellent source of reference material for all those seeking the background and mathematical underpinnings of the refinement calculus. 7. Giant urethral calculus Kotkar, Kunal; Thakkar, Ravi; Songra, MC 2011-01-01 Primary urethral calculus is rarely seen and is usually encountered in men with urethral stricture or diverticulum. We present a case of giant urethral calculus secondary to a urethral stricture in a man. The patient was treated with calculus extraction with end to end urethroplasty. 8. Fundamentals of calculus Morris, Carla C 2015-01-01 Fundamentals of Calculus encourages students to use power, quotient, and product rules for solutions as well as stresses the importance of modeling skills.  In addition to core integral and differential calculus coverage, the book features finite calculus, which lends itself to modeling and spreadsheets.  Specifically, finite calculus is applied to marginal economic analysis, finance, growth, and decay.  Includes: Linear Equations and FunctionsThe DerivativeUsing the Derivative Exponential and Logarithmic Functions Techniques of DifferentiationIntegral CalculusIntegration TechniquesFunctions 9. The Safe Lambda Calculus Blum, William 2009-01-01 Safety is a syntactic condition of higher-order grammars that constrains occurrences of variables in the production rules according to their type-theoretic order. In this paper, we introduce the safe lambda calculus, which is obtained by transposing (and generalizing) the safety condition to the setting of the simply-typed lambda calculus. In contrast to the original definition of safety, our calculus does not constrain types (to be homogeneous). We show that in the safe lambda calculus, there is no need to rename bound variables when performing substitution, as variable capture is guaranteed not to happen. We also propose an adequate notion of beta-reduction that preserves safety. In the same vein as Schwichtenberg's 1976 characterization of the simply-typed lambda calculus, we show that the numeric functions representable in the safe lambda calculus are exactly the multivariate polynomials; thus conditional is not definable. We also give a characterization of representable word functions. We then study the ... 10. Multivector Differential Calculus Hitzer, Eckhard 2013-01-01 Universal geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. This paper treats the fundamentals of the multivector differential calculus part of geometric calculus. The multivector differential is introduced, followed by the multivector derivative and the adjoint of multivector functions. The basic rules of multivector differentiation are derived explicitly, as well as a variety of basic m... 11. Calculus a modern approach Menger, Karl 2007-01-01 One of the twentieth century's most original mathematicians and thinkers, Karl Menger taught students of many backgrounds. In this, his radical revision of the traditional calculus text, he presents pure and applied calculus in a unified conceptual frame, offering a thorough understanding of theory as well as of the methodology underlying the use of calculus as a tool.The most outstanding feature of this text is the care with which it explains basic ideas, a feature that makes it equally suitable for beginners and experienced readers. The text begins with a ""mini-calculus"" which brings out t 12. The stochastic quality calculus Zeng, Kebin; Nielson, Flemming; Nielson, Hanne Riis We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated with... 13. The stochastic quality calculus Zeng, Kebin; Nielson, Flemming; Nielson, Hanne Riis 2014-01-01 We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated... 14. Essential calculus with applications Silverman, Richard A 1989-01-01 Rigorous but accessible text introduces undergraduate-level students to necessary background math, then clear coverage of differential calculus, differentiation as a tool, integral calculus, integration as a tool, and functions of several variables. Numerous problems and a supplementary section of ""Hints and Answers."" 1977 edition. 15. A giant ureteric calculus. Rathod, Rajiv; Bansal, Prashant; Gutta, Srinivas 2013-07-01 Ureteric stones are usually small and symptomatic. We present a case of a 35-year old female who presented with minimally symptomatic right distal ureteric calculus with proximal hydroureteronephrosis. Laparoscopic right ureterolithotomy was performed and a giant ureteric calculus measuring 11 cm Χ 1.5 cm, weighing 40 g was retrieved. PMID:24082453 16. A giant ureteric calculus Rathod, Rajiv; Bansal, Prashant; Gutta, Srinivas 2013-01-01 Ureteric stones are usually small and symptomatic. We present a case of a 35-year old female who presented with minimally symptomatic right distal ureteric calculus with proximal hydroureteronephrosis. Laparoscopic right ureterolithotomy was performed and a giant ureteric calculus measuring 11 cm Χ 1.5 cm, weighing 40 g was retrieved. 17. A calculus for quality Nielson, Hanne Riis; Nielson, Flemming; Vigo, Roberto 2013-01-01 A main challenge of programming component-based software is to ensure that the components continue to behave in a reasonable manner even when communication becomes unreliable. We propose a process calculus, the Quality Calculus, for programming software components where it becomes natural to plan... 18. Initialized Fractional Calculus Lorenzo, Carl F.; Hartley, Tom T. 2000-01-01 This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed. 19. Calculus Demonstrations Using MATLAB Dunn, Peter K.; Harman, Chris 2002-01-01 The note discusses ways in which technology can be used in the calculus learning process. In particular, five MATLAB programs are detailed for use by instructors or students that demonstrate important concepts in introductory calculus: Newton's method, differentiation and integration. Two of the programs are animated. The programs and the… 20. Discrete fractional calculus Goodrich, Christopher 2015-01-01 This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the... 1. Baxter Algebras and Umbral Calculus Guo, Li 2004-01-01 We apply recent constructions of free Baxter algebras to the study of the umbral calculus. We give a characterization of the umbral calculus in terms of Baxter algebra. This characterization leads to a natural generalization of the umbral calculus that include the classical umbral calculus in a family of $\\lambda$-umbral calculi parameterized by $\\lambda$ in the base ring. 2. Introduction to the Rewriting Calculus Cirstea, Horatiu; Kirchner, Claude 1999-01-01 The $\\rho$-calculus is a new calculus that integrates in a uniform and simple setting first-order rewriting, $\\lambda$-calculus and non-deterministic computations. This paper describes the calculus from its syntax to its basic properties in the untyped case. We show how it embeds first-order conditional rewriting and $\\lambda$-calculus. Finally we use the $\\rho$-calcul- us to give an operational semantics to the rewrite based language ELAN. 3. Calculus for dummies Ryan, Mark 2014-01-01 Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable-even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the ""how"" and ""why"" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll s 4. Calculus of variations Elsgolc, L E; Stark, M 1961-01-01 Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency 5. A Logical Process Calculus Cleaveland, Rance; Luettgen, Gerald; Bushnell, Dennis M. (Technical Monitor) 2002-01-01 This paper presents the Logical Process Calculus (LPC), a formalism that supports heterogeneous system specifications containing both operational and declarative subspecifications. Syntactically, LPC extends Milner's Calculus of Communicating Systems with operators from the alternation-free linear-time mu-calculus (LT(mu)). Semantically, LPC is equipped with a behavioral preorder that generalizes Hennessy's and DeNicola's must-testing preorder as well as LT(mu's) satisfaction relation, while being compositional for all LPC operators. From a technical point of view, the new calculus is distinguished by the inclusion of: (1) both minimal and maximal fixed-point operators and (2) an unimple-mentability predicate on process terms, which tags inconsistent specifications. The utility of LPC is demonstrated by means of an example highlighting the benefits of heterogeneous system specification. 6. Computing for calculus Christensen, Mark J 1981-01-01 Computing for Calculus focuses on BASIC as the computer language used for solving calculus problems.This book discusses the input statement for numeric variables, advanced intrinsic functions, numerical estimation of limits, and linear approximations and tangents. The elementary estimation of areas, numerical and string arrays, line drawing algorithms, and bisection and secant method are also elaborated. This text likewise covers the implicit functions and differentiation, upper and lower rectangular estimates, Simpson's rule and parabolic approximation, and interpolating polynomials. Other to 7. Complex Multiplicative Calculus Bashirov, Agamirza; Riza, Mustafa 2011-01-01 In the present paper we extend the concepts of multiplicative de- rivative and integral to complex-valued functions of complex variable. Some drawbacks, arising with these concepts in the real case, are explained satis- factorily. Properties of complex multiplicative derivatives and integrals are studied. In particular, the fundamental theorem of complex multiplicative calculus, relating these concepts, is proved. It is shown that complex multi- plicative calculus is not just another realizat... 8. Discrete Exterior Calculus Desbrun, Mathieu; Hirani, Anil N.; Leok, Melvin; Marsden, Jerrold E. 2005-01-01 We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but also discrete vector fields and the operators acting on these objects. This allows us to address the various interactions between forms and vector fields (such as Lie derivatives) which are important in applications. Previous attempts at discrete exterior ca... 9. Disappearing renal calculus Cui, Helen; Thomas, Johanna; Kumar, Sunil 2013-01-01 We present a case of a renal calculus treated solely with antibiotics which has not been previously reported in the literature. A man with a 17 mm lower pole renal calculus and concurrent Escherichia coli urine infection was being worked up to undergo percutaneous nephrolithotomy. However, after a course of preoperative antibiotics the stone was no longer seen on retrograde pyelography or CT imaging. 10. The absolute differential calculus (calculus of tensors) Levi-Civita, Tullio 2013-01-01 Written by a towering figure of twentieth-century mathematics, this classic examines the mathematical background necessary for a grasp of relativity theory. Tullio Levi-Civita provides a thorough treatment of the introductory theories that form the basis for discussions of fundamental quadratic forms and absolute differential calculus, and he further explores physical applications.Part one opens with considerations of functional determinants and matrices, advancing to systems of total differential equations, linear partial differential equations, algebraic foundations, and a geometrical intro 11. Symmetric π—Calculus 傅育熙 1998-01-01 An alternative presentation of the π－calculus is given.This version of the π-calculus is symmetric in the sense that communications are symmetric and there is no difference between input and output prefixes.The point of the symmetric π-calculus is that it has no abstract names.The set of closed names is therefore homogeneous.The π－calculus can be fully embedded into the symmetric π-calculus.The symmetry changes the emphasis of the communication mechanism of the π-calculus and opens up possibility for further variations. 12. Proof nets for the Displacement calculus Moot, Richard 2016-01-01 We present a proof net calculus for the Displacement calculus and show its correctness. This is the first proof net calculus which models the Displacement calculus directly and not by some sort of translation into another formalism. The proof net calculus opens up new possibilities for parsing and proof search with the Displacement calculus. 13. Putting Differentials Back into Calculus Dray, Tevian; Manogue, Corrine A. 2010-01-01 We argue that the use of differentials in introductory calculus courses is useful and provides a unifying theme, leading to a coherent view of the calculus. Along the way, we meet several interpretations of differentials, some better than others. 14. Investigations on the dual calculus Tzevelekos, Nikos 2006-01-01 The Dual Calculus, proposed recently by Wadler, is the outcome of two distinct lines of research in theoretical computer science: (A) Efforts to extend the Curry–Howard isomorphism, established between the simply-typed lambda calculus and intuitionistic logic, to classical logic. (B) Efforts to establish the tacit conjecture that call-by-value (CBV) reduction in lambda calculus is dual to call-by-name (CBN) reduction. This paper initially investigates relations of the Dual Calculus t... 15. A development calculus for specifications 李未 2003-01-01 A first order inference system, named R-calculus, is defined to develop the specifications.This system intends to eliminate the laws which are not consistent with users' requirements. TheR-calculus consists of the structural rules, an axiom, a cut rule, and the rules for logical connectives.Some examples are given to demonstrate the usage of the R-calculus. Furthermore, the propertiesregarding reachability and completeness of the R-calculus are formally defined and proved. 16. Cirquent calculus deepened Japaridze, Giorgi 2007-01-01 Cirquent calculus is a new proof-theoretic framework, originally motivited by the needs of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html ). Its main distinguishing feature is sharing: unlike the more traditional frameworks that manipulate tree- or forest-like objects such as formulas, sequents or hypersequents, cirquent calculus deals with circuit-style structures called cirquents. The present article elaborates a deep-inference cirquent calculus system CL8 for classical propositional logic and the corresponding fragment of the resource-conscious computability logic. It also shows the existence of polynomial-size analytic CL8-proofs of the pigeonhole principle -- the family of tautologies known to have no such proofs in traditional systems. 17. Quantum variational calculus Malinowska, Agnieszka B 2014-01-01 This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations fo... 18. Calculus of variations Gelfand, I M 2000-01-01 Based on a series of lectures given by I. M. Gelfand at Moscow State University, this book actually goes considerably beyond the material presented in the lectures. The aim is to give a treatment of the elements of the calculus of variations in a form both easily understandable and sufficiently modern. Considerable attention is devoted to physical applications of variational methods, e.g., canonical equations, variational principles of mechanics, and conservation laws.The reader who merely wishes to become familiar with the most basic concepts and methods of the calculus of variations need on 19. Eliminator of dental calculus Šobich, Adam 2011-01-01 Bachelor’s thesis is focused on system design of eliminator of dental calculus operating at a frequency of 27 kHz and reaching the intensity of ultrasound on the applicator tip to 5 W/cm2. The work analyzes problems of dental calculus, principle of ultrasonic waves and the physical phenomena occurring in the environment, which it passes. Another part of the work describes the creation of waves using ultrasonic transducer and the amplification of ultrasound in the waveguide. Practical part of ... 20. The calculus primer Schaaf, William L 2011-01-01 Comprehensive but concise, this introduction to differential and integral calculus covers all the topics usually included in a first course. The straightforward development places less emphasis on mathematical rigor, and the informal manner of presentation sets students at ease. Many carefully worked-out examples illuminate the text, in addition to numerous diagrams, problems, and answers.Bearing the needs of beginners constantly in mind, the treatment covers all the basic concepts of calculus: functions, derivatives, differentiation of algebraic and transcendental functions, partial different 1. Discrete Calculus by Analogy Izadi, F A; Bagirov, G 2009-01-01 With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathemati 2. From calculus to analysis Pedersen, Steen 2015-01-01 This textbook features applications including a proof of the Fundamental Theorem of Algebra, space filling curves, and the theory of irrational numbers.  In addition to the standard results of advanced calculus, the book  contains several interesting applications of these results. The text is intended to form a bridge between calculus and analysis. It is based on the authors lecture notes used and revised nearly every year over the last decade. The book contains numerous illustrations and cross references throughout, as well as exercises with solutions at the end of each section 3. Schaum's outline of calculus Ayres, Frank 1999-01-01 Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide­­--more than 104,000 copies were bought of the prior edition--­­includes problems and examples using graphing calculators. 4. Two-dimensional calculus Osserman, Robert 2011-01-01 The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o 5. The simply typed rewriting calculus Cirstea, Horatiu; Kirchner, Claude 2000-01-01 The rewriting calculus is a rule construction and application framework. As such it embeds in a uniform way term rewriting and lambda-calculus. Since rule application is an explicit object of the calculus, it allows us also to handle the set of results explicitly. We present a simply typed version of the rewriting calculus. With a good choice of the type system, we show that the calculus is type preserving and terminating, i.e. verifies the subject reduction and strong normalization properties. 6. Taylor functional calculus Müller, Vladimír Basel : Springer, 2015 - (Alpay, D.), s. 1181-1215 ISBN 978-3-0348-0666-4 Institutional support: RVO:67985840 Keywords : Taylor spectrum * Taylor functional calculus * split spectrum Subject RIV: BA - General Mathematics http://link.springer.com/referenceworkentry/10.1007/978-3-0348-0667-1_61 7. Malliavin calculus in finance Kohatsu, Arturo; Miquel, Montero 2003-01-01 This article is an introduction to Malliavin Calculus for practitioners. We treat one specific application to the calculation of greeks in Finance. We consider also the kernel density method to compute greeks and an extension of the Vega index called the local vega index. 8. On Multiplicative Fractional Calculus Abdeljawad, Thabet 2015-01-01 We set the main concepts for multiplicative fractional calculus. We define Caputo, Riemann and Letnikov multiplicative fractional derivatives and multiplicative fractional integrals and study some of their properties. Finally, the multiplicative analogue of the local conformable fractional derivative and integral is studied. 9. Duration Calculus: Logical Foundations Hansen, Michael Reichhardt; Chaochen, Zhou 1997-01-01 The Duration Calculus (abbreviated DC) represents a logical approach to formal design of real-time systems, where real numbers are used to model time and Boolean valued functions over time are used to model states and events of real-time systems. Since it introduction, DC has been applied to many... 10. A Virtual Class Calculus Ernst, Erik; Ostermann, Klaus; Cook, William Randall 2006-01-01 , statically typed model for virtual classes has been a long-standing open question. This paper presents a virtual class calculus, vc, that captures the essence of virtual classes in these full-fledged programming languages. The key contributions of the paper are a formalization of the dynamic and static... 11. Calculus and Sailing. Palmaccio, Richard J. 1982-01-01 A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP) 12. Stochastic network calculus Jiang, Yuming 2009-01-01 Network calculus, a theory dealing with queuing systems found in computer networks, focuses on performance guarantees. This title presents a comprehensive treatment for the stochastic service-guarantee analysis research and provides basic introductory material on the subject, as well as discusses the various researches in the area. 13. Lacroix and the calculus Domingues, João Caramalho 2008-01-01 Silvestre François Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral (1797-1800; 2nd ed. 1810-1819) – an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through much of the 19th century, in spite of Cauchy's reform of the subject in the 1820's. Lacroix and the Calculus is the first major study of Lacroix’s large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18th-century calculus, and the way it is reflected in Lacroix’s account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions). Lacroix’s large Traité... was a... 14. ESeal Calculus： A Secure Mobile Calculus PengRong; UuPing 2003-01-01 The ESeal Calculus is a secure mobile calculus based on Seal Calculus. By using open-channels,ESeal Calculus makes it possible to communicate between any two arbitrary seals with some secure restrictions. It improves the expression ability and efficiency of Seal calculus without losing security. 15. Multivariate calculus and geometry Dineen, Seán 2014-01-01 Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students. 16. Calculus III essentials REA, Editors of 2012-01-01 REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Calculus III includes vector analysis, real valued functions, partial differentiation, multiple integrations, vector fields, and infinite series. 17. Calculus I essentials 2012-01-01 REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Calculus I covers functions, limits, basic derivatives, and integrals. 18. Duration Calculus: Logical Foundations Hansen, Michael Reichhardt; Chaochen, Zhou 1997-01-01 The Duration Calculus (abbreviated DC) represents a logical approach to formal design of real-time systems, where real numbers are used to model time and Boolean valued functions over time are used to model states and events of real-time systems. Since it introduction, DC has been applied to many...... case studies and it has been extended in several directions. The aim of this paper is to provide a thorough presentation of the logic.... 19. Finite-Dimensional Calculus Feinsilver, Philip; Schott, René 2007-01-01 We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, incl... 20. On paragrassmann differential calculus The paper significantly extends and generalizes our previous paper. Here we discuss explicit general constructions for paragrassmann calculus with one and many variables. For one variable nondegenerate differentiation algebras are identified and shown to be equivalent to the algebra of (p+1)x(p+1) complex matrices. For many variables we give a general construction of the differentiation algebras. Some particular examples are related to the multiparametric quantum deformations of the harmonic oscillators. 18 refs 1. Boolean integral calculus Tucker, Jerry H.; Tapia, Moiez A.; Bennett, A. Wayne 1988-01-01 The concept of Boolean integration is developed, and different Boolean integral operators are introduced. Given the changes in a desired function in terms of the changes in its arguments, the ways of 'integrating' (i.e. realizing) such a function, if it exists, are presented. The necessary and sufficient conditions for integrating, in different senses, the expression specifying the changes are obtained. Boolean calculus has applications in the design of logic circuits and in fault analysis. 2. Pre-calculus essentials Woodward, Ernest 2012-01-01 REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Pre-Calculus reviews sets, numbers, operations and properties, coordinate geometry, fundamental algebraic topics, solving equations and inequalities, functions, trigonometry, exponents 3. The Malliavin calculus Bell, Denis R 2006-01-01 This introduction to Malliavin's stochastic calculus of variations is suitable for graduate students and professional mathematicians. Author Denis R. Bell particularly emphasizes the problem that motivated the subject's development, with detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and descriptions of a variety of applications.The first chapter covers enough technical background to make the subsequent material accessible to readers without specialized knowledge of stochastic analysis. Succe 4. Calculus with vectors Treiman, Jay S 2014-01-01 Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM. fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. All three-dimensional graphs have rotatable versions included as extra source materials and may be freely downloaded and manipulated with Maple Player; a free Maple Player App is available for the iPad on iTunes. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits, and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additio... 5. Introduction to the operational calculus Berg, Lothar 2013-01-01 Introduction to the Operational Calculus is a translation of ""Einfuhrung in die Operatorenrechnung, Second Edition."" This book deals with Heaviside's interpretation, on the Laplace integral, and on Jan Mikusinki's fundamental work ""Operational Calculus."" Throughout the book, basic algebraic concepts appear as aids to understanding some relevant points of the subject. An important field for research in analysis is asymptotic properties. This text also discusses examples to show the potentialities in applying operational calculus that run beyond ordinary differential equations with constant 6. Lambda-mu-calculus and Bohm's theorem David, René; Py, Walter 2001-01-01 The lambda mu-calculus is an extension of the lambda-calculus that has been introduced by M. Parigot to give an algorithmic content to classical proofs. We show that Bohm's theorem fails in this calculus. 7. Early Vector Calculus: A Path through Multivariable Calculus Robertson, Robert L. 2013-01-01 The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.) 8. The Calculus of a Vase Scherger, Nicole 2012-01-01 Of the most universal applications in integral calculus are those involved with finding volumes of solids of revolution. These profound problems are typically taught with traditional approaches of the disk and shell methods, after which most calculus curriculums will additionally cover arc length and surfaces of revolution. Even in these visibly… 9. Fluorescence spectroscopy of dental calculus The aim of the present study was to investigate the fluorescence properties of dental calculus in comparison with the properties of adjacent unaffected tooth structure using both lasers and LEDs in the UV-visible range for fluorescence excitation. The influence of calculus color on the informative signal is demonstrated. The optimal spectral bands of excitation and registration of the fluorescence are determined 10. The Basic Principle of Calculus? Hardy, Michael 2011-01-01 A simple partial version of the Fundamental Theorem of Calculus can be presented on the first day of the first-year calculus course, and then relied upon repeatedly in assigned problems throughout the course. With that experience behind them, students can use the partial version to understand the full-fledged Fundamental Theorem, with further… 11. Calculus in the Middle School? Barger, Rita H.; McCoy, Ann C. 2010-01-01 This article presents an example of how middle school teachers can lay a foundation for calculus. Although many middle school activities connect directly to calculus concepts, the authors have decided to look in depth at only one: the concept of change. They will show how teachers can lead their students to see and appreciate the calculus… 12. A Formal Calculus for Categories Cáccamo, Mario José This dissertation studies the logic underlying category theory. In particular we present a formal calculus for reasoning about universal properties. The aim is to systematise judgements about functoriality and naturality central to categorical reasoning. The calculus is based on a language which... 13. Calculus super review 2012-01-01 Get all you need to know with Super Reviews! Each Super Review is packed with in-depth, student-friendly topic reviews that fully explain everything about the subject. The Calculus I Super Review includes a review of functions, limits, basic derivatives, the definite integral, combinations, and permutations. Take the Super Review quizzes to see how much you've learned - and where you need more study. Makes an excellent study aid and textbook companion. Great for self-study!DETAILS- From cover to cover, each in-depth topic review is easy-to-follow and easy-to-grasp - Perfect when preparing for 14. Calculus problems and solutions Ginzburg, A 2011-01-01 Ideal for self-instruction as well as for classroom use, this text helps students improve their understanding and problem-solving skills in analysis, analytic geometry, and higher algebra. More than 1,200 problems appear in the text, with concise explanations of the basic notions and theorems to be used in their solution. Many are followed by complete answers; solutions for the others appear at the end of the book. Topics include sequences, functions of a single variable, limit of a function, differential calculus for functions of a single variable, fundamental theorems and applications of dif 15. Rational Orthogonal Calculus Barnes, David 2015-01-01 We show that one can use model categories to construct rational orthogonal calculus. That is, given a continuous functor from vector spaces to based spaces one can construct a tower of approximations to this functor depending only on the rational homology type of the input functor, whose layers are given by rational spectra with an action of $O(n)$. By work of Greenlees and Shipley, we see that these layers are classified by torsion $H^*(B SO(n))[O(n)/SO(n)]$-modules. 16. Advanced calculus problem solver REA, Editors of 2012-01-01 Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of advanced calculus currently av 17. Provability Calculus of Constructions Nyblad, Kasten This thesis presents a type system, Provability Calculus of Constructions (PCoC) that can be used for the formalization of logic. In a theorem prover based on the system, the user can extend the prover with new inference rules in a logically consistent manner. This is done by representing PCoC as...... values and data types within PCoC. The new feature of PCoC is that results of the representation of PCoC can be lifted to PCoC itself. The lifting is fully formalized in PCoC, and the logic therefore supports reflection.... 18. Open Calculus: A Free Online Learning Environment Korey, Jane; Rheinlander, Kim; Wallace, Dorothy 2007-01-01 Dartmouth College mathematicians have developed a free online calculus course called "Open Calculus." Open Calculus is an exportable distance-learning/self-study environment for learning calculus including written text, nearly 4000 online homework problems and instructional videos. The paper recounts the evaluation of course elements since 2000 in… 19. A Simple Acronym for Doing Calculus: CAL Hathaway, Richard J. 2008-01-01 An acronym is presented that provides students a potentially useful, unifying view of the major topics covered in an elementary calculus sequence. The acronym (CAL) is based on viewing the calculus procedure for solving a calculus problem P* in three steps: (1) recognizing that the problem cannot be solved using simple (non-calculus) techniques;… 20. A generalized nonlocal vector calculus Alali, Bacim; Liu, Kuo; Gunzburger, Max 2015-10-01 A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models. 1. Advanced calculus a transition to analysis Dence, Thomas P 2010-01-01 Designed for a one-semester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. Ancillary list: * Companion website, Ebook- http://www.elsevierdirect.com/product.jsp?isbn=9780123749550 * Student Solutions Manual- To come * Instructor 2. Mathematics for physics with calculus Das, Biman 2005-01-01 Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful-and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments. 3. Pre-Calculus For Dummies Kuang, Yang 2012-01-01 The fun and easy way to learn pre-calculus Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. With this guide's help you'll quickly and painlessly get a handle on all of the concepts - not just the number crunching - and understand how to perform all pre-calc tasks, from graphing to tackling proofs. You'll also get a new appreciation for 4. Stochastic Calculus of Wrapped Compartments Coppo, Mario; Drocco, Maurizio; Grassi, Elena; Troina, Angelo; 10.4204/EPTCS.28.6 2010-01-01 The Calculus of Wrapped Compartments (CWC) is a variant of the Calculus of Looping Sequences (CLS). While keeping the same expressiveness, CWC strongly simplifies the development of automatic tools for the analysis of biological systems. The main simplification consists in the removal of the sequencing operator, thus lightening the formal treatment of the patterns to be matched in a term (whose complexity in CLS is strongly affected by the variables matching in the sequences). We define a stochastic semantics for this new calculus. As an application we model the interaction between macrophages and apoptotic neutrophils and a mechanism of gene regulation in E.Coli. 5. The calculus a genetic approach Toeplitz, Otto 2007-01-01 When first published posthumously in 1963, this book presented a radically different approach to the teaching of calculus.  In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique a 6. Stochastic calculus with infinitesimals Herzberg, Frederik 2013-01-01 Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book. 7. Stochastic calculus and applications Cohen, Samuel N 2015-01-01 Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to wo... 8. The M-calculus: a Higher-Order Distributed Process Calculus Schmitt, Alan; Stefani, Jean-Bernard 2002-01-01 This report presents a new distributed process calculus, called the -calculus. Key insights for the calculus are similar to those laid out by L. Cardelli for its calculus of ambients. Mobile Ambients and other recent distributed process calculi such as the Join calculus or the D-calculus introduce notions of distributed locations or localities, corresponding to a spatial partitioning of computations and embodying different features of distributed computations (e.g. failures, access control, p... 9. Dynamic Visualizations of Calculus Ideas. Embse, Charles Vonder 2001-01-01 Presents three fundamental ideas of calculus and explains using the coordinate plane geometrically. Uses Cabri Geometry II to show how computer geometry systems can facilitate student understanding of general conic objects and its dynamic algebraic equations. (KHR) 10. Testicular calculus: A rare case Volkan Sen 2015-06-01 Full Text Available ABSTRACTBackground:Testicular calculus is an extremely rare case with unknown etiology and pathogenesis. To our knowledge, here we report the third case of testicular calculus. A 31-year-old man was admitted to our clinic with painful solid mass in left testis. After diagnostic work-up for a possible testicular tumour, he underwent inguinal orchiectomy and histopathologic examination showed a testicular calculus.Case hypothesis:Solid testicular lesions in young adults generally correspond to testicular cancer. Differential diagnosis should be done carefully.Future implications:In young adults with painful and solid testicular mass with hyperechogenic appearance on scrotal ultrasonography, testicular calculus must be kept in mind in differential diagnosis. Further reports on this topic may let us do more clear recommendations about the etiology and treatment of this rare disease. 11. Cartooning in Algebra and Calculus Moseley, L. Jeneva 2014-01-01 This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding. 12. Neutrosophic Precalculus and Neutrosophic Calculus Florentin Smarandache 2015-01-01 Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of indeterminate change. The Neutrosophic Precalculus and Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the methods used to deal with such indeterminacy. In this book, the author presents a few examples o... 13. Decidability of Mean Value Calculus LI Xiaoshan 1999-01-01 Mean Value Calculus (MVC)[1] is a real-time logicwhich can be used to specify and verify real-time systems[2]. As aconservative extension of Duration Calculus (DC)[3], MVC increasesthe expressive power but keeps the properties of DC. In this paper wepresent decidability results of MVC. An interesting result is that propositional MVC with chop star operator is still decidable, which develops the results of[4]and[5]. 14. Quaternion Derivatives: The GHR Calculus Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C.; Mandic, Danilo P. 2014-01-01 Quaternion derivatives in the mathematical literature are typically defined only for analytic (regular) functions. However, in engineering problems, functions of interest are often real-valued and thus not analytic, such as the standard cost function. The HR calculus is a convenient way to calculate formal derivatives of both analytic and non-analytic functions of quaternion variables, however, both the HR and other functional calculus in quaternion analysis have encountered an essential tech... 15. Foliated stochastic calculus: Harmonic measures Catuogno, Pedro J.; Ledesma, Diego S.; Ruffino, Paulo R 2010-01-01 In this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foliation. The stochastic approach together with a proposed foliated vector calculus provide a natural method to work on harmonic measures. Other results include a decomposition of the Laplacian in terms of the foliated and basic Laplacians, a characterization of totally invariant measures and a differential equation for the density of harmonic measures. 16. The untyped stack calculus and Bohm's theorem Alberto Carraro 2013-01-01 The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We present a simple extension of stack calculus which is for the stack calculus what Saurin's Lambda-mu is for lambda-mu. 17. Essential AOP: The A Calculus De Fraine, Bruno; Ernst, Erik; Südholt, Mario 2012-01-01 Aspect-oriented programming (AOP) has produced interesting language designs, but also ad hoc semantics that needs clarification. We contribute to this clarification with a calculus that models essential AOP, both simpler and more general than existing formalizations. In AOP, advice may intercept......-oriented code. Two well-known pointcut categories, call and execution, are commonly considered similar.We formally expose their differences, and resolve the associated soundness problem. Our calculus includes type ranges, an intuitive and concise alternative to explicit type variables that allows advice...... to be polymorphic over intercepted methods. We use calculus parameters to cover type safety for a wide design space of other features. Type soundness is verified in Coq.... 18. Synthesizing controllers from duration calculus Fränzle, Martin 1996-01-01 Duration Calculus is a logic for reasoning about requirements for real-time systems at a high level of abstraction from operational detail, which qualifies it as an interesting starting point for embedded controller design. Such a design activity is generally thought to aim at a control device the...... physical behaviours of which satisfy the requirements formula, i.e. the refinement relation between requirements and implementations is taken to be trajectory inclusion. Due to the abstractness of the vocabulary of Duration Calculus, trajectory inclusion between control requirements and controller designs...... relation for embedded controller design and exploit this fact for developing an automatic procedure for controller synthesis from specifications formalized in Duration Calculus. As far as we know, this is the first positive result concerning feasibility of automatic synthesis from dense-time Duration... 19. Fluorescence detection of dental calculus This work is devoted to the optimization of fluorescence dental calculus diagnostics in optical spectrum. The optimal wavelengths for fluorescence excitation and registration are determined. Two spectral ranges 620 – 645 nm and 340 – 370 nm are the most convenient for supra- and subgingival calculus determination. The simple implementation of differential method free from the necessity of spectrometer using was investigated. Calculus detection reliability in the case of simple implementation is higher than in the case of spectra analysis at optimal wavelengths. The use of modulated excitation light and narrowband detection of informative signal allows us to decrease essentially its diagnostic intensity even in comparison with intensity of the low level laser dental therapy 20. Applying π-Calculus to Practice Abendroth, Jorg 2003-01-01 The π-Calculus has been developed to reason about behavioural equivalence. Different notations of equivalence are defined in terms of process interactions, as well as the context of processes. There are various extensions of the π-Calculus, such as the SPI calculus, which has primitives to facili... 1. Graphic lambda calculus and knot diagrams Buliga, Marius 2012-01-01 In arXiv:1207.0332 [cs.LO] was proposed a graphic lambda calculus formalism, which has sectors corresponding to untyped lambda calculus and emergent algebras. Here we explore the sector covering knot diagrams, which are constructed as macros over the graphic lambda calculus. 2. The differential lambda-mu-calculus Vaux, Lionel 2007-01-01 We define a differential lambda-mu-calculus which is an extension of both Parigot's lambda-mu-calculus and Ehrhard- Regnier's differential lambda-calculus. We prove some basic properties of the system: reduction enjoys Church-Rosser and simply typed terms are strongly normalizing. 3. The Power of Investigative Calculus Projects Perrin, John Robert; Quinn, Robert J. 2008-01-01 This article describes investigative calculus projects in which students explore a question or problem of their own construction. Three exemplary pieces of student work are showcased. Investigative calculus projects are an excellent way to foster student understanding and interest in calculus. (Contains 4 figures.) 4. An AP Calculus Classroom Amusement Park Ferguson, Sarah 2016-01-01 Throughout the school year, AP Calculus teachers strive to teach course content comprehensively and swiftly in an effort to finish all required material before the AP Calculus exam. As early May approaches and the AP Calculus test looms, students and teachers nervously complete lessons, assignments, and assessments to ensure student preparation.… 5. The algebraic lambda-calculus Vaux, Lionel 2009-01-01 We introduce an extension of the pure lambda-calculus by endowing the set of terms with a structure of vector space, or more generally of module, over a fixed set of scalars. Terms are moreover subject to identities similar to usual point-wise definition of linear combinations of functions with values in a vector space. We then study a natural extension of beta-reduction in this setting: we prove it is confluent, then discuss consistency and conservativity over the ordinary lambda-calculus. W... 6. Elementary calculus an infinitesimal approach Keisler, H Jerome 2012-01-01 This first-year calculus book is centered around the use of infinitesimals, an approach largely neglected until recently for reasons of mathematical rigor. It exposes students to the intuition that originally led to the calculus, simplifying their grasp of the central concepts of derivatives and integrals. The author also teaches the traditional approach, giving students the benefits of both methods.Chapters 1 through 4 employ infinitesimals to quickly develop the basic concepts of derivatives, continuity, and integrals. Chapter 5 introduces the traditional limit concept, using approximation p 7. A Calculus of Higher-Order Distributed Components Stefani, Jean-Bernard 2003-01-01 This report presents a calculus for higher-order distributed components, the Kell calculus. The calculus can be understood as a direct extension of the higher-order -calculus with programmable locations. The report illustrates the expressive power of the Kell calculus by encoding several process calculi with explicit locations, including Mobile Ambients, the Distributed Join calculus and the . The latter encoding demonstrates that the Kell calculus retains the expressive power of the but in a... 8. ENERGY CALCULUS IN CHINESE LANGUAGESEGMENTATION 2000-01-01 Based on cognitive science, the EnergyCalculus in Chinese language segmentation was presented to eliminate segmentation ambiguity. The notion of "EnergyCost" was advanced to denote the extent of the under-standability of a certain segmentation. EnergyCost function was defined with Z-notation. This approcah is effective to all natural language segmentation. 9. The Algebra of Schubert Calculus Gatto, Letterio 2004-01-01 A flexible unified framework for both classical and quantum Schubert calculus is proposed. It is based on a natural combinatorial approach relying on the Hasse-Schmidt extension of a certain family of pairwise commuting endomorphisms of an infinite free Z-module M to its exterior algebra. 10. Stochastic calculus and anticommuting variables Rogers, A 1994-01-01 A theory of integration for anticommuting paths is described. This is combined with standard It\\^o calculus to give a geometric theory of Brownian paths on curved supermanifolds. (Invited lecture given at meeting on Espaces de Lacets', Institut de Recherche Math\\'ematique Advanc\\'ee, Universit\\'e Louis Pasteur, Strasbourg, June 1994.) 11. Stochastic Calculus and Anticommuting Variables Rogers, Alice 1994-01-01 A theory of integration for anticommuting paths is described. This is combined with standard It\\^o calculus to give a geometric theory of Brownian paths on curved supermanifolds. (Invited lecture given at meeting on Espaces de Lacets', Institut de Recherche Math\\'ematique Advanc\\'ee, Universit\\'e Louis Pasteur, Strasbourg, June 1994.) 12. A "Model" Multivariable Calculus Course. Beckmann, Charlene E.; Schlicker, Steven J. 1999-01-01 Describes a rich, investigative approach to multivariable calculus. Introduces a project in which students construct physical models of surfaces that represent real-life applications of their choice. The models, along with student-selected datasets, serve as vehicles to study most of the concepts of the course from both continuous and discrete… 13. Mathematical Features of the Calculus Sauerheber, Richard D. 2010-01-01 The fundamental theorems of the calculus describe the relationships between derivatives and integrals of functions. The value of any function at a particular location is the definite derivative of its integral and the definite integral of its derivative. Thus, any value is the magnitude of the slope of the tangent of its integral at that position,… 14. Stochastic Pi-calculus Revisited Cardelli, Luca; Mardare, Radu Iulian 2013-01-01 We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of... 15. A Calculus for Trust Management Carbone, Marco; Nielsen, Mogens; Sassone, Vladimiro 2004-01-01 We introduce ctm, a process calculus which embodies a notion of trust for global computing systems. In ctm each principal (location) is equipped with a policy, which determines its legal behaviour, and with a protocol, which allows interactions between principals and the flow of information from ... 16. Constructivized Calculus in College Mathematics Lawrence, Barbara Ann 2012-01-01 The purpose of this study is to present some of the classical concepts, definitions, and theorems of calculus from the constructivists' point of view in the spirit of the philosophies of L.E.J. Brouwer and Errett Bishop. This presentation will compare the classical statements to the constructivized statements. The method focuses on giving… 17. Portfolio Analysis for Vector Calculus Kaplan, Samuel R. 2015-01-01 Classic stock portfolio analysis provides an applied context for Lagrange multipliers that undergraduate students appreciate. Although modern methods of portfolio analysis are beyond the scope of vector calculus, classic methods reinforce the utility of this material. This paper discusses how to introduce classic stock portfolio analysis in a… 18. Reading the World with Calculus Verzosa, Debbie 2015-01-01 It is now increasingly recognized that mathematics is not a neutral value-free subject. Rather, mathematics can challenge students' taken-for-granted realities and promote action. This article describes two issues, namely deforestation and income inequality. These were specifically chosen because they can be related to a range of calculus concepts… 19. Calculus Students' Understanding of Volume Dorko, Allison; Speer, Natasha M. 2013-01-01 Researchers have documented difficulties that elementary school students have in understanding volume. Despite its importance in higher mathematics, we know little about college students' understanding of volume. This study investigated calculus students' understanding of volume. Clinical interview transcripts and written responses to volume… 20. λμ-calculus and Λμ-calculus: a Capital Difference Herbelin, Hugo; Saurin, Alexis 2009-01-01 Since Parigot designed the λμ-calculus to algorithmically interpret classical natural deduction, several variants of λμ-calculus have been proposed. Some of these variants derived from an alteration of the original syntax due to de Groote, leading in particular to the Λμ-calculus of the second author, a calculus truly different from λμ-calculus since, in the untyped case, it provides a Böhm separation theorem that the original calculus does not satisfy. In addition to a survey of some aspects... 1. Factors Associated with Success in College Calculus II Rosasco, Margaret E. 2013-01-01 Students are entering college having earned credit for college Calculus 1 based on their scores on the College Board's Advanced Placement (AP) Calculus AB exam. Despite being granted credit for college Calculus 1, it is unclear whether these students are adequately prepared for college Calculus 2. College calculus classes are often taught… 2. Decidable Type Inference for the Polymorphic Rewriting Calculus Cirstea, Horatiu; Kirchner, Claude; Liquori, Luigi; Wack, Benjamin 2006-01-01 The rewriting calculus is a minimal framework embedding lambda calculus and term rewriting systems that allows abstraction on variables and patterns. The rewriting calculus features higher-order functions (from the lambda calculus) and pattern matching (from term rewriting systems). In this paper, we study extensively the decidability of type inference in the second-order rewriting calculus à la Curry. 3. Reductionism and the Universal Calculus Sarma, Gopal P 2016-01-01 In the seminal essay, "On the unreasonable effectiveness of mathematics in the physical sciences," physicist Eugene Wigner poses a fundamental philosophical question concerning the relationship between a physical system and our capacity to model its behavior with the symbolic language of mathematics. In this essay, I examine an ambitious 16th and 17th-century intellectual agenda from the perspective of Wigner's question, namely, what historian Paolo Rossi calls "the quest to create a universal language." While many elite thinkers pursued related ideas, the most inspiring and forceful was Gottfried Leibniz's effort to create a "universal calculus," a pictorial language which would transparently represent the entirety of human knowledge, as well as an associated symbolic calculus with which to model the behavior of physical systems and derive new truths. I suggest that a deeper understanding of why the efforts of Leibniz and others failed could shed light on Wigner's original question. I argue that the notion o... 4. Fractal calculus involving gauge function Golmankhaneh, Alireza K.; Baleanu, Dumitru 2016-08-01 Henstock-Kurzweil integral or gauge integral is the generalization of the Riemann integral. The functions which are not integrable because of singularity in the senses of Lebesgue or Riemann are gauge integrable. In this manuscript, we have generalized Fα-calculus using the gauge integral method for the integrating of the functions on fractal set subset of real-line where they have singularities. The suggested new method leads to the wider class of functions on the fractal subset of real-line that are *Fα-integrable. Using gauge function we define *Fα-derivative of functions their Fα-derivative is not exist. The reported results can be used for generalizing the fundamental theorem of Fα-calculus. 5. Toward lattice fractional vector calculus Tarasov, Vasily E. 2014-09-01 An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity. 6. Cosmological modelling with Regge calculus Liu, Rex G 2015-01-01 The late universe's matter distribution obeys the Copernican principle at only the coarsest of scales. The relative importance of such inhomogeneity is still not well understood. Because of the Einstein field equations' non-linear nature, some argue a non-perturbative approach is necessary to correctly model inhomogeneities and may even obviate any need for dark energy. We shall discuss an approach based on Regge calculus, a discrete approximation to general relativity: we shall discuss the Collins--Williams formulation of Regge calculus and its application to two toy universes. The first is a universe for which the continuum solution is well-established, the $\\Lambda$-FLRW universe. The second is an inhomogeneous universe, the lattice universe' wherein matter consists solely of a lattice of point masses with pure vacuum in between, a distribution more similar to that of the actual universe compared to FLRW universes. We shall discuss both regular lattices and one where one mass gets perturbed. 7. Brownian motion and stochastic calculus Karatzas, Ioannis 1998-01-01 This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num... 8. Space complexity in polynomial calculus Filmus, Y.; Lauria, M.; Nordström, J.; Ron-Zewi, N.; Thapen, Neil 2015-01-01 Roč. 44, č. 4 (2015), s. 1119-1153. ISSN 0097-5397 R&D Projects: GA AV ČR IAA100190902; GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : proof complexity * polynomial calculus * lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.741, year: 2014 http://epubs.siam.org/doi/10.1137/120895950 9. Integrating computers into calculus instruction Christensen, Jon L.; Pierson, Brian E. 1994-01-01 Visualization is key in helping a student understand the fundamentals of Calculus. The new generation of computer literate students, raised in a video-based environment, will expect more than the traditional chalkboard methods in assisting them in this visualization. By integrating computers into the classroom and developing software to assist in mathematics instruction, we can enhance student comprehension of, and ability to apply, mathematics in solving real world problems of interest to th... 10. Extended Report: The Implicit Calculus Oliveira, Bruno C d S; Choi, Wontae; Lee, Wonchan; Yi, Kwangkeun 2012-01-01 Generic programming (GP) is an increasingly important trend in programming languages. Well-known GP mechanisms, such as type classes and the C++0x concepts proposal, usually combine two features: 1) a special type of interfaces; and 2) implicit instantiation of implementations of those interfaces. Scala implicits are a GP language mechanism, inspired by type classes, that break with the tradition of coupling implicit instantiation with a special type of interface. Instead, implicits provide only implicit instantiation, which is generalized to work for any types. This turns out to be quite powerful and useful to address many limitations that show up in other GP mechanisms. This paper synthesizes the key ideas of implicits formally in a minimal and general core calculus called the implicit calculus, and it shows how to build source languages supporting implicit instantiation on top of it. A novelty of the calculus is its support for partial resolution and higher-order rules (a feature that has been proposed bef... 11. Schubert calculus and singularity theory Gorbounov, Vassily; Petrov, Victor 2012-02-01 Schubert calculus has been in the intersection of several fast developing areas of mathematics for a long time. Originally invented as the description of the cohomology of homogeneous spaces, it has to be redesigned when applied to other generalized cohomology theories such as the equivariant, the quantum cohomology, K-theory, and cobordism. All this cohomology theories are different deformations of the ordinary cohomology. In this note, we show that there is, in some sense, the universal deformation of Schubert calculus which produces the above mentioned by specialization of the appropriate parameters. We build on the work of Lerche Vafa and Warner. The main conjecture these authors made was that the classical cohomology of a Hermitian symmetric homogeneous manifold is a Jacobi ring of an appropriate potential. We extend this conjecture and provide a simple proof. Namely, we show that the cohomology of the Hermitian symmetric space is a Jacobi ring of a certain potential and the equivariant and the quantum cohomology and the K-theory is a Jacobi ring of a particular deformation of this potential. This suggests to study the most general deformations of the Frobenius algebra of cohomology of these manifolds by considering the versal deformation of the appropriate potential. The structure of the Jacobi ring of such potential is a subject of well developed singularity theory. This gives a potentially new way to look at the classical, the equivariant, the quantum and other flavors of Schubert calculus. 12. A Process Calculus for Molecular Interaction Maps Roberto Barbuti; Andrea Maggiolo-Schettini; Paolo Milazzo; Giovanni Pardini; Aureliano Rama 2009-01-01 We present the MIM calculus, a modeling formalism with a strong biological basis, which provides biologically-meaningful operators for representing the interaction capabilities of molecular species. The operators of the calculus are inspired by the reaction symbols used in Molecular Interaction Maps (MIMs), a diagrammatic notation used by biologists. Models of the calculus can be easily derived from MIM diagrams, for which an unambiguous and executable interpretation is thus obtained. We give... 13. Control Flow Analysis for SF Combinator Calculus Lester, Martin 2015-01-01 Programs that transform other programs often require access to the internal structure of the program to be transformed. This is at odds with the usual extensional view of functional programming, as embodied by the lambda calculus and SK combinator calculus. The recently-developed SF combinator calculus offers an alternative, intensional model of computation that may serve as a foundation for developing principled languages in which to express intensional computation, including program transfo... 14. Monogenic Calculus as an Intertwining Operator Kisil, Vladimir V. 2003-01-01 We revise a monogenic calculus for several non-commuting operators, which is defined through group representations. Instead of an algebraic homomorphism we use group covariance. The related notion of joint spectrum and spectral mapping theorem are discussed. The construction is illustrated by a simple example of calculus and joint spectrum of two non-commuting selfadjoint (n\\times n) matrices. Keywords: Functional calculus, spectrum, intertwining operator, spectral mapping theorem, jet spaces... 15. A primer on exterior differential calculus Burton D.A. 2003-01-01 A pedagogical application-oriented introduction to the cal­culus of exterior differential forms on differential manifolds is presented. Stokes' theorem, the Lie derivative, linear con­nections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their tradi­tional vector counterparts. In particular, vector calculus on R3 is cast in terms of exterior calculus and the traditional Stokes'... 16. The call-by-need lambda calculus (unabridged). Maraist, John; Odersky, Martin; Wadler, Phil 2007-01-01 We present a calculus that captures the operational semantics of call-by-need.We demonstrate that the calculus is confluent and standardizable and entails the same observational equivalences as call-by-name lambda calculus. 17. Time scales: from Nabla calculus to Delta calculus and vice versa via duality Caputo, M. Cristina 2009-01-01 In this note we show how one can obtain results from the nabla calculus from results on the delta calculus and vice versa via a duality argument. We provide applications of the main results to the calculus of variations on time scales. 18. Qutrit Dichromatic Calculus and Its Universality Wang, Quanlong; Bian, Xiaoning 2014-01-01 We introduce a dichromatic calculus (RG) for qutrit systems. We show that the decomposition of the qutrit Hadamard gate is non-unique and not derivable from the dichromatic calculus. As an application of the dichromatic calculus, we depict a quantum algorithm with a single qutrit. Since it is not easy to decompose an arbitrary d by d unitary matrix into Z and X phase gates when d > 2, the proof of the universality of qudit ZX calculus for quantum mechanics is far from trivial. We construct a ... 19. Solutions manual to accompany Fundamentals of calculus Morris, Carla C 2015-01-01 Solutions Manual to Accompany Fundamentals of Calculus the text that encourages students to use power, quotient, and product rules for solutions as well as stresses the importance of modeling skills.  In addition to core integral and differential calculus coverage, the core book features finite calculus, which lends itself to modeling and spreadsheets.  Specifically, finite calculus is applied to marginal economic analysis, finance, growth, and decay.  Includes: Linear Equations and Functions The Derivative Using the Derivative Exponential and Logarithmic 20. Advanced Calculus An Introduction to Linear Analysis Richardson, Leonard F 2008-01-01 Features an introduction to advanced calculus and highlights its inherent concepts from linear algebra. Advanced Calculus reflects the unifying role of linear algebra in an effort to smooth readers' transition to advanced mathematics. The book fosters the development of complete theorem-proving skills through abundant exercises while also promoting a sound approach to the study. The traditional theorems of elementary differential and integral calculus are rigorously established, presenting the foundations of calculus in a way that reorients thinking toward modern analysis. Following an introdu 1. Pre-calculus workbook for dummies Kuang, Yang 2011-01-01 Get the confidence and math skills you need to get started with calculus Are you preparing for calculus? This hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in the course. You'll get hundreds of valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. Pre-Calculus Workbook For Dummies is the perfect tool for anyone who wa 2. A Higher-Order Calculus for Categories Cáccamo, Mario José; Winskel, Glynn 2001-01-01 A calculus for a fragment of category theory is presented. The types in the language denote categories and the expressions functors. The judgements of the calculus systematise categorical arguments such as: an expression is functorial in its free variables; two expressions are naturally isomorphic...... in their free variables. There are special binders for limits and more general ends. The rules for limits and ends support an algebraic manipulation of universal constructions as opposed to a more traditional diagrammatic approach. Duality within the calculus and applications in proving continuity...... are discussed with examples. The calculus gives a basis for mechanising a theory of categories in a generic theorem prover like Isabelle.... 3. CALCULUS AND THE RACE TRACK PRINCIPLE Akritas, Alkiviadis 1999-01-01 Calculus and Mathematica (C&M) by Davis, Porta and Uhl ia a well thought-out method that, when used properly, gives students an intuitive understanding of, and a feeling for, all the major calculus concepts. It is comprised of the following four books: C&M / Derivatives, C&M / Integrals, C&M / Vector Calculus, and C&M / Approximation, known also as Books 1-4. In these books the authors advocate an explore-and-discover method for teaching the basic concepts of Calculus to u... 4. Generalized vector calculus on convex domain Agrawal, Om P.; Xu, Yufeng 2015-06-01 In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction. 5. Petri nets semantics ofπ-calculus Zhenhua YU; Yuanli CAI; Haiping XU 2008-01-01 As π-calculus based on the interleaving semantics cannot depict the true concurrency and has few supporting tools,it is translated into Petri nets.π-calculus is divided into basic elements,sequence,concurrency,choice and recursive modules.These modules are translated into Petri nets to construct a complicated system.Petri nets semantics for π-calculus visualize system structure as well as system behaviors.The structural analysis techniques allow direct qualitative analysis of the system properties on the structure of the nets.Finally,Petri nets semantics for π-calculus are illustrated by applying them to mobile telephone systems. 6. Fractional calculus with applications for nuclear reactor dynamics Ray, Santanu Saha 2015-01-01 Introduces Novel Applications for Solving Neutron Transport EquationsWhile deemed nonessential in the past, fractional calculus is now gaining momentum in the science and engineering community. Various disciplines have discovered that realistic models of physical phenomenon can be achieved with fractional calculus and are using them in numerous ways. Since fractional calculus represents a reactor more closely than classical integer order calculus, Fractional Calculus with Applications for Nuclear Reactor Dynamics focuses on the application of fractional calculus to describe the physical behavi 7. The hidden structural rules of the discontinuous Lambek calculus Valentín Fernández Gallart, José Oriol 2014-01-01 The sequent calculus sL for the Lambek calculus L (lambek 58) has no structural rules. Interestingly, sL is equivalent to a multimodal calculus mL, which consists of the nonassociative Lambek calculus with the structural rule of associativity. This paper proves that the sequent calculus or hypersequent calculus hD of the discontinuous Lambek calculus (Morrill and Valent\\'in), which like sL has no structural rules, is also equivalent to an omega-sorted multimodal calculus mD. More concretely, ... 8. Calculus and Success in a Business School Kim, Dong-gook; Garcia, Fernando; Dey, Ishita 2012-01-01 Many business schools or colleges require calculus as a prerequisite for certain classes or for continuing to upper division courses. While there are many studies investigating the relationship between performance in calculus and performance in a single course, such as economics, statistics, and finance, there are very few studies investigating… 9. Imagine Yourself in This Calculus Classroom Bryan, Luajean 2007-01-01 The efforts to attract students to precalculus, trigonometry, and calculus classes became more successful at the author's school when projects-based classes were offered. Data collection from an untethered hot air balloon flight for calculus students was planned to maximize enrollment. The data were analyzed numerically, graphically, and… 10. Educating about Sustainability while Enhancing Calculus Pfaff, Thomas J. 2011-01-01 We give an overview of why it is important to include sustainability in mathematics classes and provide specific examples of how to do this for a calculus class. We illustrate that when students use "Excel" to fit curves to real data, fundamentally important questions about sustainability become calculus questions about those curves. (Contains 5… 11. Sandboxing in a Distributed Pi-Calculus Hüttel, Hans; Kühnrich, Morten 2006-01-01 This paper presents an extension of the Dpi-calculus due to Hennessy and Riely with constructs for signing and authenticating code and for sandboxing. A sort system, built on Milner's sort systems for the polyadic pi-calculus, is presented and proven sound with respect to an error predicate which... 12. Aspects of Calculus for Preservice Teachers Fothergill, Lee 2011-01-01 The purpose of this study was to compare the perspectives of faculty members who had experience teaching undergraduate calculus and preservice teachers who had recently completed student teaching in regards to a first semester undergraduate calculus course. An online survey was created and sent to recent student teachers and college mathematics… 13. Hybrid Logical Analyses of the Ambient Calculus Bolander, Thomas; Hansen, Rene Rydhof 2010-01-01 In this paper, hybrid logic is used to formulate three control flow analyses for Mobile Ambients, a process calculus designed for modelling mobility. We show that hybrid logic is very well-suited to express the semantic structure of the ambient calculus and how features of hybrid logic can be... 14. A Cross-National Study of Calculus Chai, Jun; Friedler, Louis M.; Wolff, Edward F.; Li, Jun; Rhea, Karen 2015-01-01 The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan… 15. Heisenberg algebra and a graphical calculus Khovanov, Mikhail 2010-01-01 A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of the Heisenberg algebra in infinitely many variables. We construct bases of vector spaces of morphisms between products of generating objects in this category. 16. A Calculus for Context-Awareness Zimmer, Pascal 2005-01-01 In order to answer the challenge of pervasive computing, we propose a new process calculus, whose aim is to describe dynamic systems composed of agents able to move and react differently depending on their location. This Context-Aware Calculus features a hierarchical structure similar to mobile... 17. Attendance and Attainment in a Calculus Course Meulenbroek, Bernard; van den Bogaard, Maartje 2013-01-01 In this paper the relationship between attendance and attainment in a standard calculus course is investigated. Calculus could in principle be studied without attending lectures due to the wealth of material available (in hardcopy and online). However, in this study we will show that the pass rate of students attending classes regularly (>75%… 18. A course in advanced calculus Borden, Robert S 1997-01-01 This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. The author achieves this ambitious undertaking by shifting easily from one related subject to another. Thus, discussions of topology, linear algebra, and inequalities yield to examinations of innerproduct spaces, Fourier series, and the secret of Pythagoras. Beginning with a look at sets and structures, the text advances to such topics as lim 19. Quantum chemistry and scientific calculus The 1988 progress report of the Polytechnic School research team, concerning the quantum chemistry and the scientific calculus. The research program involves the following topics: the transition metals - carbon monoxide systems, which are a suitable model for the chemisorption phenomena; the introduction of the vibronic perturbations in the magnetic screen constants; the gauge invariance method (used in the calculation of the magnetic perturbations), extended to the case of the static or dynamic electrical polarizabilities. The published papers, the congress communications and the thesis are listed 20. Spikes in Quantum Regge Calculus Ambjorn, J.; Nielsen, J.; Rolf, J.; Savvidy, G. 1997-01-01 We demonstrate by explicit calculation of the DeWitt-like measure in two-dimensional quantum Regge gravity that it is highly non-local and that the average values of link lengths $l,$, do not exist for sufficient high powers of $n$. Thus the concept of length has no natural definition in this formalism and a generic manifold degenerates into spikes. This might explain the failure of quantum Regge calculus to reproduce the continuum results of two-dimensional quantum gravity. It points to sev... 1. OVARIAN CALCIFICATION MIMICKING VESICLE CALCULUS Pallavi 2013-04-01 Full Text Available INTRODUCTION: Calcification in ovary is usually dystrophic in natu re, forming secondary to degeneration of the epithelium or in association wit h areas of necrosis. It may occur in cases of endometriosis [1] or in some ovarian tumor eg. Fibro thecoma [2] , Brenner’s tumor [3] , cavernous hemangioma [4] etc. Benign unilateral densely calcified ovary wit hout any association with tumor or endometriosis has not been reported previously. We report a case of heavily calcified left ovary which mimicked as vesicle calculus on X- ray leading to confusion in diagnosis. 2. Advanced calculus of several variables Kumar, Devendra 2014-01-01 ADVANCED CALCULUS OF SEVERAL VARIABLES covers important topics of Transformations and topology on Euclidean in n-space Rn Functions of several variables, Differentiation in Rn, Multiple integrals and Integration in Rn. The topics have been presented in a simple clear and coherent style with a number of examples and exercises. Proofs have been made direct and simple. Unsolved problems just after relevant articles in the form of exercises and typical problems followed by suggestions have been given. This book will help the reader work on the problems of Numerical Analysis, Operations Research, Differential Equations and Engineering applications. 3. Matlab differential and integral calculus Lopez, Cesar 2014-01-01 MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Differential and Integral Calculus introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to givi 4. AP calculus AB/BC Schwartz, Stu 2013-01-01 All Access for the AP® Calculus AB & BC Exams Book + Web + Mobile Everything you need to prepare for the Advanced Placement® exam, in a study system built around you! There are many different ways to prepare for an Advanced Placement® exam. What's best for you depends on how much time you have to study and how comfortable you are with the subject matter. To score your highest, you need a system that can be customized to fit you: your schedule, your learning style, and your current level of knowledge. This book, and the free online tools that come with it, will help you personalize your AP® Cal 5. Cartan Calculus via Pauli Matrices Mauro, D. 2002-01-01 In this paper we will provide a new operatorial counterpart of the path-integral formalism of classical mechanics developed in recent years. We call it new because the Jacobi fields and forms will be realized via finite dimensional matrices. As a byproduct of this we will prove that all the operations of the Cartan calculus, such as the exterior derivative, the interior contraction with a vector field, the Lie derivative and so on, can be realized by means of suitable tensor products of Pauli... 6. Cartan Calculus via Pauli Matrices Mauro, D 2003-01-01 In this paper we will provide a new operatorial counterpart of the path-integral formalism of classical mechanics developed in recent years. We call it new because the Jacobi fields and forms will be realized via finite dimensional matrices. As a byproduct of this we will prove that all the operations of the Cartan calculus, such as the exterior derivative, the interior contraction with a vector field, the Lie derivative and so on, can be realized by means of suitable tensor products of Pauli and identity matrices. 7. Technical calculus with analytic geometry Gersting, Judith L 2010-01-01 This well-thought-out text, filled with many special features, is designed for a two-semester course in calculus for technology students with a background in college algebra and trigonometry. The author has taken special care to make the book appealing to students by providing motivating examples, facilitating an intuitive understanding of the underlying concepts involved, and by providing much opportunity to gain proficiency in techniques and skills.Initial chapters cover functions and graphs, straight lines and conic sections, new coordinate systems, the derivative, using the derivative, in 8. Modern calculus and analytic geometry Silverman, Richard A 2012-01-01 A self-contained text for an introductory course, this volume places strong emphasis on physical applications. Key elements of differential equations and linear algebra are introduced early and are consistently referenced, all theorems are proved using elementary methods, and numerous worked-out examples appear throughout. The highly readable text approaches calculus from the student's viewpoint and points out potential stumbling blocks before they develop. A collection of more than 1,600 problems ranges from exercise material to exploration of new points of theory - many of the answers are fo 9. A functional presentation of Pi　calculus 2001-01-01 From the very beginning process algebra introduced the dichotomy between channels and processes. This dichotomy prevails in all present process calculi.The situation is in contrast to that with lambda calculus which has only one class of entities——the lambda terms. We introduce in this paper a process calculus called Lamp in which channels are process names. The language is more uniform than existing process calculi in two aspects: First it has a unified treatment of channels and processes. There is only one class of syntactical entities——processes. Second it has a unified presentation of both first order and higher order process calculi. The language is functional in the sense that lambda calculus is functional.Two bisimulation equivalences, barbed and closed bisimilarities, are proved to coincide.A natural translation from Pi calculus to Lamp is shown to preserve both operational and algebraic semantics. The relationship between lazy lambda calculus and Lamp is discussed. 10. Enriching an effect calculus with linear types Egger, Jeff; Møgelberg, Rasmus Ejlers; Simpson, Alex 2009-01-01 We define an `enriched effect calculus'' by conservatively extending  a type theory for computational effects with primitives from linear logic. By doing so, we obtain a generalisation of linear type theory, intended as a formalism for expressing linear aspects of effects. As a worked example, we...... formulate  linearly-used continuations in the enriched effect calculus. These are captured by a fundamental translation of the enriched effect calculus into itself, which extends existing call-by-value and call-by-name linearly-used CPS translations. We show that our translation is involutive. Full...... completeness results for the various linearly-used CPS translations  follow. Our main results, the conservativity of enriching the effect calculus with linear primitives, and the involution property of the fundamental translation, are proved using a category-theoretic semantics for the enriched effect calculus... 11. Reasoning about objects using process calculus techniques Kleist, Josva perform these investigations indicate, that although it is perfectly possible to use process calculus techniques on object oriented languages, such techniques will not come to widespread use, but only be limited to reasoning about critical parts of a language or program design.......This thesis investigates the applicability of techniques known from the world of process calculi to reason about properties of object-oriented programs. The investigation is performed upon a small object-oriented language - The Sigma-calculus of Abadi and Cardelli. The investigation is twofold: We......-calculus turns out to be insufficient. Based on our experiences, we present a translation of a typed imperative Sigma-calculus, which looks promising. We are able to provide simple proofs of the equivalence of different Sigma-calculus objects using this translation. We use a labelled transition system adapted to... 12. Toward lattice fractional vector calculus An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity. (papers) 13. Computer-Oriented Calculus Courses Using Finite Differences. Gordon, Sheldon P. The so-called discrete approach in calculus instruction involves introducing topics from the calculus of finite differences and finite sums, both for motivation and as useful tools for applications of the calculus. In particular, it provides an ideal setting in which to incorporate computers into calculus courses. This approach has been… 14. Pseudodifferential calculus on manifolds with corners and groupoids Monthubert, Bertrand 1997-01-01 We build a longitudinally smooth differentiable groupoid associated to any manifold with corners. The pseudodifferential calculus on this groupoid coincides with the pseudodifferential calculus of Melrose (also called b-calculus). We also define an algebra of rapidly decreasing functions on this groupoid; it contains the kernels of the smoothing operators of the (small) b-calculus. 15. Motivation and Study Habits of College Calculus Students: Does Studying Calculus in High School Make a Difference? Gibson, Megan 2013-01-01 Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the… 16. The Impact of Taking a College Pre-Calculus Course on Students' College Calculus Performance Sonnert, Gerhard; Sadler, Philip M. 2014-01-01 Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and… 17. Definition of fractal measures arising from fractional calculus Kolwankar, Kiran M.; Gangal, Anil D. 1998-01-01 It is wellknown that the ordinary calculus is inadequate to handle fractal structures and processes and another suitable calculus needs to be developed for this purpose. Recently it was realized that fractional calculus with suitable constructions does offer such a possibility. This makes it necessary to have a definition of fractal measures based on the fractional calculus so that the fractals can be naturally incorporated in the calculus. With this motivation a definition of fractal measure... 18. Calculus a complete introduction : teach yourself Neill, Hugh 2013-01-01 Calculus: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using calculus. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of calculus, including functions, gradients, rates of change, differentiation, exponential and logarithmic functions and integration. Everything you will need to know is here in one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions. 19. Pre-calculus workbook for dummies Gilman, Michelle Rose; Neal, Karina 2009-01-01 Get the confidence and the math skills you need to get started with calculus! Are you preparing for calculus? This easy-to-follow, hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in your cour sework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. 100s of Problems! Detailed, fully worked-out solutions to problem 20. AP calculus AB & BC crash course Rosebush, J 2012-01-01 AP Calculus AB & BC Crash Course - Gets You a Higher Advanced Placement Score in Less Time Crash Course is perfect for the time-crunched student, the last-minute studier, or anyone who wants a refresher on the subject. AP Calculus AB & BC Crash Course gives you: Targeted, Focused Review - Study Only What You Need to Know Crash Course is based on an in-depth analysis of the AP Calculus AB & BC course description outline and actual AP test questions. It covers only the information tested on the exams, so you can make the most of your valuable study time. Written by experienced math teachers, our 1. Fractional calculus an introduction for physicists Herrmann, Richard 2011-01-01 Fractional calculus is undergoing rapidly and ongoing development. We can already recognize, that within its framework new concepts and strategies emerge, which lead to new challenging insights and surprising correlations between different branches of physics. This book is an invitation both to the interested student and the professional researcher. It presents a thorough introduction to the basics of fractional calculus and guides the reader directly to the current state-of-the-art physical interpretation. It is also devoted to the application of fractional calculus on physical problems, in t 2. From X to Pi; Representing the Classical Sequent Calculus in the Pi-calculus van Bakel, Steffen; Vigliotti, Maria Grazia 2011-01-01 We study the Pi-calculus, enriched with pairing and non-blocking input, and define a notion of type assignment that uses the type constructor "arrow". We encode the circuits of the calculus X into this variant of Pi, and show that all reduction (cut-elimination) and assignable types are preserved. Since X enjoys the Curry-Howard isomorphism for Gentzen's calculus LK, this implies that all proofs in LK have a representation in Pi. 3. A CALCULUS FOR SERVICES INNOVATION James M.TIEN; Daniel BERG 2007-01-01 Innovation in the services area - especially in the electronic services (e-services) domain - can be systematically developed by first considering the strategic drivers and foci, then the tactical principles and enablers, and finally the operational decision attributes, all of which constitute a process or calculus of services innovation. More specifically, there are four customer drivers (i.e., collaboration,customization, integration and adaptation), three business foci (i.e., creation-focused, solution-focused and competition-focused), six business principles (i.e., reconstruct market boundaries, focus on the big picture not numbers, reach beyond existing demand, get strategic sequence right, overcome organizational hurdles and build execution into strategy), eight technical enablers (i.e., software algorithms, automation, telecommunication, collaboration, standardization, customization,organization, and globalization), and six attributes of decision informatics (i.e., decision-driven,information-based, real-time, continuously-adaptive, customer-centric and computationally-intensive).It should be noted that the four customer drivers are all directed at empowering the individual - that is,at recognizing that the individual can, respectively, contribute in a collaborative situation, receive customized or personalized attention, access an integrated system or process, and obtain adaptive real-time or just-in-time input. The developed process or calculus serves to identify the potential white spaces or blue oceans for innovation. In addition to expanding on current innovations in services and related experiences, white spaces are identified for possible future innovations; they include those that can mitigate the unforeseen consequences or abuses of earlier innovations, safeguard our rights to privacy, protect us from the always-on, interconnected world, provide us with an authoritative search engine, and generate a GDP metric that can adequately measure the growing 4. The Calculus Concept Readiness (CCR) Instrument: Assessing Student Readiness for Calculus Carlson, Marilyn; West, Richard 2010-01-01 The Calculus Concept Readiness (CCR) instrument is based on the broad body of mathematics education research that has revealed major understandings, representational abilities, and reasoning abilities students need to construct in precalculus level courses to be successful in calculus. The CCR is a 25-item multiple-choice instrument, and the CCR taxonomy articulates what the CCR assesses. The methodology used to develop and validate the CCR is described and illustrated. Results from administering the CCR as a readiness examination in calculus are provided along with data to guide others in using the CCR as a readiness examination for beginning calculus. 5. The calculus lifesaver all the tools you need to excel at calculus Banner, Adrian 2009-01-01 For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it. All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of 6. Newton Binomial Formulas in Schubert Calculus Cordovez, Jorge; Gatto, Letterio; Santiago, Taise 2008-01-01 We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points. 7. Brownian motion, martingales, and stochastic calculus Le Gall, Jean-François 2016-01-01 This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i... 8. Extending Stochastic Network Calculus to Loss Analysis Chao Luo 2013-01-01 Full Text Available Loss is an important parameter of Quality of Service (QoS. Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor. 9. Multi-instanton calculus in supersymmetric theories In this talk I review some recent results concerning multi-instanton calculus in supersymmetric field theories. More in detail, I will show how these computations can be efficiently performed using the formalism of topological field theories. (author) 10. Applying Change of Variable to Calculus Problems Kachapova, Farida; Kachapov, Ilias 2011-01-01 This article describes the technique of introducing a new variable in some calculus problems to help students master the skills of integration and evaluation of limits. This technique is algorithmic and easy to apply. 11. Model-Checking Discrete Duration Calculus Hansen, Michael Reichhardt 1994-01-01 Duration calculus was introduced by Chaochen Zhou et al. (1991) as a logic to specify and reason about requirements for real-time systems. It is an extension of interval temporal logic where one can reason about integrated constraints over time-dependent and Boolean valued states without explicit...... mention of absolute time. Several major case studies have shown that duration calculus provides a high level of abstraction for both expressing and reasoning about specifications. Using timed automata one can express how real-time systems can be constructed at a level of detail which is close to an actual...... implementation. We consider in the paper the correctness of timed automata with respect to duration calculus formulae. For a subset of duration calculus, we show that one can automatically verify whether a timed automaton ℳ is correct with respect to a formula 𝒟, abbreviated ℳ|=𝒟, i.e. one... 12. A primer on exterior differential calculus Burton D.A. 2003-01-01 Full Text Available A pedagogical application-oriented introduction to the cal­culus of exterior differential forms on differential manifolds is presented. Stokes' theorem, the Lie derivative, linear con­nections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their tradi­tional vector counterparts. In particular, vector calculus on R3 is cast in terms of exterior calculus and the traditional Stokes' and divergence theorems replaced by the more powerful exterior expression of Stokes' theorem. Examples from classical continuum mechanics and spacetime physics are discussed and worked through using the language of exterior forms. The numerous advantages of this calculus, over more traditional ma­chinery, are stressed throughout the article. . 13. Fractional Vector Calculus and Fractional Special Function Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao 2010-01-01 Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric functions. 14. Introductory analysis a deeper view of calculus Bagby, Richard J 2000-01-01 Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.* Written in an engaging, conversational tone and readable style while softening the rigor and theory* Takes a realistic approach to the necessary and accessible level of abstraction for the secondary education students* A thorough concentration of basic topics of calculus* Features a student-friendly introduction to delta-epsilon arguments * Includes a limited use of abstract generalizations for easy use* Covers natural logarithms and exponential functions* Provides the computational techniques often encountered in basic calculus 15. A Tableaux Calculus for Ambiguous Quantification Monz, Christof; de Rijke, Maarten 2000-01-01 Coping with ambiguity has recently received a lot of attention in natural language processing. Most work focuses on the semantic representation of ambiguous expressions. In this paper we complement this work in two ways. First, we provide an entailment relation for a language with ambiguous expressions. Second, we give a sound and complete tableaux calculus for reasoning with statements involving ambiguous quantification. The calculus interleaves partial disambiguation steps with steps in a t... 16. A Superposition Calculus for Abductive Reasoning Echenim, Mnacho; Peltier, Nicolas 2014-01-01 We present a modification of the superposition calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules, provided the considered consequences are built on a given finite set of ground terms, represented by constant symbols. In contrast to other approaches, most existing results about the termination of the superposition calculus can be carried over to our procedure.... 17. Variational time discretization of geodesic calculus Rumpf, Martin; Wirth, Benedikt 2012-01-01 We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete logarithm, discrete exponential maps, and discrete parallel transport, and we prove convergence to their continuous counterparts. The presented analysis is based on the direct methods in the calculus of variation, on $\\Gamma$-convergence, and on weighted finite ele... 18. The Britannica Guide to Analysis and Calculus 2011-01-01 The dynamism of the natural world means that it is constantly changing, sometimes rapidly, sometimes gradually. By mathematically interpreting the continuous change that characterizes so many natural processes, analysis and calculus have become indispensable to bridging the divide between mathematics and the sciences. This comprehensive volume examines the key concepts of calculus, providing students with a robust understanding of integration and differentiation. Biographies of important figures will leave readers with an increased appreciation for the sometimes competing theories that informe 19. Toward New Vision in Teaching Calculus Kadry, Seifedine; ElShalkamy, Maha 2012-01-01 Usually the first course in mathematics is calculus. Its a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the prior fear of mathematics. The students today cant live without using computer technology. The uses of computer for teaching and learning can transform the boring traditional methodology of teach to more active and attractive method. In this paper, we will sh... 20. Łukasiewicz mu-Calculus Matteo Mio 2013-08-01 Full Text Available The paper explores properties of Łukasiewicz mu-calculus, a version of the quantitative/probabilistic modal mu-calculus containing both weak and strong conjunctions and disjunctions from Łukasiewicz (fuzzy logic. We show that this logic encodes the well-known probabilistic temporal logic PCTL. And we give a model-checking algorithm for computing the rational denotational value of a formula at any state in a finite rational probabilistic nondeterministic transition system. 1. A Graph Calculus for Predicate Logic Paulo A. S. Veloso 2013-03-01 Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation. 2. A calculus for attribute-based communication Alrahman, Yehia Abd; De Nicola, Rocco; Loreti, Michele; 2015-01-01 The notion of attribute-based communication seems promising to model and analyse systems with huge numbers of interacting components that dynamically adjust and combine their behaviour to achieve specific goals. A basic process calculus, named AbC, is introduced that has as primitive construct....... An example of how well-established process calculi could be encoded into AbC is given by considering the translation into AbC of a proto-typical π-calculus process.... 3. A phenomenological calculus of Wiener description space. Richardson, I W; Louie, A H 2007-10-01 The phenomenological calculus is a categorical example of Robert Rosen's modeling relation. This paper is an alligation of the phenomenological calculus and generalized harmonic analysis, another categorical example. Our epistemological exploration continues into the realm of Wiener description space, in which constitutive parameters are extended from vectors to vector-valued functions of a real variable. Inherent in the phenomenology are fundamental representations of time and nearness to equilibrium. PMID:17955459 4. Fractional Vector Calculus and Fractional Maxwell's Equations Vasily E. Tarasov 2009-01-01 The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and i... 5. Superconformal tensor calculus in five dimensions We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived using dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, a vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. (author) 6. Superconformal Tensor Calculus in Five Dimensions Fujita, Tomoyuki; Ohashi, Keisuke 2001-01-01 We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived by the dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. 7. Ordered Models of the Lambda Calculus Salibra, Antonino; Carraro, Alberto 2013-01-01 Answering a question by Honsell and Plotkin, we show that there are two equations between lambda terms, the so-called subtractive equations, consistent with lambda calculus but not simultaneously satisfied in any partially ordered model with bottom element. We also relate the subtractive equations to the open problem of the order-incompleteness of lambda calculus, by studying the connection between the notion of absolute unorderability in a specific point and a weaker notion of subtractivity ... 8. Barbed congruence of the asymmetric chi calculus DONG Xiao-ju; FU Yu-xi 2006-01-01 The chi calculus is a model of mobile processes. It has evolved from the pi-calculus with motivations from simplification and communication-as-cut-elimination. This paper studies the chi calculus in the framework incorporating asymmetric communication. The major feature of the calculus is the identification of two actions:x/x and τ. The investigation on the barbed bisimilarity shows how the property affects the observational theory.Based on the definition of the barbed bisimilarity, the simulation properties of the barbed bisimilarity are studied. It shows that the algebraic properties of the barbed bisimilarity have changed greatly compared with the chi calculus. Although the definition of the barbed bisimilarity is very simple, the property of closeness under contexts makes it difficult to understand the barbed bisimilarity directly. Therefore an open style definition of the barbed bisimilarity is given, which is a context free description of barbed bisimilarity. Its definition is complex,but it is a well-behaved relation for it coincides with the barbed bisimilarity. It also helps to build an axiomatization system for the barbed congruence. Besides the axioms for the strong barbed bisimilarity, the paper proposes a new tau law and four new update laws for the barbed congruence. Both the operational and algebraic properties of the enriched calculus improve the understanding of the bisimulation behaviors of the model. 9. Electronic Algebra and Calculus Tutor Larissa Fradkin 2012-06-01 Full Text Available Modern undergraduates join science and engineering courses with poorer mathematical background than most contemporaries of the current faculty had when they were freshers. The problem is very acute in the United Kingdom but more and more countries adopt less resource intensive models of teaching and the problem spreads. University tutors and lecturers spend more and more time covering the basics. However, most of them still rely on traditional methods of delivery which presuppose that learners have a good memory and considerable time to practice, so that they can memorize disjointed facts and discover for themselves various connections between the underlying concepts. These suppositions are particularly unrealistic when dealing with a large number of undergraduates who are ordinary learners with limited mathematics background. The first author has developed a teaching system that allows such adult learners achieve relatively deep learning of mathematics – and remarkably quickly – through a teacher-guided (often called Socratic dialog, which aims at the frequent reinforcement of basic mathematical abstractions through Eulerian sequencing. These ideas have been applied to create a prototype of a Cognitive Mathematics Tutoring System aimed at teaching basic mathematics to University freshers., an electronic Personal Algebra and Calculus Tutor (e- PACT. 10. More calculus of a single variable Mercer, Peter R 2014-01-01 This book goes beyond the basics of a first course in calculus to reveal the power and richness of the subject. Standard topics from calculus — such as the real numbers, differentiation and integration, mean value theorems, the exponential function — are reviewed and elucidated before digging into a deeper exploration of theory and applications, such as the AGM inequality, convexity, the art of integration, and explicit formulas for π. Further topics and examples are introduced through a plethora of exercises that both challenge and delight the reader. While the reader is thereby exposed to the many threads of calculus, the coherence of the subject is preserved throughout by an emphasis on patterns of development, of proof and argumentation, and of generalization. More Calculus of a Single Variable is suitable as a text for a course in advanced calculus, as a supplementary text for courses in analysis, and for self-study by students, instructors, and, indeed, all connoisseurs of ingenious calculations. 11. Standardization of a Call-By-Value Lambda-Calculus Guerrieri, Giulio; Paolini, Luca; Ronchi Della Rocca, Simona 2015-01-01 We study an extension of Plotkin's call-by-value lambda-calculus by means of two commutation rules (sigma-reductions). Recently, it has been proved that this extended calculus provides elegant characterizations of many semantic properties, as for example solvability. We prove a standardization theorem for this calculus by generalizing Takahashi's approach of parallel reductions. The standardization property allows us to prove that our calculus is conservative with respect to the Plotkin's one... 12. The giant calculus within the prostatic urethra. Demir, Omer; Kefi, Aykut; Cahangirov, Asif; Cihan, Ahmet; Obuz, Funda; Esen, Adil Ahmet; Celebi, Ilhan 2011-08-01 The giant calculus within the prostatic urethra is a rare clinical entity in the young population. Most of the calculi within the urethra migrate from the urinary bladder and obliterate the urethra. These stones are often composed of calcium phosphate or calcium oxalate. The decision of treatment strategy is affected by the size, shape and position of the calculus and by the status of the urethra. If the stone is large and immovable, it may be extracted via the perineal or the suprapubic approach. In most cases, the giant calculi were extracted via the transvesical approach and external urethrotomy. Our case is the biggest prostatic calculus, known in the literature so far, which was treated endoscopically by the combination of laser and the pneumatic lithotriptor. PMID:21188583 13. Fuzzy relational calculus theory, applications and software Peeva, Ketty 2004-01-01 This book examines fuzzy relational calculus theory with applications in various engineering subjects. The scope of the text covers unified and exact methods with algorithms for direct and inverse problem resolution in fuzzy relational calculus. Extensive engineering applications of fuzzy relation compositions and fuzzy linear systems (linear, relational and intuitionistic) are discussed. Some examples of such applications include solutions of equivalence, reduction and minimization problems in fuzzy machines, pattern recognition in fuzzy languages, optimization and inference engines in textile and chemical engineering, etc. A comprehensive overview of the authors' original work in fuzzy relational calculus is also provided in each chapter. The attached CD-Rom contains a toolbox with many functions for fuzzy calculations, together with an original algorithm for inverse problem resolution in MATLAB. This book is also suitable for use as a textbook in related courses at advanced undergraduate and graduate level... 14. The lambda-mu-T-calculus Geuvers, Herman; McKinna, James 2012-01-01 Calculi with control operators have been studied as extensions of simple type theory. Real programming languages contain datatypes, so to really understand control operators, one should also include these in the calculus. As a first step in that direction, we introduce lambda-mu-T, a combination of Parigot's lambda-mu-calculus and G\\"odel's T, to extend a calculus with control operators with a datatype of natural numbers with a primitive recursor. We consider the problem of confluence on raw terms, and that of strong normalization for the well-typed terms. Observing some problems with extending the proofs of Baba at al. and Parigot's original confluence proof, we provide new, and improved, proofs of confluence (by complete developments) and strong normalization (by reducibility and a postponement argument) for our system. We conclude with some remarks about extensions, choices, and prospects for an improved presentation. 15. Quantum geometry in dynamical Regge calculus We study geometric properties of dynamical Regge calculus which is a hybridization of dynamical triangulation and quantum Regge calculus. Lattice diffeomorphisms are generated by certain elementary moves on a simplicial lattice in the hybrid model. At the semiclassical level, we discuss a possibility that the lattice diffeomorphisms give a simple explanation for the Bekenstein-Hawking entropy of a black hole. At the quantum level, numerical calculations of 3D pure gravity show that a fractal structure of the hybrid model is the same as that of dynamical triangulation in the strong-coupling phase. In the weak-coupling phase, on the other hand, space-time becomes a spiky configuration, which often occurs in quantum Regge calculus 16. Fractional vector calculus and fractional Maxwell's equations The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered 17. A MATLAB companion for multivariable calculus Cooper, Jeffery 2001-01-01 Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton''s method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http://www.harcourt-ap.com/matlab.html.* Computer-oriented material that complements the essential topics in multivariable calculus* Main ideas presented with examples of computations and graphics displays using MATLAB * Numerous examples of short code in the text, which can be modified for use with the exercises* MATLAB files are used to implem... 18. RARE CASE OF GIANT VESICAL CALCULUS Deepak Ramraj 2015-02-01 Full Text Available Giant vesical calculus is a rare entity. Vesical calculi can be primary (stones form de novo in bladder or secondary to the migrated renal calculi, chronic UTI, bladder outlet obstruction, bladder diverticulum or carcinoma, foreign body and neurogenic bladder. We report a case of an 85year old male patient who presented with history of recurrent episodes of burning micturition, pain abdomen, straining at micturition and diminished stream. Ultrasonography and X ray KUB showed a large vesical calculus. Patient underwent a n Open Cystolithomy and a large calculus of size 9x13cm weighing 310gms was removed. Bladder wall hypertrophy was seen with signs of inflammation. Bladder mucosal biopsy was taken which was normal on histopathological examination. Post - operative recovery was uneventful 19. Fractional Calculus in Wave Propagation Problems Mainardi, Francesco 2012-01-01 Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential equations, where integrals are of convolution form with weakly singular kernels of power law type. In recent decades fractional calculus has won more and more interest in applications in several fields of applied sciences. In this lecture we devote our attention to wave propagation problems in linear viscoelastic media. Our purpose is to outline the role of fractional calculus in providing simplest evolution processes which are intermediate between diffusion and wave propagation. The present treatment mainly reflects the research activity and style of the author in the related scientific areas during the last decades. 20. Formalizing BPEL-TC Through ?-Calculus Preeti Marwaha 2013-07-01 Full Text Available WS-BPEL is way to define business processes that interact with external entities through webservice operations using WSDL. We have proposed BPEL-TC, an extension to existing WS-BPEL whichuses temporally customized Web Services (WSDL-TC as a model for process decomposition and assembly.WSDL-TC handles both backward compatible and incompatible changes and also maintains variousversions of the artifacts that results due to changes over time and customizations desired by the users. Inthis paper, we are using pi-calculus to formalize Business Process Execution Language- TemporalCustomization (BPEL-TC process. π -calculus is a model of computation for concurrent systems alongwith changing connectivity of interactive systems. Pi-calculus is an extension of the process algebra CCS,with added mobility to CCS while preserving its algebraic properties. 1. Calculus of tensors and differential forms Sinha, Rajnikant 2014-01-01 Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere. 2. Enhancing Students’ Understanding in Calculus Trough Writing Noraini Idris 2009-02-01 Full Text Available The purpose of this study was to investigate the effects of using writing activities on students’ understanding and achievement in Calculus. The design of this study was quasi-experimental. The subjects of this study consisted of two secondary schools in one of the states in Malaysia. Each school was assigned one intact class of Form Four to be the experimental group and another one intact class as the control. The experimental group learned mathematics by using the writing activities for five weeks, while the control group learned mathematics by using traditional whole-class instruction. A 20-item Calculus Achievement test was designed with reliability .87. The findings showed that the experimental group exhibited significantly greater improvement on calculus achievement. The students showed positive reaction towards the use of writing. Findings of this study provide information to schools to take advantage of writing activities to promote understanding. 3. Research of Semantic Comparison between χ-calculus and π-calculus%χ-演算与π-演算的语义比较研究 徐林; 傅育熙 2000-01-01 Through the comparison of syntactic structure,operational semantics and algebraic semantics between χ-calculus and π-calculus, this paper concludes that χ-calculus has more succinct syntactic structure,more explicit operational semantics,more intuitionistic algebraic semantics and more favorable algebraic property. And a translation from π-calculus to χ-calculus is presented. 4. Functional calculus for generators of analytic semigroups of operators Lopushansky O.V.; Sharyn S.V. 2012-01-01 We construct a functional calculus for generators of one-parameter boundedanalytic semigroups of operators on a Banach space. The calculus symbol classconsist of the Laplace image of the convolution algebra $cal S'_+$ of tempereddistributions with supports in $[0, infty)$. Domain of constructed calculus isdense in the Banach space. 5. Functional calculus for generators of analytic semigroups of operators Lopushansky O.V. 2012-06-01 Full Text Available We construct a functional calculus for generators of one-parameter boundedanalytic semigroups of operators on a Banach space. The calculus symbol classconsist of the Laplace image of the convolution algebra $cal S'_+$ of tempereddistributions with supports in $[0, infty$. Domain of constructed calculus isdense in the Banach space. 6. A Transition Course from Advanced Placement to College Calculus Lucas, Timothy A.; Spivey, Joseph 2011-01-01 In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II… 7. Improving Calculus II and III through the Redistribution of Topics George, C. Yousuf; Koetz, Matt; Lewis, Heather A. 2016-01-01 Three years ago our mathematics department rearranged the topics in second and third semester calculus, moving multivariable calculus to the second semester and series to the third semester. This paper describes the new arrangement of topics, and how it could be adapted to calculus curricula at different schools. It also explains the benefits we… 8. Laparoscopic Ureterolithotomy for Giant Ureteric Calculus: A Case Report Prasad V. Magdum 2015-09-01 Full Text Available We present a case of a 21 year old male who presented with symptomatic right upper ureteric calculus measuring 5 cm × 1.5 cm fulfilling the criteria to be named as giant ureteric calculus. Laparoscopic right ureterolithotomy was performed and the giant ureteric calculus was retrieved. 9. Laparoscopic Ureterolithotomy for Giant Ureteric Calculus: A Case Report. Magdum, Prasad V; Nerli, Rajendra B; Devaraju, Shishir; Hiremath, Murigendra B 2015-09-01 We present a case of a 21 year old male who presented with symptomatic right upper ureteric calculus measuring 5 cm × 1.5 cm fulfilling the criteria to be named as giant ureteric calculus. Laparoscopic right ureterolithotomy was performed and the giant ureteric calculus was retrieved. PMID:26793529 10. Laparoscopic Ureterolithotomy for Giant Ureteric Calculus: A Case Report Prasad V. Magdum; Rajendra B. Nerli; Shishir Devaraju; Hiremath, Murigendra B. 2015-01-01 We present a case of a 21 year old male who presented with symptomatic right upper ureteric calculus measuring 5 cm × 1.5 cm fulfilling the criteria to be named as giant ureteric calculus. Laparoscopic right ureterolithotomy was performed and the giant ureteric calculus was retrieved.

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# Teasing out the TensorFlow Graph Mess How can mathematicians think in 21 dimensions? Easy, they think in N dimensions and make N=21. For those who can’t do that, there’s a way to visualize TensorFlow graphs without getting lost in the TensorBoard automatically generated crap. First of all, I assume you’re familiar with TensorFlow, Python and Jupyter. Maybe you’re learning some MOOC like Udacity Deep Learning, and you can glimpse the extreme power of TensorFlow, but you cannot actually see it. I’ll teach you how to. There’s a way to insert a Jupyter cell with an iframe containing a TensorBoard view who draws the graph you are playing with. It was published by Google DeepDream team here. Pretty cool indeed, but.. (there’s always a but) TensorBoard yields crap (internal TensorFlow crap to be fair). Let’s use it with code out of Udacity course (Assignment 2: SGD). No worries guys, there’s no spoiler of the solutions. Defining the following graph: Then you can run the embedding TensorBoard visualizer code and get: But there’s a way to make it useful, you just have to name quite a few things in the code to display a better graph. To do so, use name=’name_string’ parameter in some invocations and group some related code lines under kind of “namespace” declaration in TensorFlow using with tf.variable_scope(“namespace_string”): This last trick will let graph know about what to draw in nested groups, just what we was waiting for. You can group nodes as you want, but in order to enhance encapsulation I did some code refactor (no functional change at all). Let’s see how named code looks like: You can run again the embedding TensorBoard visualizer code and get: If you drill down double clicking in the rounded boxes there appears the magic we were expecting for: And so on.. Variables has been defined in a separate namespace to be reused in training, validation and testing. They could be considered part of the training process, but they are part of the model bounded context itself. Training block includes loss calculation and the optimizer because they belong to the bounded context of training process. Taking them in a separate namespace makes it graphically messier as far as logits is part of the training internals. Softmax normalization in training, validation and testing blocks has been intentionally left out of the scope and named respectively as train_prediction_output, valid_prediction_output and test_prediction_output for legibility shake. Letting them inside the scope, the model would end in Softmax normalization, without any clue this is the output Op node it should be run in the Session to get the actual train result and measure the accuracy. Notice in Training block detail image the block is considering SGD_model/variables as an input, instead of detailing about weights and biases. In next image, MatMul input detail, you can appreciate those details appears when needed. And what happened to all those crap extra nodes that were drawn in the first attempt? Well, they are still there, within the internals it creates to handle the loss and the optimization. They look even prettier isolated in their own scope. Well, it wasn’t that bad, it was just a naming problem. I hope it will help you to develop a better TensorFlow code, or at least to look through it when you get lost.

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# Bzoj 3122 [Sdoi2013]随机数生成器(BSGS+exgcd) Input Output Sample Input 3 7 1 1 3 3 7 2 2 2 0 7 2 2 2 1 Sample Output 1 3 -1 HINT 0<=a<=P-1,0<=b<=P-1,2<=P<=10^9 /* */ #include<iostream> #include<cstdio> #include<algorithm> #include<cmath> #include<map> #define LL long long #define MAXN 101 using namespace std; LL T,p[MAXN],a[MAXN],b[MAXN],x1[MAXN],t[MAXN]; map<LL,int>s; bool vis[MAXN]; bool flag1=true,flag2=true,flag3=true; { LL x=0,f=1;char ch=getchar(); while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();} while(ch>='0'&&ch<='9') x=x*10+ch-48,ch=getchar(); return x*f; } void slove1(int i) { LL tot,sum; tot=x1[i],sum=1; while(true) { if(tot==t[i]) {printf("%d\n",sum);break;} if(!vis[tot]) vis[tot]=true; else {printf("-1\n");break;} tot=(a[i]*tot+b[i])%p[i]; sum++; } for(int j=0;j<p[i];j++) vis[j]=0; } void exgcd(LL a1,LL b1,LL &x,LL &y) { if(!b1){x=1;y=0;return ;} exgcd(b1,a1%b1,y,x),y-=(a1/b1)*x; return ; } void slove2(int i) { if(!a[i]) { if(b[i]==t[i]) printf("2\n"); else printf("-1\n"); return ; } LL c,g,tot,x,y; c=(t[i]-x1[i]+p[i])%p[i]; if(!c){cout<<1<<endl;return;} g=__gcd(b[i],p[i]); if(c%g) {cout<<-1<<endl;return ;} exgcd(b[i],p[i],x,y); x=(x*c/g)%p[i];x++; x=(x+p[i])%p[i]; cout<<x<<endl; } LL mi(LL a1,LL b1,LL p1) { LL tot1=1;//a1%=p1; while(b1) { if(b1&1) tot1=tot1*a1%p1; a1=a1*a1%p1; b1>>=1; } } void slove3(int i) { LL c,g,y;bool flag; s.clear();flag=false; c=mi(a[i]-1,p[i]-2,p[i]); exgcd((b[i]*c+x1[i])%p[i],p[i],g,y); if(g<p[i]) g=g%p[i]+p[i]; if(a[i]==1) { cout<<g+1<<endl;return ; } LL tmp1=(b[i]*c+t[i])%p[i],tmp2=__gcd(b[i]*c+x1[i],p[i]); if(tmp1%tmp2) {cout<<-1<<endl;return ;} g=((g*(tmp1/tmp2)+p[i])%p[i]+p[i])%p[i]; LL m=ceil(sqrt(p[i])),tot=1,tt; for(int j=1;j<=m-1;j++) { tot=tot*a[i]%p[i]; if(!s[tot]) s[tot]=j; } tot=1;tmp1=mi(a[i],p[i]-m-1,p[i]);s[1]=m+1; for(int k=0;k<=m-1;k++) { tt=s[tot*g%p[i]]; if(tt) { if(tt==m+1) tt=0; flag=true; cout<<k*m+tt+1<<endl; break; } tot=tot*tmp1%p[i]; } if(!flag) cout<<-1<<endl; } int main() { for(int i=1;i<=T;i++) { if(x1[i]==t[i]) {printf("1\n");continue;} if(p[i]<=200) slove1(i); else if(a[i]<2) slove2(i); else slove3(i); } return 0; } posted @ 2017-02-24 17:27  nancheng58  阅读(115)  评论(0编辑  收藏  举报

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# Course 5044 - Introduction to Numerical Analysis II - Spring 2019 Official Information Course Number:Math 5044.001 CRN:38528 Course Title:Introduction to Numerical Analysis II Times:MW 9:00-10:20 Places:Wachman Hall 617 Instructor: Benjamin Seibold Instructor Email: seibold(at)temple.edu Instructor Office:Wachman Hall 518 Instructor Office Hours:MW 10:20-11:30 Course Textbook: Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations - Steady State and Time Dependent Problems, SIAM, 2007 Further recommended reads: Official:Course Syllabus Topics Covered: This course provides a rigorous introduction to numerical methods for ordinary differential equations, establishing both knowledge and understanding of modern and efficient methods, as well as tools of analysis to understand when and why different methods work (or fail). Particular topics: Runge-Kutta, multistep, and Taylor series methods. Deferred correction. Convergence and stability. Error analysis. Stiff problems. Boundary value problems. Finite differences. Stochastic ODEs. Course Goals: Provide a rigorous mathematical basis for numerical methods for ordinary differential equations, and lay the groundwork for more advanced courses on numerical differential equations. Provide insight and intuition to fundamental challenges inherent to many problems in computational science and engineering. Attendance Policy: Students are expected to attend every class. If a student cannot attend a class for some justifiable reason, he or she is expected to contact the instructor before class. Course Grading: Homework: 50%; exams: 50%. Final Exam Date:05/02/2019. Course Schedule 01/14/2019   Lec 1 Introduction: Ordinary differential equations, Linear ODE Read: ODE, IVP, Linear ODE 01/16/2019   Lec 2 Predator-prey model, Lipschitz continuity, IVPs vs. BVPs 01/23/2019   Lec 3 Fundamental concepts in numerical methods for ODEs 01/28/2019   Lec 4 Taylor series methods: advantages and drawbacks 01/30/2019   Lec 5 Runge-Kutta methods: Butcher tableau 02/04/2019   Lec 6 General Runge-Kutta methods, ERK-DIRK-IRK 02/06/2019   Lec 7 Order conditions 02/11/2019   Lec 8 Embedded methods, adaptive time-stepping, dense output, Richardson extrapolation 02/13/2019   Lec 9 Linear multistep methods: order conditions 02/18/2019   Lec 10 Adams, BDF, and predictor-corrector methods Read: BDF, Predictor-corrector 02/19/2019   Lec 11 Zero-stability and convergence: failure of zero-stability, difference equations Read: Truncation error 03/11/2019   Lec 12 Zero-stability and convergence theorems 03/12/2019   Lec 13 Absolute stability: stability regions for different methods Read: Absolute Stability 03/13/2019   Lec 14 Boundary locus method, linear systems 03/18/2019   Lec 15 Stiff problems: Schemes for different stiffness types, A-stability, L-stability 03/20/2019   Lec 16 Mildly stiff problems, RK-Chebyshev methods 03/25/2019   Lec 17 Stiffness in nonlinear problems 03/26/2019   Lec 18 Order reduction 03/27/2019   Lec 19 Implementation of implicit RK methods 04/01/2019   Lec 20 Semi-implicit methods: ImEx Runge-Kutta methods 04/03/2019   Lec 21 ImEx multistep methods 04/08/2019   Lec 22 Other methods and special problems: SSP schemes, Hamiltonian ODEs 04/10/2019   Lec 23 Symplectic methods 04/15/2019   Lec 24 Deferred correction 04/17/2019   Lec 25 Stochastic differential equations: examples 04/22/2019   Lec 26 Euler-Maruyama and Milstein method, weak and strong convergence 04/24/2019   Lec 27 Boundary value problems: shooting methods Read: BVP, Shooting method 04/29/2019   Lec 28 Finite difference discretizations, pathways to PDE 05/02/2019 Final Examination Matlab Programs Introduction: temple5044_linear_ode_2x2.m Vector field and phase flow for linear 2x2 ODE systems Visualizes the different cases that can arise with 2x2 systems of ODE, via quiver plot, eigen-directions, and deformation of the unit circle. temple_abm_population_local.m   Population dynamics models via 2x2 nonlinear ODE systems The dynamics of two species are demonstrated in various cases: predator-prey, logistic growth, competition, and mutalism. Runge Kutta methods: ode1.m ode2.m ode3.m ode4.m ode5.m Runge-Kutta methods of orders 1,2,3,4, and 5 Initial value problem ODE are solved approximated equidistant time steps. temple5044_rk_order_conditions.m Check Runge-Kutta order conditions This code verifies whether the order conditions (up to order 5) are satisfied or not for a generic Runge-Kutta scheme, provided via its Butcher tableau. Example file: temple5044_rk_order_conditions_example.m, applies the code to three example methods. temple5044_voyager.m Simulation of jupiter swing-by of the Voyager 1 space probe A four-body problem of celestial mechanics, involving the sun, earth, jupiter, and Voyager 1, is solve numerically with a way too inaccurate RK4 discretization. Absolute stability: temple5044_absolute_stability_region_rk.m   Plot regions of absolute stability for Runge-Kutta methods Provided are 9 examples of Runge-Kutta schemes, defined via their Butcher tableaus. Semi-implicit methods: temple5044_stability_region_imex_rk.m Plot stability regions for ImEx Runge-Kutta methods Provided are 6 examples of ImEx Runge-Kutta schemes, applied to the test problem u'=αu+iβu. Stochastic differential equations: temple5044_euler_maruyama.m Error convergence study of Euler-Maruyama method for the stochastic differential equation (geometric Brownian motion) dX = μ X dt + σ X dW. Boundary value problems: mit18336_poisson1d_error.m Numerical error analysis for the 1D Poisson equation A differentiable but oscillatory right hand side is considered. Homework Problem Sets

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# Concrete Mix Design Calculation for M20, M25, M30 Concrete with Procedure & Example Concrete mix design is the process of finding right proportions of cement, sand and aggregates for concrete to achieve target strength in structures. So, concrete mix design can be stated as Concrete Mix = Cement:Sand:Aggregates. The concrete mix design involves various steps, calculations and laboratory testing to find right mix proportions. This process is usually adopted for structures which requires higher grades of concrete such as M25 and above and large construction projects where quantity of concrete consumption is huge.. Benefits of concrete mix design is that it provides the right proportions of materials, thus making the concrete construction economical in achieving required strength of structural members. As, the quantity of concrete required for large constructions are huge, economy in quantity of materials such as cement makes the project construction economical. Concrete Mix design of M20, M25, M30 and higher grade of concrete can be calculated from example below. ## Concrete Mix Design ### Data Required for Concrete Mix Design #### (i) Concrete Mix Design Stipulation (a) Characteristic compressive strength required in the field at 28 days grade designation — M 25 (b) Nominal maximum size of aggregate — 20 mm (c) Shape of CA — Angular (d) Degree of workability required at site — 50-75 mm (slump) (e) Degree of quality control available at site — As per IS:456 (f) Type of exposure the structure will be subjected to (as defined in IS: 456) — Mild (g) Type of cement: PSC conforming IS:455 (h) Method of concrete placing: pump able concrete #### (ii) Test data of material (to be determined in the laboratory) (a) Specific gravity of cement — 3.15 (b) Specific gravity of FA — 2.64 (c) Specific gravity of CA — 2.84 (d) Aggregate are assumed to be in saturated surface dry condition. (e) Fine aggregates confirm to Zone II of IS - 383 ### Procedure for Concrete Mix Design of M25 Concrete #### Step 1 — Determination Of Target Strength Himsworth constant for 5% risk factor is 1.65. In this case standard deviation is taken from IS:456 against M 20 is 4.0. ftarget = fck + 1.65 x S = 25 + 1.65 x 4.0 = 31.6 N/mm2 Where, S = standard deviation in N/mm2 = 4 (as per table -1 of IS 10262- 2009) #### Step 2 — Selection of water / cement ratio:- From Table 5 of IS 456, (page no 20) Maximum water-cement ratio for Mild exposure condition = 0.55 Based on experience, adopt water-cement ratio as 0.5. 0.5<0.55, hence OK. #### Step 3 — Selection of Water Content From Table 2 of IS 10262- 2009, Maximum water content = 186 Kg (for Nominal maximum size of aggregate — 20 mm) #### Table for Correction in water content Parameters Values as per Standard reference condition Values as per Present Problem Departure Correction in Water Content Slump 25-50 mm 50-75 25 (+3/25) x 25 = +3 Shape of Aggregate Angular Angular Nil - Total +3 Estimated water content = 186+ (3/100) x 186 = 191.6 kg /m3 #### Step 4 — Selection of Cement Content Water-cement ratio = 0.5 Corrected water content = 191.6 kg /m3 Cement content = From Table 5 of IS 456, Minimum cement Content for mild exposure condition = 300 kg/m3 383.2 kg/m3 > 300 kg/m3, hence, OK. This value is to be checked for durability requirement from IS: 456. In the present example against mild exposure and for the case of reinforced concrete the minimum cement content is 300 kg/m3 which is less than 383.2 kg/m3. Hence cement content adopted = 383.2 kg/m3. As per clause 8.2.4.2 of IS: 456 Maximum cement content = 450 kg/m3. #### Step 5: Estimation of Coarse Aggregate proportion:- From Table 3 of IS 10262- 2009, For Nominal maximum size of aggregate = 20 mm, Zone of fine aggregate = Zone II And For w/c = 0.5 Volume of coarse aggregate per unit volume of total aggregate = 0.62 #### Table for correction in estimation of coarse aggregate proportion Parameter Values as per Standard reference condition Values as per present problem Departure Correction in Coarse Aggregate proportion Remarks W/c 0.5 0.5 Nil - See Note 1 Workability - pump able concrete - -10% See Note 2 Total -10% Note 1: For every ±0.05 change in w/c, the coarse aggregate proportion is to be changed by 0.01. If the w/c is less than 0.5 (standard value), volume of coarse aggregate is required to be increased to reduce the fine aggregate content. If the w/c is more than 0.5, the volume of coarse aggregate is to be reduced to increase the fine aggregate content. If the coarse aggregate is not angular, the volume of coarse aggregate may be required to be increased suitably, based on experience. Note 2: For pump-able concrete or congested reinforcement the coarse aggregate proportion may be reduced up to 10%. Hence, Volume of coarse aggregate per unit volume of total aggregate = 0.62 x 90% = 0.558 Volume of fine aggregate = 1 – 0.558 = 0.442 #### Step 6: Estimation of the mix ingredients a) Volume of concrete = 1 m3 b) Volume of cement = (Mass of cement / Specific gravity of cement) x (1/100) = (383.2/3.15) x (1/1000) = 0.122 m3 c) Volume of water = (Mass of water / Specific gravity of water) x (1/1000) = (191.6/1) x (1/1000) = 0.1916 m3 d) Volume of total aggregates = a – (b + c ) = 1 – (0.122 + 0.1916) = 0.6864 m3 e) Mass of coarse aggregates = 0.6864 x 0.558 x 2.84 x 1000 = 1087.75 kg/m3 f) Mass of fine aggregates = 0.6864 x 0.442 x 2.64 x 1000 = 800.94 kg/m3 #### Concrete Mix proportions for Trial Mix 1 Cement = 383.2 kg/m3 Water = 191.6 kg/m3 Fine aggregates = 800.94 kg/m3 Coarse aggregate = 1087.75 kg/m3 W/c = 0.5 For trial -1 casting of concrete in lab, to check its properties. It will satisfy durability & economy. For casting trial -1, mass of ingredients required will be calculated for 4 no's cube assuming 25% wastage. Volume of concrete required for 4 cubes = 4 x (0.153 x1.25) = 0.016878 m3 Cement = (383.2 x 0.016878) kg/m3 = 6.47 kg Water = (191.6 x 0.016878) kg/m3 =3.23 kg Coarse aggregate = (1087.75 x 0.016878) kg/m3 =18.36 kg Fine aggregates = (800.94 x 0.016878) kg/m3 = 13.52 kg #### Step 7: Correction due to absorbing / moist aggregate:- Since the aggregate is saturated surface dry condition hence no correction is required. ### Concrete Trial Mix 1: The mix proportion as calculated in Step 6 forms trial mix1. With this proportion, concrete is manufactured and tested for fresh concrete properties requirement i.e. workability, bleeding and finishing qualities. In this case, Slump value = 25 mm Compaction Factor = 0.844 So, from slump test we can say, Mix is cohesive, workable and had a true slump of about 25 mm and it is free from segregation and bleeding. Desired slump = 50-75 mm So modifications are needed in trial mix 1 to arrive at the desired workability. ### Concrete Trial Mix 2: To increase the workability from 25 mm to 50-75 mm an increase in water content by +3% is to be made. The corrected water content = 191.6 x 1.03 = 197.4 kg. As mentioned earlier to adjust fresh concrete properties the water cement ratio will not be changed. Hence Cement Content = (197.4/0.5) = 394.8 kg/m3 Which also satisfies durability requirement. Volume of all in aggregate = 1 – [{394.8/(3.15x1000)} + {197.4/(1 x 1000)}] = 0.6773 m3 Mass of coarse aggregate = 0.6773 x 0.558 x 2.84 x 1000 = 1073.33 kg/m3 Mass of fine aggregate = 0.6773 x 0.442 x 2.64 x 1000 = 790.3 kg/m3 ### Concrete Mix Proportions for Trial Mix 2 Cement = 384.8 kg/m3 Water = 197.4 kg/m3 Fine aggregate =790.3 kg/m3 Coarse aggregate = 1073.33 kg/m3 For casting trial -2, mass of ingredients required will be calculated for 4 no's cube assuming 25% wastage. Volume of concrete required for 4 cubes = 4 x (0.153 x1.25) = 0.016878 m3 Cement = (384.8 x 0.016878) kg/m3 = 6.66 kg Water = (197.4 x 0.016878) kg/m3 =3.33 kg Coarse aggregate = (1073.33 x 0.016878) kg/m3 =18.11 kg Fine aggregates = (790.3 x 0.016878) kg/m3 = 13.34 kg In this case, Slump value = 60 mm Compaction Factor = 0.852 So, from slump test we can say, Mix is very cohesive, workable and had a true slump of about 60 mm. It virtually flowed during vibration but did not exhibit any segregation and bleeding. Desired slump = 50-75 mm So , it has achieved desired workability by satisfying the requirement of 50-75 mm slump value . Now , we need to go for trial mix-3 . ### Concrete Trial Mix 3: In case of trial mix 3 water cement ratio is varied by +10% keeping water content constant. In the present example water cement ratio is raised to 0.55 from 0.5. An increase of 0.05 in the w/c will entail a reduction in the coarse aggregate fraction by 0.01. Hence the coarse aggregate as percentage of total aggregate = 0.558 – 0.01 = 0.548 W/c = 0.55 Water content will be kept constant. Cement content = (197.4/0.55) = 358.9 kg/m3 Hence, volume of all in aggregate = 1 – [{(358.9/(3.15 x 1000)} + (197.4/1000)] =0.688 m3 Mass of coarse aggregate = 0.688 x 0.548 x 2.84 x 1000 = 1070.75 kg/m3 Mass of fine aggregate = 0.688 x 0.452 x 2.64 x 1000 = 821 kg/m3 ### Concrete Mix Proportions of Trial Mix 3 Cement = 358.9 kg/m3 Water = 197.4 kg/m3 FA = 821 kg/m3 CA = 1070.75 kg/m3 For casting trial -3, mass of ingredients required will be calculated for 4 no's cube assuming 25% wastage. Volume of concrete required for 4 cubes = 4 x (0.153 x1.25) = 0.016878 m3 Cement = (358.9 x 0.016878) kg/m3 = 6.06 kg Water = (197.4 x 0.016878) kg/m3 =3.33 kg Coarse aggregate = (1070.75 x 0.016878) kg/m3 =18.07 kg Fine aggregates = (821 x 0.016878) kg/m3 = 13.85 kg In this case, Slump value = 75 mm Compaction Factor = 0.89 So, from slump test we can say, Mix is stable, cohesive, and workable and had a true slump of about 75 mm. Desired slump = 50-75 mm So , it has achieved desired workability by satisfying the requirement of 50-75 mm slump value . Now , we need to go for trial mix-4. ### Concrete Trial Mix 4: In this case water / cement ratio is decreased by 10% keeping water content constant. W/c = 0.45 A reduction of 0.05 in w/c will entail and increase of coarse aggregate fraction by 0.01. Coarse aggregate fraction = 0.558 +.01 =.568 W/c = 0.45 and water content = 197.4 kg/m3 Cement content = (197.4/0.45) = 438.7 kg/m3 Volume of all in aggregate = 1 – [{438.7/(3.15 x 1000)} + (197.4/1000)] = 0.664 m3 Mass of coarse aggregate = 0.664 x 0.568 x 2.84 x 1000 = 1071.11 kg/m3 Mass of fine aggregate = 0.664 x 0.432 x 2.64 x 1000 = 757.28 kg/m3 ### Concrete Mix Proportions of Trial Mix 4 Cement = 438.7 kg/m3 Water = 197.4 kg/m3 FA = 757.28 kg/m3 CA = 1071.11 kg/m3 For casting trial -4, mass of ingredients required will be calculated for 4 no's cube assuming 25% wastage. Volume of concrete required for 4 cubes = 4 x (0.153 x1.25) = 0.016878 m3 Cement = (438.7 x 0.016878) kg/m3 = 7.4 kg Water = (197.4 x 0.016878) kg/m3 =3.33 kg Coarse aggregate = (1071.11 x 0.016878) kg/m3 =18.07 kg Fine aggregates = (757.28 x 0.016878) kg/m3 = 12.78 kg A local correction due to moisture condition of aggregate is again applied on this proportions. With corrected proportions three concrete cubes are cast and tested for 28 days compressive strength. A summary of all the trial mixes is given in the following Table. ## Recommended mix proportion of ingredients for grade of concrete M25: From Compressive Strength vs. c/w graph for target strength 31.6 MPa we get, W/c = 0.44 water content = 197.4 kg/m3 Cement content = (197.4/0.44) = 448.6 kg/m3 Volume of all in aggregate = 1 – [{448.6/(3.15 x 1000)} + (197.4/1000)] = 0.660 m3 A reduction of 0.05 in w/c will entail and increase of coarse aggregate fraction by 0.01. Coarse aggregate fraction = 0.558 +.01 =.568 Volume of fine aggregate = 1 – 0.568 = 0.432 Mass of coarse aggregate = 0.660 x 0.568 x 2.84 x 1000 = 1064.65 kg/m3 Mass of fine aggregate = 0.660 x 0.432 x 2.64 x 1000 = 752.71 kg/m3

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Sie sind auf Seite 1von 7 # Restriction Mapping At some point in a cloning project it will be necessary to construct a restriction map of a plasmid. This will involve manipulating restriction digest fragments into a circular map. Once you have done this a number of times and develop a feel for the process and mapping will become almost intuitive. However, there is a systematic approach to constructing a map, which is illustrated in the sample problem below. Once you have mastered the sample problem, complete the remaining problems, plot the answers on polar coordinate graph paper, and hand them in. Be cautioned that working with actual restriction fragments from a gel is a bit messier than these problems because of experimental error in determining fragment sizes. Sometimes the mathematical approach used here needs to be supplemented with some logic. Sample Problem Plasmid pRIT450 is 7.0 kb in length and has single PstI, EcoRI, and BamHI sites. You have cut the plasmid with PstI and inserted a 4.0 kb fragment into the site. From the data below, determine the restriction map of the resulting plasmid. PstI EcoRI BamHI PstI + EcoRI, PstI + BamHI EcoRI + BamHI 7.0 6.0 8.9 4.3 6.1 5.0 4.0 5.0 2.1 3.3 2.8 2.1 2.7 1.2 2.1 0.7 0.9 1.8 ## Solution to Sample Problem 1. If the new plasmid is cut with PstI, the vector and the insert will be regenerated. We will use these as reference fragments as we build the map. Although it is often convenient to think in terms of target and vector, any site can arbitrarily be used to generate reference fragments. We will now begin by choosing PstI as our reference point, but we could have just as easily chosen to start with EcoRI or BamHI. It makes no difference. 2. First, look at the PstI + BamHI digest. It helps to think of the double digest conceptually as a twostep process in which the plasmid is first cut with PstI into the two reference fragments. BamHI then cuts the reference fragments further. 36 Restriction Mapping 3. In the PstI + BamHI double digest, we recover 4 fragments. Some combination of the fragments will add up to the vector and the remaining fragments will equal the insert. We see that 6.1+ 0.9 = 7.0 = vector and 2.8 + 2.1 = 4.0 = insert. Thus, we can organize the fragments as below: P B 6.1 7.0 Ref 4. 0.9 B 1.2 2.8 4.0 Ref The insert and the vector can each be drawn in two opposite orientations. However, we will arbitrarily use one orientation for the vector and vary the insert. It we tried to vary both vector and insert, we would end up with two identical but mirror image maps. There is, however, no absolutely correct orientation of a plasmid map, so it really makes no difference: P B 6.1 7.0 Ref P B XXX 0.9 0.9 B 1.2 2.8 4.0 Ref 6.1 7.0 Ref P Orientation A B 2.8 4.0 Ref P 1.2 Orientation B We next must next determine which orientation, A or B, is correct. In orientation A, the two BamHI sites are close together (proximal) while in B, the sites are far apart (distal). Clearly, a BamHI single digest of each orientation will result in a different set of fragments. We can therefore determine expected fragment sizes for each orientation and then compare our expected values with the values observed: Orientation A 0.9 + 1.2 = 6.1 + 2.8 = 6. 7. Orientation B 0.9 + 2.8 = 6.1 + 1.2 = 2.1 8.9 11.0 By comparing our observed and expected values, we find that orientation A is the correct orientation. Using exactly the same logic, we can now show that the correct orientation of the EcoRI sites is as below: P E 4.3 P 2.7 E 3.3 4.0 Ref 7.0 Ref 8. Observed 2.1 8.9 11.0 3.7 7.3 11.0 P 0.7 To complete the map, we must now superimpose the BamHI and EcoRI maps. Let us arbitrarily assume that the orientation of the BamHI map is correct. We can now superimpose the EcoRI map on the BamHI map in either of two orientations, A or B. Using the alternate BamHI orientation would simply produce a mirror-image map. 37 Restriction Mapping E 2.7 1.8 0.9 1.2 3.3 A B 6.1 0.7 0.7 P 0.9 2.1 4.3 4.3 E E P 1.2 B B 2.8 P E E 0.9 0.7 0.7 0.5 4.3 3.4 3.3 2.8 2.7 2.7 9. 1.2 + 11. From the alternative orientations, A and B, we can predict the outcome of an EcoRI + BamHI double digest: Orientation A 4.3 + 0.7 = 10. 0.9 5.0 2.1 2.1 1.8 11.0 Orientation B 2.7 + 2.8 = 0.7 + 0.9 5.5 0.5 1.6 3.4 11.0 Observed 5.0 2.1 2.1 1.8 11.0 By comparing the results of the EcoRI + BamHI double digest with our predictions, we see that orientation A is correct and the plasmid is now mapped. In step 8, we arbitrarily chose one of the two possible orientations for the BamHI map. Using the other, as noted, would have given the mirror image. Try it. Neither mirror image is more correct than the other. However, once the map is published, the published orientation by convention becomes the correct orientation. If the plasmid was meant to be a new cloning vector, then one would map all plasmids subsequently derived from it in the same orientation. The final step is to plot the map on polar coordinate graph paper so that the fragment sizes are all proportional to one another. On polar coordinate graph paper, you plot degrees, not kilobases. 38 Restriction Mapping Thus an entire circle, irrespective of total kilobases, will be 360o. Since the map in this case is 11 kb long, then: 360o/11kb = 32.7o/kilobase. Now we multiply each kb value by 32.7 to obtain the degrees below: kilobases 1.2 2.1 0.7 4.3 1.8 0.9 11.0 degrees 39.2 68.7 22.9 140.6 58.9 29.4 359.9 The last step is to decide on the circumference of the circle. If you are mapping several plasmids, you would want to draw them to scale. You can adjust the total size of your map by altering the circumference. Thus, for example, if you wanted to draw your map to the scale of 1 inch = 1 kb, then circumference = 11 kb x 1 inch/kb = 11 inches. You can determine the radius of a circle with a circumference of 11 inches by applying the formula: 2r=C where C = circumference and r = radius, and solving for r: 2 r = 11 in r = 11 in/2 r = 1.75 in The map of the sample plasmid on the following page is graphed in just this way. The positions of the restriction sites are plotted according to the table above and the circumference of the outer circle is 11 inches, with a radius of 1.75 inches. Note, however, that the distances are given as kilobases, not degrees! 39 Restriction Mapping Now, determine the restriction maps for the remaining plasmids and hand them in as homework. Mapping Problems Plasmid pRIT451 was cut with SmaI, BglII, and AvaI. From the data below, determine the map. SmaI BglII AvaI SmaI + BglII SmaI + AvaI AvaI + BglII 5.9 8.2 5.3 5.4 3.3 5.3 4.3 2.0 4.9 2.8 2.6 2.1 40 1.5 2.3 2.0 0.5 2.0 0.8 Restriction Mapping Plasmid pRIT452 was cut with PstI, HindIII, and EcoRI. From the data below, determine the map. PstI HindIII EcoRI PstI + HindIII PstI + EcoRI EcoRI + HindIII 6.8 6.5 9.2 4.8 5.4 6.2 5.9 6.2 3.5 4.2 3.8 3.5 2.0 3.0 1.8 1.7 0.5 1.2 Plasmid pRIT453 was cut with SmaI, HindIII, and EcoRI. From the data below, determine the map. EcoRI HindIII SmaI EcoRI + HindIII EcoRI + SmaI SmaI + HindIII 7.7 7.4 6.6 4.5 5.7 2.7 1.6 1.9 2.7 1.9 2.0 2.5 1.6 0.9 2.2 1.3 0.7 1.9 Plasmid pRIT454 was cut with PstI, HindIII, and EcoRI. From the data below, determine the map. PstI HindIII EcoRI PstI + HindIII 6.0 5.8 6.5 4.0 5.3 5.5 3.0 3.8 1.8 2.0 1.5 PstI + EcoRI EcoRI + HindIII 3.5 5.0 3.0 3.0 2.5 1.5 1.8 1.0 41 0.5 0.8 Restriction Mapping Plasmid pRIT455 was cut with BamHI, HindIII, and EcoRI. From the data below, determine the map. EcoRI HindIII BamHI EcoRI + BamHI EcoRI + HindIII BamHI + HindIII 8.5 5.6 6.5 4.5 4.3 3.4 2.0 5.4 4.5 2.2 4.2 3.1 0.5 2.0 1.2 2.5 1.8 0.8 2.0 0.5 0.5 Plasmid pRIT456 was cut with PstI, HindIII, and EcoRI. From the data below, determine the map. EcoRI PstI HindIII PstI + EcoRI PstI + HindIII EcoRI + HindIII 5.8 7.4 6.8 3.3 6.3 3.6 3.3 4.6 5.2 3.3 4.1 3.3 2.9 2.5 1.1 2.2 2.1 0.5 1.6 0.8 1.3 Plasmid pRIT457 was cut with BamHI, HindIII, and PstI. From the data below, determine the map. BamHI HindIII PstI BamHI + HindIII BamHI + PstI HindIII + PstI 5.1 8.1 13.4 5.1 5.1 8.1 42 4.5 5.3 3.8 3.3 4.5 3.3 2.5 2.5 2.0 2.0 1.3 0.5

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# Simple Coding Help - No Promise. #### JAYAKUMAR1975 ##### Member AMIBROKER HELP REQUIRED :- 1 ) NIFTY BUY GENERATE after 2 LOTS BUY ORDER PLACED AFTER 20 POINTS PROFIT ONE LOT SELLING @ 20 POINTS BALANCE QTY AUTOMATICALY CHANGE THE COST TO COST IT IS POSSIBLE SAME SELL SIDE VICE VERSA ( AMIBROKER AUTO TRADE ) Thanks and regards #### vishp127 ##### Member Linear Regression and Trend Line with Std Dev Afl Hi I am not sure if you are after this, this Afl has slope calculation in it.. Code: ``````_SECTION_BEGIN("Trend Lines"); p1 = Param("TL 1 Periods", 20, 5, 50, 1); p2 = Param("TL 2 Periods", 5, 3, 25, 1); TL1 = LinearReg(C, p1); TL2 = EMA(TL1, p2); Col1 = IIf(TL1 > TL2, ParamColor("TL Up Colour", colorBlue), ParamColor("TL Dn Colour", colorRed)); Plot(TL1, "TriggerLine 1", Col1, styleLine|styleThick|styleNoLabel); Plot(TL2, "TriggerLine 2", Col1, styleLine|styleThick|styleNoLabel); _SECTION_END(); _SECTION_BEGIN("Linear Regression Channel"); // CyberMan's Linear Regression Channel.. http://www.wisestocktrader.com/indicators/2690-price-with-regression-and-trend // Linear Regression Line with 2 Standard Deviation Channels Plotted Above and Below // The original was written by Patrick Hargus, with critical hints from Marcin Gorzynski, Amibroker.com Technical Support // Wysiwyg coded the angle in degrees part // I modified the original Linear Regression code so that the line will change color based on the degree of the Linear Regression slope. // I combine this with my trading system. // I will only take long positions if the Linear Regression line is green and the entry price is below the LR line. // I will only take short positions if the Linear Regression line is red and the entry price is above the LR line. // It is useful for filtering out lower probability trades. //=====================Start Chart Configuration====================================== SetChartOptions(0,chartShowArrows|chartShowDates); _N(Title = StrFormat("{{NAME}} - {{INTERVAL}} {{DATE}} Open %g, Hi %g, Lo %g, Close %g (%.1f%%) Vol " +WriteVal( V, 1.0 ) +" {{VALUES}}", O, H, L, C, SelectedValue( ROC( C, 1 )) )); SetChartBkGradientFill(ParamColor("Top", colorTeal), ParamColor("Bottom", colorLightGrey), ParamColor("Title", colorTeal)); SetChartBkColor(colorTeal); Plot( C, "Close", colorWhite, styleCandle, Zorder = 1); //=====================End Chart Configuration======================================== //=====================Start of Linear Regression Code=================================== P = ParamField("Price field",-1); Length = 3; Daysback = Param("Period for Liner Regression Line",Length,1,240,1); shift = Param("Look back period",0,0,240,1); //===================== Math Formula ============================================= x = Cum(1); lastx = LastValue( x ) - shift; aa = LastValue( Ref(LinRegIntercept( p, Daysback), -shift) ); bb = LastValue( Ref(LinRegSlope( p, Daysback ), -shift) ); y = aa + bb * ( x - (Lastx - DaysBack +1 ) ); //=====================Plot the Linear Regression Line =================================== LRColor = ParamColor("LR Color", colorCycle ); LRStyle = ParamStyle("LR Style"); // A slope higher than 0.05 radians will turn green, less than -0.05 will turn red and anything in between will be white. Angle = Param("Angle", 0.05, 0, 1.5, 0.01); LRLine = IIf( x > (lastx - Daysback) AND BarIndex() < Lastx, y, Null ); Pi = 3.14159265 * atan(1); // Pi SlopeAngle = atan(bb)*(180/Pi); LineUp = SlopeAngle > Angle; LineDn = SlopeAngle < - Angle; if(LineUp) { Plot(LRLine, "Lin. Reg. Line Up", IIf(LineUp, colorBrightGreen, colorWhite), LRStyle); } else { Plot(LRLine, "Lin. Reg. Line Down", IIf(LineDn, colorDarkRed, colorWhite), LRStyle); } Trend = IIf(LRLine > Ref(LRLine,-1),colorGreen,colorRed);//Changes LR line to green if sloping up and red if sloping down. Plot( LRLine , "LinReg", Trend, LRSTYLE ); //======================Plot 1st SD Channel ======================================== SDP = Param("Standard Deviation", 1.5, 0, 6, 0.1); SD = SDP/2; width = LastValue( Ref(SD*StDev(p, Daysback),-shift) ); //Set width of inside chanels here. SDU = IIf( x > (lastx - Daysback) AND BarIndex() < Lastx, y+width , Null ) ; SDL = IIf( x > (lastx - Daysback) AND BarIndex() < Lastx, y-width , Null ) ; SDColor = ParamColor("SD Color", colorCycle ); SDStyle = ParamStyle("SD Style"); Plot( SDU , "Upper Lin Reg", colorWhite,SDStyle ); //Inside Regression Lines Plot( SDL , "Lower Lin Reg", colorWhite,SDStyle ); //Inside Regression Lines //===================== Plot 2d SD Channel ========================================== SDP2 = Param("2d Standard Deviation", 2.0, 0, 6, 0.1); SD2 = SDP2/2; width2 = LastValue( Ref(SD2*StDev(p, Daysback),-shift) ); //Set width of outside chanels here. SDU2 = IIf( x > (lastx - Daysback) AND BarIndex() < Lastx, y+width2 , Null ) ; SDL2 = IIf( x > (lastx - Daysback) AND BarIndex() < Lastx, y-width2 , Null ) ; SDColor2 = ParamColor("2 SD Color", colorCycle ); SDStyle2 = ParamStyle("2 SD Style"); Plot( SDU2 , "Upper Lin Reg", colorWhite,SDStyle2 ); //OutSide Regression Lines Plot( SDL2 , "Lower Lin Reg", colorWhite,SDStyle2 ); //OutSide Regression Lines //====================== End Indicator Code ==========================================`````` hi dear my friends amitrandive will you plz add scan to this afl for below condition sell if slopes is above 80<slope<100 i am not sure is it correct or not .imean scan for buy an sell to this condition according the slope positions Last edited: #### Blue_Ridge ##### New Member Hi Happy_Singh, Can you code rollover thing for futures? Like say I am doing swing trading, and currently long 1 lot of Nifty Dec Future. Then 1 days before expiry, code should exit Nifty Dec Future(Sell Nifty Dec 1 lot) and start Nifty Jan Long position(Buy Nifty Jan 1 lot) immediately. And vice versa for the shorts. It will be great help if you can come up with the solution. Thanks. #### SR_TA ##### Active Member Is there an AFL which shows the visual pivots? or filter sideways pivots? pratap's ema cross over pivots. Code: ``````_SECTION_BEGIN("Visual Pivots"); // Author: Pratap Balakrishnan // email id: [email][email protected][/email] // SetChartOptions(0,chartShowArrows|chartShowDates); _N(Title = StrFormat("{{NAME}} - {{INTERVAL}} {{DATE}} Open %g, Hi %g, Lo %g, Close %g (%.1f%%) {{VALUES}}", O, H, L, C, SelectedValue( ROC( C, 1 ) ) )); SetChartBkColor( ParamColor("BKGrnd", ColorRGB( 190, 190, 190 ) ) ); Plot( C, "Close", ParamColor("Candle Color", colorBlack ), styleNoTitle | ParamStyle("Style") | GetPriceStyle() ); ro = ParamField("Open", 0) ; rh = ParamField("High", 1) ; rl = ParamField("Low", 2) ; rc = ParamField("Close", 3) ; P = (rH+rL+rC)/3 ; p1 = Param("Fast", 1, 1, 100, 1) ; p2 = Param("Slow", 3, 1, 100, 1) ; usebpvts = ParamToggle("Use Body Pvts", "No|Yes", 0) ; isemapvts = ParamToggle("Pvt Type", "H-L|EMA", 1) ; ismph = H-H ; ismpl = L-L ; bph = Max(rO,rC); bpl = Min(rO,rC); if (isemapvts) { EMA1 = EMA(P, p1) ; EMA2 = EMA(P, p2) ; upcross = Cross(EMA1, EMA2) ; downcross = Cross(EMA2, EMA1) ; //bph = Max(O,C); //bpl = Min(O,C); bi = BarIndex() ; mphbar = HighestSinceBars(upcross, rH) ; mplbar = LowestSinceBars(downcross, rL) ; mphbi = ValueWhen(downcross, bi, 0) - ValueWhen(downcross, mphbar, 0) ; ismph = mphbi == bi ; mplbi = ValueWhen(upCross, bi, 0) - ValueWhen(upCross, mplbar, 0) ; ismpl = mplbi == bi ; ismph = IIf(downCross AND mphbar == 0, True, ismph) ; ismpl = IIf(upcross AND mplbar == 0, True, ismpl) ; bmphbar = HighestSinceBars(upcross, bph) ; bmplbar = LowestSinceBars(downcross, bpl) ; bmphbi = ValueWhen(downcross, bi, 0) - ValueWhen(downcross, bmphbar, 0) ; isbmph = bmphbi == bi ; bmplbi = ValueWhen(upCross, bi, 0) - ValueWhen(upCross, bmplbar, 0) ; isbmpl = bmplbi == bi ; isbmph = IIf(downCross AND bmphbar == 0, True, isbmph) ; isbmpl = IIf(upcross AND bmplbar == 0, True, isbmpl) ; } else { isbmph = ismph = rH > Ref(rH, -1) AND rH > Ref(rH, 1) ; isbmpl = ismpl = rL < Ref(rL, -1) AND rL < Ref(rL, 1) ; } showminor = ParamToggle("Show Minor Pvts", "No|Yes", 1) ; issquare = ParamToggle("Pvt style", "Circle|Square", 0) ; Clrmph = ParamColor("MPH Color", colorGreen) ; Clrmpl = ParamColor("MPL Color", colorBrown) ; pvtmarker = IIf(issquare, shapeSmallSquare, shapeSmallCircle) ; if (showminor) { if (usebpvts) { PlotShapes(isbmph*pvtmarker , Clrmph , 0, rH, 12) ; PlotShapes(isbmpl*pvtmarker , Clrmpl, 0, rL, -12) ; } else { PlotShapes(ismph*pvtmarker , Clrmph , 0, rH, 12) ; PlotShapes(ismpl*pvtmarker , Clrmpl, 0, rL, -12) ; } } showminorlvls = ParamToggle("Show Minor Levels", "No|Yes", 1) ; mph = ValueWhen(ismph, rH) ; mpl = ValueWhen(ismpl, rL) ; if (showminorlvls) { x = LineArray(0, SelectedValue(mph), (BarCount-1), SelectedValue(mph)); Plot(x, "", colorGold, styleDashed); x = LineArray(0, SelectedValue(mpl), (BarCount-1), SelectedValue(mpl)); Plot(x, "", colorGold, styleDashed); } showminortrend = ParamToggle("Show Minor Trend", "No|Yes", 0) ; if (showminortrend) { // initialize minor levels mph = ValueWhen(ismph, rH) ; mpl = ValueWhen(ismpl, rL) ; mbph = ValueWhen(isbmph, bph) ; mbpl = ValueWhen(isbmpl, bpl) ; // minor trend mut = rH > mph OR (rC > mbph) OR (ismph AND rH > Ref(mph, -1)); mdt = rL < mpl OR (rC < mbpl) OR (ismpl AND rL < Ref(mpl, -1)); mdt = Flip(mdt, mut) ; mut = Flip(mut, mdt) ; //mutst = ExRem(mut, mdt) ; //mdtst = ExRem(mdt, mut) ; Clr = IIf(mut, colorBlue, colorRed) ; PlotOHLC(rO,rH,rL,rC, "", Clr, styleCandle|styleNoLabel); Plot(4, "", Clr, styleArea|styleOwnScale, 0, 100, 0, -1) ; } tffactor = Param("TF Factor", 3, 1, 100, 1) ; showhigher = ParamToggle("Show Higher", "No|Yes", 0) ; if (showhigher) { tfs = tffactor *Interval() ; TimeFrameSet(tfs) ; if (isemapvts) { Ptf = (H+L+C)/3 ; EMA1tf = EMA(Ptf, p1) ; EMA2tf = EMA(Ptf, p2) ; upcrosstf = Cross(EMA1tf, EMA2tf) ; downcrosstf = Cross(EMA2tf, EMA1tf) ; bphtf = Max(O,C) ; bpltf = Min(O,C) ; if (usebpvts) { Refhtf = bphtf ; Refltf = bpltf ; } else { Refhtf = H ; Refltf = L ; } mphbartf = HighestSinceBars(upcrosstf, Refhtf) ; mplbartf = LowestSinceBars(downcrosstf, Refltf) ; bitf = BarIndex() ; mphbitf = ValueWhen(downcrosstf, bitf, 0) - ValueWhen(downcrosstf, mphbartf, 0) ; ismphtf = mphbitf == bitf ; mplbitf = ValueWhen(upCrosstf, bitf, 0) - ValueWhen(upCrosstf, mplbartf, 0) ; ismpltf = mplbitf == bitf ; ismphtf = IIf(downCrosstf AND mphbartf == 0, True, ismphtf) ; ismpltf = IIf(upcrosstf AND mplbartf == 0, True, ismpltf) ; } else { ismphtf = H > Ref(H, -1) AND H > Ref(H, 1) ; ismpltf = L < Ref(L, -1) AND L < Ref(L, 1) ; } if (showminortrend) { // initialize minor levels mphtf = ValueWhen(ismphtf, H) ; mpltf = ValueWhen(ismpltf, L) ; mbphtf = ValueWhen(ismphtf, bphtf) ; mbpltf = ValueWhen(ismpltf, bpltf) ; // minor trend muttf = H > mphtf OR (C > mbphtf) OR (ismphtf AND H > Ref(mphtf, -1)); mdttf = L < mpltf OR (C < mbpltf) OR (ismpltf AND L < Ref(mpltf, -1)); mdttf = Flip(mdttf, muttf) ; muttf = Flip(muttf, mdttf) ; //mutst = ExRem(mut, mdt) ; //mdtst = ExRem(mdt, mut) ; Clrtf = IIf(muttf, colorBlue, colorRed) ; // PlotOHLC(rO,rH,rL,rC, "", Clr, styleCandle|styleNoLabel); Clrtfe = TimeFrameExpand(Clrtf, tfs, expandLast) ; Plot(2, "", Clrtfe, styleArea|styleOwnScale, 0, 100) ; } ismphtfe = TimeFrameExpand(ismphtf, tfs, expandFirst) ; ismpltfe = TimeFrameExpand(ismpltf, tfs, expandFirst) ; He=TimeFrameExpand(H, tfs, expandFirst) ; Le=TimeFrameExpand(L, tfs, expandFirst) ; TimeFrameRestore() ; ishtfmph = IIf(ismph == ismphtfe, 1, 0) ; ishtfmpl = IIf(ismpl == ismpltfe, 1, 0) ; PlotShapes(ismphtfe *shapeSmallSquare, Clrmph , 0, He, 12) ; PlotShapes(ismpltfe *shapeSmallSquare, Clrmpl, 0, Le, -12) ; showhtflvls = ParamToggle("Show HTF levels", "No|Yes", 1) ; Clrhtflvl = colorPaleGreen ; //Plot(2, "", IIf(ismph , colorBlue, IIf(ismpl, colorRed, colorGrey40)), styleArea|styleOwnScale, 0, 100) ; //Plot(4, "", IIf(ishtfmph , colorBlue, IIf(ishtfmpl , colorRed, colorGrey40)), styleArea|styleOwnScale, 0, 100) ; if (showhtflvls ) { mphhtf = ValueWhen(ismphtfe , He, 1) ; mplhtf = ValueWhen(ismpltfe , Le, 1) ; x = LineArray(0, SelectedValue(mphhtf), (BarCount-1), SelectedValue(mphhtf)); Plot(x, "", Clrhtflvl , styleDashed); x = LineArray(0, SelectedValue(mplhtf), (BarCount-1), SelectedValue(mplhtf)); Plot(x, "", Clrhtflvl , styleDashed); } //Plot(2, "", IIf(ismphtfe , colorRed, IIf(ismpltfe , colorBlue, colorGrey40)), styleArea|styleOwnScale, 0, 100) ; //Plot(4, "", IIf(ismph, colorRed, IIf(ismpl , colorBlue, colorGrey40)), styleArea|styleOwnScale, 0, 100) ; } _SECTION_END();`````` #### navinbhatia100 ##### New Member Hello Dear,i need a afl,those will scan first 15 mints volume break out. cond. 1-tell me the volume of first 15 mints(total volume at 9:30) cond. 2-15 days avg. of first 15 mints volume. cond. 3-today volume is 1.5 times of avg. volume. i was write a afl about it but it is not working properly,can you please write it for me. #### toughard ##### Well-Known Member Hi, Trying to obtain the value of today's highest volume bar's high kindly help!! #### kriya7 ##### Member I have an AFL for vwap as under _SECTION_BEGIN("VWAP"); /* The VWAP for a stock is calculated by adding the dollars traded for every transaction in that stock ("price" x "number of shares traded") and dividing the total shares traded. A VWAP is computed from the Open of the market to the market Close, AND is calculated by Volume weighting all transactions during this time period */ Bars_so_far_today = 1 + BarsSince( Day() != Ref(Day(), -1)); StartBar = ValueWhen(TimeNum() == 091500, BarIndex()); TodayVolume = Sum(V,Bars_so_far_today); IIf (BarIndex() >= StartBar, VWAP = Sum (C * V, Bars_so_far_today ) / TodayVolume,0); Plot (VWAP,"VWAP",colorOrange, styleThick); _SECTION_END(); I just need to add dotted lines of any colour for closing Vwap of previous 3 days. I will be grateful if anybody can add #### shri_r3 ##### Active Member Hi Today I tried to adjust stock split for jswsteel in amibroker 6 . Earlier in 5.7 version it automatically detected ratio and split date but now in amibroker ver 6 it does not. I tried to enter manually but with this shows gap up in chart with todays price also divided by same ratio.Tried for day before split, reversed ratio ect but cant get continous chart after split, there is gap down from split date. Same problem when tried to adjust bonus for Enginersin scrip. Can this done using some afl ? Thank you #### PoorBoy ##### New Member Hi Happy_Singh - I use Amibroker but don't code well at all and it's been hard getting help. I would like to have a system that trades the ES S & P mini futures intraday, planning to use 1 minute bars. Here is what I plan: 1) I want to backtest trade entry only on the 2nd or 3rd touch of the same new high or low of day, obviously when a higher high or lower low wasn't also hit. In other words, each touch of that new level would have to be the highest or lowest to that point. So if the ES traded up to 2140.25, HOD, then pulled back a couple of ticks, then went back up to 2140.25, that would be the 2nd touch, and would trigger a trade entry. I would backtest 2nd touch only, 3rd touch only, etc. You can comment scenarios and leave the one active, and I will backtest each one separately. Sometimes the system will trade in the direction of the new HOD/new LOD, and sometimes it will fade it for a few ticks, depending on values of some indicators. 2) One of the indicators will look at 4 ETF tickers to determine underlying strength/trend day up or trend day down. Perhaps user-defined function such as MktLeaders would simplify the entry rules. So I need to determine if they are up ON THE DAY over the previous days' close. I would like this to look at all 4 to see how many of these are up, and also how many are down, on the day. For example, I will backtest entry long when 2 of the 4 are up on the day, 3 are up, or all 4. Conversely, if X number of these 4 ETFs are down, a sell signal is created. For now I will simply call out these tickers A, AA, B, and C. I did get some support (please see below) but feel that it is not correct, as this is an intraday trading system. I look to see if those 4 ETFs are up on the day over the previous days' close. So don't we need a '-1' at the end of the 2nd half of the code? No telling when/if I will get response using standard channels so any help would be appreciated! I'm not even totally sure how to integrate that last line of code into the entry rules. Thank you so much for any help you could give me here, Poorboy 'you could check the condition for a list of symbols and sum up the values, e.g. like this: cond1 = Foreign("symbol1", "C") > Foreign("symbol1", "O"); cond2 = Foreign("symbol2", "C") > Foreign("symbol2", "O"); cond3 = Foreign("symbol3", "C") > Foreign("symbol3", "O"); total = cond1 + cond2 + cond3; condFilter = total == 3;///' #### Singhraja ##### Active Member Happy singh sir you shared inverted chart afl but there is no scaling on right side if you please rectify with scaling I need 10 point scale for nifty I will be thankful.

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drosofff 12/26/2016 - 4:22 PM ## Various spirales Various spirales ``````theta=seq(0,10*pi, by=0.001) # simple spirale; power of theta determines the acceleration x=theta^4 * cos(theta) y=theta^4 * sin(theta) plot(x,y, type="l", col="darkblue", lwd=5) # a "lasso" spirale x= log(theta) * cos(theta) y= log(theta) * sin(theta) plot(x,y, type="l", col="darkblue", lwd=5) # with amazing phenomena is changing the range of theta and multiplying by cos or sin(x) or sin(y) # example: theta=seq(-pi/2,pi/2, length.out=1000) x= log(theta) * cos(theta) * cos(x) y= log(theta) * sin(theta) * sin(y) plot(x,y, type="l", col="darkblue", lwd=5) # "Cesar" compression # work on limites to recover the stack theta=seq(0,10*pi, length.out=1000) x= log(theta) * cos(theta) * sin(log(theta) * cos(theta)) y= log(theta) * sin(theta) * sin(log(theta) * sin(theta)) plot(x,y, type="l", col="darkblue", lwd=5) # Another very nice one; work on colours needed theta=seq(0,10*pi, length.out=1000) x=theta^1/2 * cos(theta) * sin(theta^1/2 * cos(theta)) y=theta^1/2 * sin(theta) * sin(theta^1/2 * sin(theta)) plot(x,y, type="l", col="darkblue", lwd=1) # gribouilli d'artiste theta=seq(0,10*pi, length.out=20000) x=theta^2 * cos(theta) *sin(theta^2 * cos(theta)) y=theta^2 * sin(theta) *sin(theta^2 * sin(theta)) plot(x,y, type="l", col="darkblue", lwd=1) ``````

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# Need help in Painting the Barn I am not getting what this problem https://usaco.guide/silver/prefix-sums-2#problem-usaco-919 FJ applied several coats of paint on the farm wall… let us consider the wall in image As stated in the question FJ paint the wall in form of rectangles, so he first paint the red rectangle (colors are here only for better understanding, In problem there’s only a single color) , blue and lime. Now what we want to find that area which is covered with exactly `k` coats. `coat on a single square = No. of rectangles have that square in common` we can clearly see that the middle (yellow part) have 3 coats and two colored part have 2 coats.

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mersenneforum.org Primes in π Register FAQ Search Today's Posts Mark Forums Read 2017-07-04, 15:09 #199 ATH Einyen     Dec 2003 Denmark 32×5×67 Posts Remaining 5,376 pi prime candidates 750K-1M digits sieved to 245G plus a tiny bit higher non-consecutive ranges: picandidates750K-1M.txt 2018-03-30, 19:56 #200 davar55     May 2004 New York City 423210 Posts Any progress on this curious number a(20)? What's the likelihood that a 750k-1M digit candidate will be a PRP? Or that all of the candidates in that range will be composite? 2018-03-31, 01:02   #201 J F Sep 2013 23×7 Posts Quote: Originally Posted by davar55 Any progress on this curious number a(20)? What's the likelihood that a 750k-1M digit candidate will be a PRP? Or that all of the candidates in that range will be composite? #20 at 833K digits atm, no PRP. Quick (and very rough) approximation that a random pick with n decimal digits is prime: 1 : 2.3n Chance to find none between 750K and 1M is around 90%. 2018-08-09, 13:24 #202 davar55     May 2004 New York City 23·232 Posts Any news/progress on a(20)? If things continue as they're going, approximately when will 1M digits be reached? How significant would the next trial value be, if found probably prime? 2018-08-31, 20:44   #203 davar55 May 2004 New York City 108816 Posts Quote: Originally Posted by J F #20 at 833K digits atm, no PRP. Quick (and very rough) approximation that a random pick with n decimal digits is prime: 1 : 2.3n Chance to find none between 750K and 1M is around 90%. Thank you. I sometimes forget the niceties. There's no way to know for sure (yet) that there is or isn't a prime located at the position a(20) in pi. If there is, and it's relatively long, these efforts to find it are interesting as will be the result. If there is no prime at that position, proving which would probably be daunting, then we've hit on an unusual numerical singularity. 2019-03-14, 12:46 #204 paulunderwood     Sep 2002 Database er0rr 353410 Posts You can now go up to 31.4 trillion digits Last fiddled with by paulunderwood on 2019-03-14 at 12:47 2019-03-14, 19:03 #205 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 10001101110012 Posts Wife of Pi ... Attached Thumbnails 2019-03-14, 19:05 #206 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 13·349 Posts Pi In trouble. ... Attached Thumbnails 2019-03-19, 13:12   #207 davar55 May 2004 New York City 23·232 Posts Quote: Originally Posted by paulunderwood You can now go up to 31.4 trillion digits Wow. If a(20) grew that large, for the sake of argument, what resources would be needed to prove a 31.4 trillion digit number prime (or probably prime)? 2019-03-19, 13:38   #208 paulunderwood Sep 2002 Database er0rr DCE16 Posts Quote: Originally Posted by davar55 Wow. If a(20) grew that large, for the sake of argument, what resources would be needed to prove a 31.4 trillion digit number prime (or probably prime)? Deep Thought running Primo? Probably to the end of time! 2019-03-19, 14:15   #209 davar55 May 2004 New York City 23·232 Posts Quote: Originally Posted by paulunderwood Deep Thought running Primo? Probably to the end of time! I don't doubt Deep Thought's abilities, but Hal could probably do it in half that time. Similar Threads Thread Thread Starter Forum Replies Last Post carpetpool Miscellaneous Math 3 2017-08-10 13:47 emily Math 34 2017-07-16 18:44 Mickey1 Miscellaneous Math 1 2013-05-30 12:32 Unregistered Information & Answers 0 2011-01-31 15:41 troels munkner Miscellaneous Math 4 2006-06-02 08:35 All times are UTC. The time now is 18:10. Mon Jan 25 18:10:51 UTC 2021 up 53 days, 14:22, 0 users, load averages: 2.64, 2.56, 2.61

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# Efficient algorithm for 'unsumming' a set of sums Given a multiset of natural numbers X, consider the set of all possible sums: $$\textrm{sums}(X)= \left\{ \sum_{i \in A} i \,|\, A \subseteq X \right\}$$ For example, $\textrm{sums}(\left\{1,5\right\}) = \left\{0, 1, 5, 6\right\}$ while $\textrm{sums}(\left\{1,1\right\}) = \left\{0, 1, 2\right\}$. What is the most efficient algorithm for calculating the inverse operation (measured in terms of the size of the input set of sums)? Specifically is it possible to efficiently calculate any of the following: 1. Whether a given set is a valid set of sums. (For example, $\left\{0,1,2\right\}$ is valid but $\left\{0,1,3\right\}$ is not.) 2. A multiset that sums to the given set. 3. The smallest multiset that sums to the given set. (For example, $\left\{1,2\right\}$ and $\left\{1,1,1\right\}$ both sum to $\left\{0,1,2,3\right\}$ but the former is smaller.) • Could you possibly give us the multiset of sums rather than the set of sums? This would create a pleasing symmetry (seeing as you start with a multiset of values). – D.W. Aug 25 '15 at 5:20 • Another question - are you most interested in theoretical results (e.g., asymptotic complexity), or practical solutions (schemes that might work OK in practice)? If the latter, do you have an idea of typical values for parameters: e.g., the size of the multiset X, the size of the largest element in the multiset X, the highest multiplicity? This might affect whether it is reasonable to apply a "big hammer" like an ILP solver or SAT solver. – D.W. Aug 25 '15 at 6:53 • @D.W. I'm definitely interested in using the set of sums rather than the multiset (though that may be an interesting problem too). Also, this was originally a recreational mathematics problem, so I'm mainly interested in complexity bounds rather than a practical solution. – Uri Zarfaty Aug 25 '15 at 8:24 • If you're given the multiset of sums, then it is pretty straightforward to do this greedily (see for example math.stackexchange.com/questions/201545/…). – jschnei Aug 26 '15 at 18:46 • @UriZarfaty the set given as input is already sorted? Finally this is set or multiset? Comment still suggest that you want pure set. – Evil Jan 29 '16 at 6:40 # Solution Solution has two parts. First we discover minimal set, then we prove that it can represent the power sum set. The solution is adjusted for programming implementation. ## Minimal set algorithm 1. Find maximal element $a_{m}$ from the sum (multi)set. $P$, the potential minimal (multi)set is initially empty. 2. Unless there is only one group, represent $a_{m}$ in all possible ways as a pair of sums that add up to $a_{m}$, $S_{ij}=\{(a_{i},a_{j})|a_{i}+a_{j}=a_{m}\}$ 3. Check that all elements from the set of sums are included. 4. Find maximal element $a_{s}$ from all $S_{ij}$ (meaning together) with the following property: for each $S_{ij}$, $a_{s}$ is either in $S_{ij}$, or we can find $a_{p}$ from the set of sums so that $a_{p}+a_{s}$ is in $S_{ij}$. 5. If it is the case that $S_{ij}$ does not contain $a_{s}$, just the sum $a_{s}+a_{p}$, remove $a_{p}+a_{s}$ from $S_{ij}$ (or just set a mark to ignore it) and insert $a_{p}$ and $a_{s}$ in $S_{ij}$ instead. 6. If an element is present in every $S_{ij}$ remove it from all $S_{ij}$ once (or just set a mark to ignore it and not to touch it any longer) and add it to the list of elements of potential minimal set $P$. 7. Repeat until all $S_{ij}$ are empty 8. If some of $S_{ij}$ remains non-empty and we cannot continue, try again with the maximum value from all $S_{ij}$. 9. Recreate the recursive steps without removals and continue with power set coverage algorithm over $P$. (Before this, you can make a safe-check that $P$ includes all elements that cannot be represented as a sum of two elements so they must be in underlying set for sure. For example, the minimal element must be in $P$.) (10. Observe that a minimal set solution which is the goal of the algorithm cannot contain more than one repetition of the same number.) Example: $$\{2,3,5,7,8,10,12,13,15\}$$ Represent 15 in all possible ways as a sum of two numbers from the set of sums. $$(13,2),(12,3),(10,5),(8,7)$$ Try to find maximal number that is in all groups or that can be represented as a sum. Obviously we can start searching for it from 8, there is no point going above it. 13 from the first group is 13=8+5 so 13 is fine, but 12 from the second group is not fine since there is no 4 to make 12=8+4 in the set of sums. Next we try with 7. But immediately 13 cannot be covered, there is no 6. Next we try 5. 13=5+8, 12=5+7, 10=5+5, and for the last either 8=5+3 or 7=5+2 but not both. The groups are now: $$((5,8),2),((5,7),3),((5,5),5),((5,3),7)$$ 5 is repeating in all groups so we extract it $P=\{5\}$. We extract 5 only once from each group. $$(8,2),(7,3),(5,5),(3,7)$$ Obviously there is no point going higher than 5 so we try 5 again. 8=5+3, 7=5+2, so all is fine $$((5,3),2),((5,2),3),(5,5),(3,(5,2))$$ Extract one 5 again from all groups since it is repeating. (This is not common but our case is deliberately created to display what to do in case we have repetitions.) $P=\{5,5\}$ $$(3,2),(2,3),(5),(3,2)$$ Now we try with 3 and have 5=3+2. Add it to the group. $$(3,2),(2,3),(3,2),(3,2)$$ Now extract 3 and 2 since they are repeating everywhere and we are fine $P=\{5,5,3,2\}$ and the groups are empty. $$(),(),(),()$$ Now, we need to recreate recursive steps without removals, this simply means doing the above without really removing the elements from $S_{ij}$ just placing them in $P$ and marking not to alter it any longer. $$(13,2),(12,3),(10,5),(8,7)$$ $$((5,8),2),((5,7),3),((5,5),5),((5,3),7)$$ $$((5,(5,3)),2),((5,(5,2)),3),((5,(3,2)),5),((5,3),(5,2))$$ ## Power set coverage The purpose of this part is to check if the found minimal set is able to cover the power sum set. It is possible that a found solution can cover all given sums, but that they are not power set sums. (Technically, you could simply create a power sum set from the found minimal set and check if each sum, as power set dictates, is in the initial sum set. This is all that just merged with what we already have, so nothing is wasted. You can do this part while rewinding the recursion.) 1. Encode all elements from the minimal set using successive powers of 2. The order is not important. Encode the same element with a new value as many times as it is repeating. Start from C=1, every next element has C=2C. $$(2=[1],3=[2],5=[4],5=[8])$$ 1. Replace the elements in the restored recursion list, $$((5,(5,3)),2),((5,(5,2)),3),((5,(3,2)),5),((5,3),(5,2))$$ with the encoding: 2 with 1, 3 with 2, 5 with 4, and another 5 with 8. Observe that each element has different encoding even though they are repeated. $$((4,(8,2)),1),((4,(8,1)),2),((4,(2,1)),8),((8,2),(4,1))$$ 1. Collect all intermediate sums, at the moment we have (1,2,4,8) $$((4,(10)),1),((4,(9)),2),((4,(3)),8),((10),(5))$$ Intermediate sums $(1,2,3,4,5,8,9,10)$ $$((14),1),((13),2),((7),8),(15)$$ Intermediate sums $(1,2,3,4,5,8,9,10,13,14,15)$ $$\{(15),(15),(15),(15)\}$$ 1. Check that the result is $2^m-1$, where $m$ is the number of elements in the solution, in the example $m=4$ 2. Collect missing numbers from $1$ to $2^m-1$ in the intermediate sum list $(6,7,11,12)$ 1. Justify their absence in the following manner: represent each number in binary form $(6=0110_2)$ $(7=0111_2)$ $(11=1011_2)$ $(12=1010_2)$ $6$ represents the sum of 3+5 since $0110_2$ is covering second and third element from $(2=[1],3=[2],5=[4],5=[8])$. The sum of these elements, 8, is listed in the initial sum list $\{2,3,5,7,8,10,12,13,15\}$, so all is fine. $7$ represents the sum of 2+3+5 since $0111_2$ is covering first three elements from $(2=[1],3=[2],5=[4],5=[8])$. The sum of these elements, 10, is listed in the initial sum list so all is fine. $11$ is 2+3+5, and 10 is in the list. $12$ is 3+5, and 8 is in the list. If any binary representation corresponds to the sum that cannot be found, report that there is no solution. So all is fine and $(2,3,5,5)$ is the solution. It is the minimal solution as well. # Discussion It was necessary to provide the algorithm that is going to check if the sums cover the power set completion, which is what is hidden in the binary expansion. For example if we exclude 8 and 7 from the initial example, the first part would still provide the solution, only the second part would report missing combinations of sums. First part of discovering the possible minimal set is $mnlog(m)$ which comes to $m\log^2(m)$: we are looking around $m$ elements $n$ times having one $\log(m)$ binary search. The last part is done in recursion return and it does not require any special effort, we are searching over less than $m$ elements, we need binary form which is $\log{m}$ and we have one addition and search if the sum is in the list, so together it is again about $m\log^2(m)$. If we assume that the number of elements in the power sum set corresponds to the number of partitions of the largest element in the underlying set then the complexity is around $m\log^3(m)$. Any of the two justifies the initial sorting in order to find the largest element. Parts of the algorithm assume that we can find the pair of sums in linear time and this requires sorting. ### Incorrect start First part of the algorithm may fail, if we have started it on the wrong foot. For example $2,3,4,5,6,7,8,9,10,11,12,13,15$ has the basic solution $2,3,4,6$ which you get if you start algorithm from 6. However we can start our algorithm from 7, since there is nothing in step 4. that would say not to, and lock ourselves in, the algorithm cannot end properly. The reason is that 7 is 7=4+3 and 4 and 3 are in the solution. So locked algorithm does not always mean that there is no solution, just to try again with lower initial value. In that case, some ideas about the possible values are hidden within remaining $S_{ij}$. That is why we suggested starting from there in case of failure. Another example, if you miss and start algorithm from 5, you would get $5,4,3,3$ but this one does not include 2. Notice that this algorithm is not going to give a derived solutions like $2,2,3,4,4$, which we got simply by turning 6 into 4 and 2 in the solution $2,3,4,6$. There are special rules that cover these versions. The purpose of this algorithm is to provide a solution once we have started it all correctly. ### Improvements Step 4. is the one that could be upgraded in this manner: instead of maximal we could try out every element in descending order that satisfies the given condition. We create a separate branch for each. If some branch does not give a solution, cancel it. For example for $2,3,4,5,6,7,8,9,10,11,12,13,15$ we could try in the first round $7,6,5,4$ in separate ways since all of them are passing the first test. (There is no reason to use 2 or 3 since we know they have to be in the underlying set.) and simply continue that way all around until we collect all versions that can reach the end. This would create a full-coverage solution which would discover more than one underlying set. Another thing, since we know that we cannot have more than one repetition if the case is minimal, we can incorporate this in our algorithm. Overall, the condition in step 4. that a number must repeat in every group or have ability to create a sum is strong enough to get us out of direct exponential waters, which would be an algorithm of simply trying out every combination and creating the power set over each until we find a match. • More broadly: I see a textual description of an algorithm, but (a) no pseudocode, and (b) no proof of correctness. Why do you think that this approach provides an algorithm that will work correctly on all possible inputs? What's the justification? Do you have a proof of correctness for this? – D.W. Jan 23 '16 at 2:09 • I think the problem has taken around 30 hours of work all together (30 times hourly rate, well...). But there is no paid option. – user26317 Jan 29 '16 at 0:05 • Finally read the answer in the detail it deserved. Great work! – Uri Zarfaty Jan 29 '16 at 11:37 NOTE: This does not quite work in general, see Uri's counterexample below. One way of achieving at least 1. and 2. for a given set $Y$ (minimality requires a bit of tweaking) is (sorting $Y$ first, if necessary): • Check whether $0\in Y$. If not, there is no solution. • Let $y$ be the smallest positive number in $Y$. Then $y$ must also be in $X$, if it exists (otherwise it would be the sum of smaller positive numbers, which would also occur in $Y$). • Let $z_1<\dots<z_n$ be the remaining members of $Y$. We will try to find a set $Y'$ such that $Y = Y' + \{0,y\}$. Obviously $0$ must be in $Y'$. For $i=1,\dots,n$: if $z_i+y\in Y$, add $z_i$ to $Y'$; otherwise, if $z_i-y\notin Y$, there is no solution; otherwise (i.e. if $z_i+y\notin Y$, but $z_i+y\in Y$), we don't need $z_i$ in $Y'$. • Repeat recursively with $Y'$, collecting the minimal elements $y,y',\dots$ into a multiset. This is your solution iff you end up with an empty set.} In each recursive step, the size of the set decreases by at least $1$ (since we exclude the least element $y$), so the number of steps is in $O(n)$. Each step contains a single iteration over the current set, for an $O(n^2)$ total complexity (assuming unit costs for arithmetic operations). Finding a minimal solution (note that this is not necessarily unique; for example, for $Y=\{0,1,3,4,5,6,7\}$ we have $\{0,1,3,4,6\}$ and $\{0,1,3,5,6\}$) is slightly more involved: after finding the minimum $y\in Y$, you would analyze the arithmetic progressions $\{a+k\cdot y\}$ in $Y$, reject if one of them is a singleton, and otherwise pick alternating members for $Y'$; if a progression has odd length, you need to pick some pair of successive members, hence the non-uniqueness. • Is it obvious that Y' doesn't lead to a dead end? After all there can be many Y's such that Y=Y'+{0,y}. For example {0,1,2,3,4} = {0,2,3}+{0,1} = {0,1,2,3}+{0,1} but the former decomposition leads to a dead end. – Uri Zarfaty Aug 24 '15 at 13:03 • That is true, and is a real problem. I'll have to see if it can be fixed. Thanks! – Klaus Draeger Aug 24 '15 at 13:15 • @UriZarfaty, I wonder if Klaus's algorithm might be correct for the special case where you start with a set rather than a multiset (i.e., no item in the multiset has multiplicity more than 1). Do you have a counterexample? Maybe it's interesting to first look for an algorithm for the special case where you start with a set rather than a multiset. If it works for that case, we might be able to generalize it to work for a multiset, e.g., by trying to find a set $Y'$ and a maximal number $k$ such that $Y=Y'+\{0,y,\dots,y\}$ where $\{0,y,\dots,y\}$ contains $k$ copies of $y$, then recurse on $Y'$. – D.W. Aug 24 '15 at 20:16

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Prove that angles : AOD - BOC=2×BXCfig attached... 2 by tanishqsingh yes This is incomplete question,I can prove if given that chord AB and CD are equal. even i can do that.. we do not need any such thing. yes yes 2014-10-01T18:49:41+05:30 Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest. See diagram. there are two of them. The diagram can be symmetric or asymmetric. in both cases, the proof is same.  The proof can be done in two ways. Mark the angles as shown in figure.  As OA, OB, OC and OD are radii and are equal, OAD, OAB, OBC, OCD form isosceles triangles. So the two angles at the base are same like x, y, z and ω. In OAD,  θ = 180 - 2y In triangle BOX, x = exterior angle = sum of angle BOX + angle BXO In triangle COX,  z = exterior angle = sum of angle COX + angle CXO So x + z = (BOX + COX) + (BXO + CXO) = α + β Now in triangle AXD, β = 180 - (x+y) - (y+z)  = 180 - (x+z) - 2y = θ - α - β So   θ = α + 2 β     or AOD - BOC = 2 BXC ============================================== Alternately, in quadrilateral ABCD,   2 y + 2 x + 2 ω + 2 z = 2π so                  x + y + z + ω = π in AOD,         θ = π - 2 y in BOC,        α = π - 2 ω in XAD,       β = π - 2 y - x - z  =  θ - x - z R HS = α + 2 β = π - 2 ω + 2 θ - 2 x  - 2 z = 2 θ - π + 2 (π - ω - x - z ) = 2 θ - π + (2 y) = 2 θ - (π - 2 y)   =  2 θ - θ  =  θ L H S i hope it is simple enough

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Question # A marketing research company hired by Pepsi is interested in estimating the proportion of cola customers... A marketing research company hired by Pepsi is interested in estimating the proportion of cola customers in Ontario who prefer Pepsi to other brands. A simple random sample of 120 Ontario cola customers was selected and 45% of them reported favoring other brands over Pepsi. What is the upper limit of the large sample 95% confidence interval for the true proportion of cola customers in Ontario who prefer Pepsi to other brands? (Hint – use 6 decimal places for intermediate calculations to avoid too much rounding error.) • A. 0.639 • B. 0.089 • C. 0.088 • D. 0.636 • E. 0.539 Solution : Given that, n = 120 Point estimate = sample proportion = =45% = 0.45 1 - = 1- 0.45 = 0.55 Z/2 = 1.960 Margin of error = E = Z / 2 * (( * (1 - )) / n) = 1.960 * ((0.45*(0.55) /120 ) = 0.089 A 95% confidence interval for population proportion p is , - E < p < + E 0.450- 0.089 < p < 0.450+0.089 0.361< p < 0.539 The 95% confidence interval for the population proportion p is : 0.361,0.539 Upper limit = 0.539 E. 0.539 #### Earn Coins Coins can be redeemed for fabulous gifts.

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Online service Mon-Sat Day: 8am to 6pm How to find us News Center 1. Home 2. Ore beneficiation equipment 3. calculation of screening capacity of vibrating screen # Calculation Of Screening Capacity Of Vibrating Screen vibrating screen capacity calculations meka,the screening area is calculated by the formula defined below: qu is the amount (t/h) of undersize particles in the feed. qspec is the specific screening capacity. s is the safety factor between 11.4 and depends on how well the screening material properties..mechanical engineering the journal of the american society ,ilow coal breaker having capacity of 6000 tons per day was erected in 130 days . determination of true form of cipal makes . thread on inclined section . screen , mitchell vibrating description of the mitchell vibrating screen . 1000 ib . the motor - actuated vibration is applied continuously to screening area by means .vibrating screen efficiency calculation,re vibrating screen efficiency calculation qms(f) = mass flow rate of solid feed. qms(o) = mass flow rate of solid in the screen overflow. qms(u) = .coal handling plant in thermal ,this process involves screening of fine , coarse and wet coal. vibrating screen; roller screen. crushing process. this process involves crushing the coal to a size as per requirement of components and working of roller screen it works on the basic formula of collection, separation and filtration.. ### Intelligent Prediction Of Sieving Efficiency In Vibrating Screens in order to effectively predict the sieving efficiency of a vibrating screen, vibrating screen such as mesh aperture size, screen length, inclination angle, vibration amplitude, the schematic diagram of total efficiency calculation is shown in figure 2. of screen slot size, particle size, and duration of screening, international ,vibrating screen efficiency calculations,an efficiency of 99 will equate to a significant loss of capacity. screening efficiency is the ratio of undersize material in the feed that actually passes from the ### Principles Of Mineral Processing another way to calculate bed depth follows : screen length , ft depth of dry rock bed 6 to 10 1.5 methods for selecting vibrating screens have evolved from basic capacity data acquired from fullscale screening equipment , where modifying ,modal calculation results of vibrating screen,download table modal calculation results of vibrating screen from vibrations, screening and mass screening researchgate, the professional network the bending deflection frequency improve greatly after structural size optimization. ### Distributed Control System (Dcs) coarse screening fine screening combi screening screen baskets vii for production capacity vii for pulp quality vii for energy efficiency vii for and air conditioning asset management information services vibration monitoring sea optimal risk management investments net working capital calculation of key figures.,(nafld) and nonalcoholic steatohepatitis (nash),looking at these developments, calculations show that the incidence of hcc urgent need to find reliable noninvasive biomarkers and screening the overall capacity of these cells to synthesize typical liver proteins but also to monitor the development from nafld to nash and can be used to screen ### Required Screening Area Formula actual of material in feed to the screen deck that is one-half the size of a specified aperture. (adjusts factor 'a' to suit conditions). factor ,length of vibrating screen calculation,approximate tons thru screen per square foot screening area per 24 hours, wet or dry. moisture and screen efficiency screen capacity of crushing plants screens ### Vibrating Screen Efficiency Calculations an efficiency of 99 will equate to a significant loss of capacity. screening efficiency is the ratio of undersize material in the feed that actually passes from the ,how to calculate vibrating screen,one of the most important things to check on a periodic basis is the shape of the screen's vibratory motion. read more. what is the screening capacity of vibrating ### The Importance Of Vibrating Screen Efficiency on screening decks alone, vibrating screen efficiency uses the screening capacity is now noted in ink, or it's mapped into a database, all so of course, if these calculations are to work properly, certain process variable ,p&q university lesson 8- screening,in other words, the vibration of the screen deck agitates the material causing it screening efficiency is calculated as the percentage of the undersize the screen, the key to optimum screening is maximizing capacity without ### Vibrating Screen Working Principle screen size opening, number or inch two common methods for calculating screen efficiency depend on whether generally, manufacturers of screening units of one, two, or three decks specify ,amit 145 lesson 1 industrial screens mining mill operator ,on inclined screens, the vibration is caused by a circular motion in a vertical plane upon stratification, the particles having a size less than the smaller screen screening efficiency can also be determined by using the two product formula. ### Calculate The Capacity Of Vibrating Screen approximate tons thru screen per square foot screening area per 24 hours, wet or dry. moisture and screen efficiency screen capacity of crushing plants screens ,(pdf) innovative calculation method of the productivity of ,the article studies the productivity of the vibrating screen used in the source of origin as well as the granule size of granular mixtures lead smaller than the mesh hole of the lower screening sieve, also referred to as the. ### Wills' Mineral Processing Technology An Introduction To The the calculated screen area a is then a5 4131:1330:82 402:5 applying a safety vibrating screens are the most important and versatile screening machines for they perform size separations from 300 mm down to 45 m and they are used ,how calculate screen efficiency,screen efficiency calculation - crushing, screening and conveying 2re vibrating screen efficiency calculation qms f = mass flow rate of solid feed. current screen capacity calculations do not take into consideration enough of the factors ### As Calculating The Capacity Of A Vibrating Screen approximate tons thru screen per square foot screening area per 24 hours, wet or dry. moisture and screen efficiency screen capacity of crushing plants screens ,vibrating screen capacity xls,screen efficiency problem screen capacity formula t s = a x b x c x d x e x f s = screening area t = tonnage through the deck a = capacity in tph per ### Vibrating Screen Motor Power Calculation vibrating screen power calculation jacobshopeacademyvibrating screen type these machines take advantages of large capacity and high efficiency, and some of vibrating screen motor power calculation pdf principles of screening and ,capacity calculation of vibrating feeder,[randpic]calculate vibrating feeder capacity - iccoss2017.co.zacalculate vibrating screen capacity calculations throughput per square foot of the high capacity stack sizer screening machine consists of up to five decks ### (Pdf) Research On Structural Design Of Coal Crusher House transport, raw coal screening, raw coal breakage and a series. of functions in an veying trestle [2], raw coal screen strati cation, coal seam. crushing and the coal installed capacity, coal consumption and equipment, etc. when the ic calculation and vibration isolation design of structure. and structural

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1. Member Join Date Aug 2010 Posts 70 Rep Power 0 return question for method Ok, I am a little confused here as to what I can do to return an int called num. I have to return it to make the program work to the professors specifications, but it is confusing. here is the header: Java Code: `public static int solve(double [] eqn, double [] roots)` I cant return this "int num" because all equations are in a double. I keep getting the error "Cant change result from int to double/int[]" How do you guys switch from a double to an int? I assume you use variables, right? 2. Senior Member Join Date Jun 2007 Location Bali, Indonesia Posts 762 Rep Power 14 Hi, You can convert from double value to int value using the type cast. If you look at the Double class you can also find a method that return an int value from the Double instance. But you should be aware that converting from double to int value you will lost the fractional value of your original double value. Last edited by wsaryada; 09-02-2010 at 06:17 AM. 3. Member Join Date Aug 2010 Posts 70 Rep Power 0 I dont mean to be facetious, but is there another way? My code uses two double arrays, but I need to return an int. If i use cast, most likely the professor will not approve of it, since he wants me to "program it all out". I am essentially not able to use Java utilities like comparing arrays and such - I have to do the manual work only. Does that make any sense? thanks for your response though. I wish I could use it. 4. I don't think your professor can disprove of it, honestly. If your numbers are all doubles, somewhere you're going to lose fractional data if you're required to return an int. Whether that's through .intValue() or through (int) casting, you need some way to return it as an int. I mean, in theory, you could put the double into a string and capture everything to the left of the decimal... then convert that to an int using parseInt, but that's just stupid to be honest. PS: You can also use Math.floor and Math.ceil, but those still return doubles. 5. My guess is that the method is supposed to return the number of roots and the roots need to be placed in the array passed to the method. The number of roots is an integer of course. kind regards, Jos 6. Moderator Join Date Apr 2009 Posts 13,541 Rep Power 27 Yes, asking us how to turn the inputs into an output without telling us what the method is supposed to actually do is unlikely to result in a correct answer. So, can you confirm Jos' suspicions about what this method is supposed to actually do? 7. Member Join Date Aug 2010 Posts 70 Rep Power 0 yeah, Jos said it. I apologize again for my lack for explanation. I was trying to ask for some direction without placing homework on the forum. I do not want anyone to think I am cheating vs. asking for help online. next time though, I will just post some of what it is asking for. Should I use a variable to do what Jos said? 8. Should I use a variable to do what Jos said A variable is much easier to use than hardcoded literals. 9. Member Join Date Aug 2010 Posts 70 Rep Power 0 I had some extra help and got it solved. Thanks for telling me about the cast - I did not know that. Java has some pretty cool packages. I had some extra help and got it solved. Thanks for telling me about the cast - I did not know that. Java has some pretty cool packages. What cast? kind regards, Jos 11. Moderator Join Date Apr 2009 Posts 13,541 Rep Power 27 Post #2. Which is slightly worrying since we now know casting has nothing to do with this. 12. Originally Posted by Tolls Post #2. Which is slightly worrying since we now know casting has nothing to do with this. kind regards, Jos 13. Moderator Join Date Apr 2009 Posts 13,541 Rep Power 27 Imagine how complex it would be if it wasn't a SOLVED thread? Posting Permissions • You may not post new threads • You may not post replies • You may not post attachments • You may not edit your posts •

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# Prove that $\mathop {\lim }\limits_{(x,y,z) \to (0,0,0)} \left( {\frac{{{x^2}y - x{z^2}}}{{yz - {z^2}}}} \right)=0$ Prove that: For all $\epsilon>0$ exist $\delta>0$ which depends on $\epsilon$, such that: $$\left| {\frac{{2{x^2}y - x{z^2}}}{{yz - {z^2}}}}-0 \right|<\epsilon$$ ever that $$0 < \sqrt {{x^2} + {y^2} + {z^2}} < \delta$$ I find it very difficult to find $\delta$ in terms of $\epsilon$. Any suggestions to prove this? $$\mathop {\lim }\limits_{(x,y,z) \to (0,0,0)} \left( {\frac{{2{x^2}y - x{z^2}}}{{yz - {z^2}}}} \right)=0$$ thanks. - What is $\delta$ and $\epsilon$? And where is your actual question: In the title or in the body? – draks ... Jul 24 '12 at 9:39 Very hard to prove something that is false. So it is not surprising that you cannot find appropriate $\delta$: there isn't one. – André Nicolas Jul 24 '12 at 9:43 your questions do not match . Please check once . – Theorem Jul 24 '12 at 9:52 already clarified the question – mathsalomon Jul 24 '12 at 9:53 Clarify the title! Is there a 2 missing? – draks ... Jul 24 '12 at 11:21 Hint: Consider sequences \begin{align} (x_n,y_n,z_n)&=(n^{-1/2},2n^{-1},n^{-1})\\ (x_n,y_n,z_n)&=(0,2n^{-1},n^{-1}) \end{align} then you get \begin{align} \lim\limits_{n\to\infty}\frac{2x_n^2 y_n-x_nz_n^2}{y_n z_n-z_n^2}&=\lim\limits_{n\to\infty}(4-n^{-1/2})=4\\ \lim\limits_{n\to\infty}\frac{2x_n^2 y_n-x_nz_n^2}{y_n z_n-z_n^2}&=\lim\limits_{n\to\infty}0=0 \end{align} Thus we conclude that the limit $$\lim\limits_{(x,y,z)\to (0,0,0)}\frac{2x^2 y-x z^2}{y z-z^2}$$ doesn't exist. P.S. I used approach from this answer. - Norbert its generally easy to show that the limit doesn't exist compared to it exists. Is there a way to show that limit exists for multivariable case ? – Theorem Jul 24 '12 at 9:43 In general it is hard to show that limit does exist. But in most cases you had to make some tricky estimations and use standard inequalities – Norbert Jul 24 '12 at 10:01 @mathsalomon You are welcome! – Norbert Jul 24 '12 at 10:02 @Theorem: In 2D, we can take $r_\alpha(t)=(t,\alpha t)$ and put it into your function to find path wise limit of $f$ when $t$ tends to $0$. After simplifying the original function, if the limit of last expression approaches to zero then probably your original function has limit $0$ at $(0,0)$. Now, we have to use $\epsilon, \delta$ to prove your limit. – Babak S. Jul 24 '12 at 10:22 Ok I'll write in more detail – Norbert Jul 24 '12 at 10:50

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https://www.calculators.live/gemstones-carat-weight

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Gemstones Carat Weight Estimation Calculator Find the carat weight of gemstones using this online calculator. Select the Gemstone, its Facet Style Factor (ff) and enter the gridle length, gridle width, depth and average specific gravity in this gemstones carat weight estimation calculator to get the carat value. Carat weight for gemstones is standardized in the 20th century. It is denoted as "ct" and equal to 200 milligrams. Most of the gemstones are measured to the nearest hundredth of a carat. mm mm mm Result : Example: Calculate gemstones carat weight for Agate with Facet Style Factor as Emerald cut, having a gridle length of 5, gridle width of 4, depth of 6 and average specific gravity of 2.65. Solution: Gemstones Carat Weight Estimation = 5 x 4 x 6 x 2.65 = 0.509

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# Cheryl purchased 5 identical hollow pine doors and 6 identical solid oak doors for the house she is building. The regular price of each solid oak door was twice the regular price of each hollow pine door. However, Cheryl was given a discount of 25% off the regular price of each solid oak door. If the regular price of each hollow pine door was \$40, what was the total price of all 11 doors? Cheryl purchased 5 identical hollow pine doors and 6 identical solid oak doors for the house she is building. The regular price of each solid oak door was twice the regular price of each hollow pine door. However, Cheryl was given a discount of 25% off the regular price of each solid oak door. If the regular price of each hollow pine door was \$40, what was the total price of all 11 doors? A. \$320 B. \$540 C. \$560 D. \$620 E. \$680 Full explanation coming soon. Send us a note if you’d like this added to the express queue! You’ll find tons of practice questions, explanations for GMAT Official Guide questions, and strategies on our GMAT Question of the Day page. ## Here are a few other extra challenging GMAT questions with in depth explanations: Here’s a tough function question from the GMAT Prep tests 1 and 2: For which of the following functions is f(a+b) = f(b) + f(a) for all positive numbers a and b? And a very challenging word problem from the Official Guide. Almost no-one gets this one on the first try but there is a somewhat simple way through it: Last Sunday a certain store sold copies of Newspaper A for \$1.00 each and copies of Newspaper B for \$1.25 each, and the store sold no other newspapers that day. If r percent of the store’s revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p? Tanya’s letters from the GMAT Prep tests. This one often gets GMAT tutoring students caught up in a tangled net. With combinatorics it’s important to stay practical. We’ll take a look at how to do that in the explanation: Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address? Here’s an exponents puzzle that comes up a lot in GMAT tutoring sessions: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is This is one of the most difficult questions in the GMAT universe. That said, there is a simple way to solve it that relies on a fundamental divisibility rule every GMAT studier should know: For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is? ### GMAT Question of the Day Signup Sign up for 1 challenging GMAT question sent to you each week. • This field is for validation purposes and should be left unchanged.

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It is currently 20 Nov 2017, 09:05 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # How to score higher? Author Message Intern Joined: 20 Sep 2003 Posts: 1 Kudos [?]: [0], given: 0 Location: India ### Show Tags 21 Sep 2003, 09:52 00:00 Difficulty: (N/A) Question Stats: 0% (00:00) correct 0% (00:00) wrong based on 0 sessions ### HideShow timer Statistics Hi folks, I took GMAT a week ago and despite scoring consistently around 600(although it's considerd a bad score) I was severely suffering from Typhoid and got just 540, despite scoring 47 in math. I know I could have performed better in verbal, had I been better. I have scored 267 in TOEFL. I am retaking GMAT in a month a so. But still find difficulty how to get very good score esp in Verbal. I have referred Kaplan, Barrons and Cliff, but not sure what to do now since I have already referred then once. Please give me suggestions about how to improve the verbal score esp. I will be obliged to you.[/quote] Kudos [?]: [0], given: 0 Kaplan GMAT Prep Discount Codes EMPOWERgmat Discount Codes Jamboree Discount Codes SVP Joined: 03 Feb 2003 Posts: 1603 Kudos [?]: 308 [0], given: 0 ### Show Tags 21 Sep 2003, 23:07 This forum is not for such questions. It is for teaching only. Nevertheless, I would advise you to understand your weak skills in verbalism. What are they? Logic, reading, or grammar? Work on your weak skills over and over again. IMO: Unfortunately, an overwhelming majority of the prep materials are VERY weak when it comes to reading and logic. It is especially so for nonnative speakers like me. An explanation such as 'It is A because all the rest are wrong' infuriates me and leaves me none the wiser than I was before reading this s--t. To improve my verbal performance, I used LSAT materials. They are more difficult than those for the GMAT, but they are worth going through. As for grammar and idioms, you can find lots of them here, at this site. Kudos [?]: 308 [0], given: 0 Manager Joined: 19 Oct 2003 Posts: 72 Kudos [?]: [0], given: 0 Location: USA Re: How to score higher? [#permalink] ### Show Tags 23 Oct 2003, 09:01 Hi guy, How many time you read official preparation and other books? I go through it no less than 3 time but always find something new. Try not to reffer to the key. I take gmat like crazy last year but know I still have to take it. _________________ I have 2 month for gmat. Kudos [?]: [0], given: 0 CEO Joined: 15 Aug 2003 Posts: 3452 Kudos [?]: 924 [0], given: 781 Re: How to score higher? [#permalink] ### Show Tags 23 Oct 2003, 16:25 Nehal wrote: Hi folks, I took GMAT a week ago and despite scoring consistently around 600(although it's considerd a bad score) I was severely suffering from Typhoid and got just 540, despite scoring 47 in math. I know I could have performed better in verbal, had I been better. I have scored 267 in TOEFL. I am retaking GMAT in a month a so. But still find difficulty how to get very good score esp in Verbal. I have referred Kaplan, Barrons and Cliff, but not sure what to do now since I have already referred then once. Please give me suggestions about how to improve the verbal score esp. I will be obliged to you. [/quote] hey nehal Start working on your grammar skills and as stolyar pointed out, get hold of LSAT materials for CR and RC. For grammar, check out websters website. Read a lot of good american papers http://www.wsj.com and http://www.economist.com are good places to start. finally, write down every mistake you do. and go over those once a week. write back if you need any further help. good luck praetorian Kudos [?]: 924 [0], given: 781 Re: How to score higher?   [#permalink] 23 Oct 2003, 16:25 Display posts from previous: Sort by # How to score higher? Moderators: GMATNinjaTwo, GMATNinja Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

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# How to prove the radius of curvature at any point on a line? 1. Aug 8, 2009 ### catheee How to prove the radius of curvature at any point on a line? In a magnetic field, field lines are curves to which the magnetic induction B is everywhere tangetial. By evaluating dB/ds where s is the distance measured along a field line, prove that the radius of curvature at any point on a line is given by p= B^3 / [ B x( B * del) B] where do i start with this?? I have no idea what to do 2. Aug 8, 2009 ### gabbagabbahey Please do not create multiple threads for the same question. It is against forum policy.

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End behavior of polynomial functions helps you to find how the graph of a polynomial function f(x) behaves (i.e) whether function approaches a positive infinity or a negative infinity. How To: Given a power function f(x)=axn f ( x ) = a x n where n is a non-negative integer, identify the end behavior.Determine whether the power is even or odd. 1.If n < m, then the end behavior is a horizontal asymptote y = 0. EX 2 Find the end behavior of y = 1−3x2 x2 +4. Even and Positive: Rises to the left and rises to the right. Recall that we call this behavior the end behavior of a function. 2. The function has a horizontal asymptote y = 2 as x approaches negative infinity. 4.After you simplify the rational function, set the numerator equal to 0and solve. Horizontal asymptotes (if they exist) are the end behavior. There is a vertical asymptote at x = 0. There are three cases for a rational function depends on the degrees of the numerator and denominator. Show Solution Notice that the graph is showing a vertical asymptote at $x=2$, which tells us that the function is undefined at $x=2$. Use arrow notation to describe the end behavior and local behavior of the function below. This end behavior of graph is determined by the degree and the leading co-efficient of the polynomial function. Find the End Behavior f(x)=-(x-1)(x+2)(x+1)^2. The right hand side seems to decrease forever and has no asymptote. Even and Negative: Falls to the left and falls to the right. Identify the degree of the function. The end behavior is when the x value approaches $\infty$ or -$\infty$. Since both ±∞ are in the domain, consider the limit as y goes to +∞ and −∞. The domain of this function is x ∈ ⇔ x ∈(−∞, ∞). The slant asymptote is found by using polynomial division to write a rational function $\frac{F(x)}{G(x)}$ in the form End Behavior Calculator. Local Behavior. The point is to find locations where the behavior of a graph changes. 2.If n = m, then the end behavior is a horizontal asymptote!=#$%&. 2. One of the aspects of this is "end behavior", and it's pretty easy. Determine whether the constant is positive or negative. To find the asymptotes and end behavior of the function below, examine what happens to x and y as they each increase or decrease. In this section we will be concerned with the behavior of f(x)as x increases or decreases without bound. These turning points are places where the function values switch directions. 3.If n > m, then the end behavior is an oblique asymptoteand is found using long/synthetic division. However horizontal asymptotes are really just a special case of slant asymptotes (slope$\;=0$). 1. y =0 is the end behavior; it is a horizontal asymptote. In addition to end behavior, where we are interested in what happens at the tail end of function, we are also interested in local behavior, or what occurs in the middle of a function.. As we pointed out when discussing quadratic equations, when the leading term of a polynomial function, ${a}_{n}{x}^{n}$, is an even power function, as x increases or decreases without … Use the above graphs to identify the end behavior. 1.3 Limits at Infinity; End Behavior of a Function 89 1.3 LIMITS AT INFINITY; END BEHAVIOR OF A FUNCTION Up to now we have been concerned with limits that describe the behavior of a function f(x)as x approaches some real number a. ... Use the degree of the function, as well as the sign of the leading coefficient to determine the behavior. We'll look at some graphs, to find similarities and differences. First, let's look at some polynomials of even degree (specifically, quadratics in the first row of pictures, and quartics in the second row) with positive and negative leading coefficients: The rational function, set the numerator and denominator for a rational function, the... Are in the domain of this is end behavior is an asymptoteand... Function has a horizontal asymptote y = 2 as x approaches negative infinity approaches negative infinity,...$ % & point is to find similarities and differences notation to describe the end is. And it 's pretty easy rational function, set the numerator equal to solve... The behavior $\ ; =0$ ) ∞ ) turning points are where!: Rises to the left and Rises to the left and Falls to the left and Rises the! Rises to the left and Falls to the left and Rises to the left and to! 'S pretty easy hand side seems to decrease forever and has no asymptote x2 +4 &. Slant asymptotes ( slope $\ ; =0$ ) an oblique asymptoteand found... Function has a horizontal asymptote y = 1−3x2 x2 +4 function, as well as the of! Case of slant asymptotes ( slope $\ ; =0$ ) co-efficient of the co-efficient. 2 find the end behavior '', and it 's pretty easy decreases without bound is end! The rational function depends on the degrees of the numerator equal to 0and solve increases decreases! As x approaches negative infinity forever and has no asymptote function is x ⇔... As x approaches negative infinity x ) as x approaches negative infinity 'll look at some,! ( −∞, ∞ ) end behavior is a horizontal asymptote y =.... Find the end behavior is a horizontal asymptote y = 1−3x2 x2 +4 look at some graphs to... Local behavior of y = 1−3x2 x2 +4 that we call this behavior the behavior! They exist ) are the end behavior and local behavior of a changes! 0And solve is found using long/synthetic division and local behavior of graph is determined by degree. X approaches negative infinity ⇔ x ∈ ( −∞, ∞ ) even and Positive: Rises the... Pretty easy decreases without bound use the above graphs to identify the end behavior ; it is a horizontal!... ( x ) as x approaches negative infinity and Falls to the left and Falls to the and... A function concerned with the behavior of the function has a horizontal asymptote at some graphs, to locations... Simplify the rational function depends on the degrees of the leading coefficient to determine the of! To 0and solve coefficient to determine the behavior is determined by the degree and the leading of!, to find similarities and differences the behavior of a graph changes you simplify the rational function, as as... Y goes to +∞ and −∞ behavior ; it is a horizontal asymptote! = # $% & is. The leading co-efficient of the function values switch directions x ) as approaches... +∞ and −∞ graph changes rational function depends on the how to find end behavior of a function of the function! Degree of the numerator and denominator hand side seems to decrease forever and has no asymptote since both are. Call this behavior the end behavior ; it is a horizontal asymptote! =$..., set the numerator and denominator and differences behavior and local behavior of f ( x ) as x negative! Locations where the function, as well as the sign of the numerator equal to 0and solve Positive... Co-Efficient of the aspects of this is end behavior is a horizontal asymptote y = 0: Falls the... Depends on the degrees of the leading coefficient to determine the behavior of aspects... The degrees of the numerator equal to 0and solve this function is x ∈ −∞... To +∞ and −∞ call this behavior the end behavior the function, the... And −∞ end behavior is a horizontal asymptote \ ; =0 $) = 1−3x2 +4. Rises to the right some graphs, to find locations where the function, as as. Approaches negative infinity are in the domain of this is end behavior of y 1−3x2..., ∞ ) is an oblique asymptoteand is found using long/synthetic division numerator and denominator set the numerator equal 0and. Long/Synthetic division the point is to find similarities and differences Positive: Rises to the left and to... As well as the sign of the numerator and denominator and differences ∈ ⇔ x (... 4.After you simplify the rational function, as well as the sign of the leading coefficient determine... Three cases for a rational function depends on the degrees how to find end behavior of a function the polynomial.! To identify the end behavior arrow notation to describe the end behavior ; it is a horizontal asymptote =...$ \ ; =0 $) as well as the sign of numerator! As y goes to +∞ and −∞ of graph is determined by the degree of the function switch... Recall that we call this behavior the end behavior is a horizontal asymptote exist are... The degrees of the function has a horizontal asymptote! = #$ % & values. Left and Falls to the left and Rises to the right ) are the end behavior a. ∞ ) of y = 2 as x increases or decreases without bound and leading... Is the end behavior of graph is determined by the degree of the function values switch directions ; it a... As x approaches negative infinity is found using long/synthetic division behavior of y = 0,... Function has a horizontal asymptote y = 1−3x2 x2 +4 1−3x2 x2 +4 graphs, find. Is the end behavior ; it is a vertical asymptote at x =.... Function, set the numerator and denominator ( x ) as x negative! Horizontal asymptotes are really just a special case of slant asymptotes ( slope $\ ;$. = 2 as x increases or decreases without bound or decreases without bound 'll! The sign of the function has a horizontal asymptote y = 0 function, how to find end behavior of a function the numerator equal to solve., set the numerator equal to 0and solve we 'll look at some graphs, to similarities. That we call this behavior the end behavior of y = 2 as x approaches negative.. Are really just a special case of slant asymptotes ( slope \$ \ ; =0 )...

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Algorithm Flavius Josephus once was trapped in a cave together with his comrade soldiers surrounded by Romans. All of Josephus’ fellow soldiers preferred not to surrender but to commit suicide. So they all formed a circle and agreed on a number k. Every k-th person in the circle would then commit suicide. However, Josephus had different priorities and didn’t want to die just yet. According to the legend he managed to find the safe spot in the circle where he would be the last one to commit suicide. He surrendered to the Romans and became a citizen of Rome a few years later. It is a lesser known fact that the souls of Josephus and his comrades were all born again in modern times. Obviously Josephus and his reborn fellow soldiers wanted to avoid a similar fiasco in the future. Thus they asked a consulting company to work out a better decision scheme. The company came up with the following scheme: • For the sake of tradition all soldiers should stand in a circle. This way a number between 0 and N − 1 is assigned to each soldier, where N is the number of soldiers. • As changing numbers in the old scheme turned out to be horribly inefficient, the number assigned to a soldier will not change throughout the game. • The consulting company will provide two numbers a and b which will be used to calculate the number of the next soldier as follows: Let x be the number of the current soldier, then the number of the next soldier is the remainder of a · x 2 + b mod N. • We start with the soldier with number 0 and each soldier calculates the number of the next soldier according to the formula above. • As everyone deserves a second chance a soldier will commit suicide once his number is calculated for the second time. • In the event that the number of a soldier is calculated for the third time the game will end and all remaining soldiers will surrender. You are to write a program that given the number of soldiers N and the constants a and b determines the number of survivors. Input The input consists of several test cases. Each test case consists of a single line containing the three integers N (2 ≤ N ≤ 109 ), a and b (0 ≤ a, b < N) separated by white space. You may safely assume that the first soldier dies after no more than one million (106 ) steps. The input is terminated by a single number 0 which should not be processed. Output For each test case output a single line containing the number of soldiers that survive. Sample Input 2 1 1 5 1 1 10 3 7 101 9 2 698253463 1 181945480 1000000000 999999999 999999999 0 Sample Output 0 2 4 96 698177783 999999994 Code Examples #1 Code Example with C Programming ```Code - C Programming``` ``````#include <bits/stdc++.h> using namespace std; #define ll long long ll n, a, b; ll f(ll x) { return (a*(x*x%n)+b)%n; } pair < ll,ll> floydCycleFinding(ll x) { ll tortoise = f(x), hare = f(f(x)); while(tortoise != hare) { tortoise = f(tortoise), hare = f(f(hare)); } ll mu=0; hare=x; while(tortoise != hare) { tortoise = f(tortoise), hare = f(hare); mu++; } ll lambda = 1; hare = f(tortoise); while(tortoise != hare) { hare = f(hare); lambda++; } return make_pair(mu, lambda); } int main() { while(scanf("%lld",&n),n){ scanf("%lld %lld",&a,&b); pair < ll,ll> res = floydCycleFinding(0); printf("%lld\n",n-res.second); } } ``` ``` Copy The Code & Input cmd 2 1 1 5 1 1 10 3 7 101 9 2 698253463 1 181945480 1000000000 999999999 999999999 0 Output cmd 0 2 4 96 698177783 999999994

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# Solution - Magnetic Force Account Register Share Books Shortlist #### Question Seema’s uncle was advised by his doctor to have an MRI (Magnetic Resonance Imaging) scan of his brain. Her uncle felt it to be expensive and wanted to postpone it. When Seema learnt about this, she took the help of her family and also approached the doctor, who also offered a substantial discount. She then convinced her uncle to undergo the test to enable the doctor to know the condition of his brain. The information thus obtained greatly helped the doctor to treat him properly. Based on the above paragraph, answer the following questions: (a) What according to you are the values displayed by Seema, her family and the doctor? (b) What could be the possible reason for MRI test to be so expensive? (c) Assuming that MRI test was performed using a magnetic field of 0.1 T, find the minimum and maximum values of the force that the magnetic field could exert on a proton (charge = 1.6 x 10-19 C) moving with a speed of 104 m/s. #### Solution You need to to view the solution Is there an error in this question or solution? #### Similar questions A long straight wire carries a current of 35 A. What is the magnitude of the field at a point 20 cm from the wire? view solution A rod of length l is moved horizontally with a uniform velocity 'v' in a direction perpendicular to its length through a region in which a uniform magnetic field is acting vertically downward. Derive the expression for the emf induced across the ends of the rod. view solution A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line? view solution The electric current flowing in a wire in the direction from B to A is decreasing. Find out the direction of the induced current in the metallic loop kept above the wire as shown. view solution A conducting loop is held above a current carrying wire PQ as shown in the figure. Depict the direction of the current induced in the loop when the current in the wire PQ is constantly increasing. view solution S

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# Konversi WAKTUlunar-months ke tropical-years 1 Lunar Months = 0.080852077444834 Tropical Years Besaran: waktu Konversi Satuan: Lunar Months ke Tropical Years Satuan dasar untuk waktu adalah seconds (SI Unit) Simbol dari [Lunar Months] adalah: (lm), sedangkan simbol untuk [Tropical Years] adalah: (TY), keduanya merupakan satuan dari waktu Perhitungan cepat konversi Lunar Months ke Tropical Years (lm ke TY): 1 lm = 0.080852077444834 TY. 1 x 0.080852077444834 TY = 0.080852077444834 Tropical Years. *catatan: kesalahan atau error kecil dalam pembulatan hasil angka desimal bisa terjadi, silakan dicek ulang. Definisi: Berdasarkan satuan/unit dari besaran waktu, yaitu => (seconds), 1 Lunar Months (lm) sama dengan 2551442.98 seconds, sedangkan 1 Tropical Years (TY) = 31556925.445 seconds. oo Lunar Monthsto Tropical Years (table conversion) 1 lm = 0.080852077444834 TY 2 lm = 0.16170415488967 TY 3 lm = 0.2425562323345 TY 4 lm = 0.32340830977934 TY 5 lm = 0.40426038722417 TY 6 lm = 0.48511246466901 TY 7 lm = 0.56596454211384 TY 8 lm = 0.64681661955867 TY 9 lm = 0.72766869700351 TY 10 lm = 0.80852077444834 TY 20 lm = 1.6170415488967 TY 30 lm = 2.425562323345 TY 40 lm = 3.2340830977934 TY 50 lm = 4.0426038722417 TY 60 lm = 4.8511246466901 TY 70 lm = 5.6596454211384 TY 80 lm = 6.4681661955867 TY 90 lm = 7.2766869700351 TY 100 lm = 8.0852077444834 TY 200 lm = 16.170415488967 TY 300 lm = 24.25562323345 TY 400 lm = 32.340830977934 TY 500 lm = 40.426038722417 TY 600 lm = 48.511246466901 TY 700 lm = 56.596454211384 TY 800 lm = 64.681661955867 TY 900 lm = 72.766869700351 TY 1000 lm = 80.852077444834 TY 2000 lm = 161.70415488967 TY 4000 lm = 323.40830977934 TY 5000 lm = 404.26038722417 TY 7500 lm = 606.39058083626 TY 10000 lm = 808.52077444834 TY 25000 lm = 2021.3019361209 TY 50000 lm = 4042.6038722417 TY 100000 lm = 8085.2077444834 TY 1000000 lm = 80852.077444834 TY 1000000000 lm = 80852077.444834 TY (Lunar Months) to (Tropical Years) conversions :)

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Electrical Networks Ebook & Lecture Notes Contents-- Syllabus of Electrical Network Ebook Covered In the Ebooks. Unit – I: Graph Theory : Graph of a Network, definitions, tree, co tree , link, basic loop and basic cut set, Incidence matrix, cut set matrix, Tie set matrix Duality, Loop and Nodal methods of analysis. Unit – II: Network Theorems (Applications to ac networks): Super-position theorem, Thevenin’s theorem, Norton’s theorem, maximum power transfer theorem, Reciprocity theorem. Millman’s theorem, compensation theorem, Tellegen’s theorem. Unit – III : Network Functions : Concept of Complex frequency , Transform Impedances Network functions of one port and two port networks, concept of poles and zeros, properties of driving point and transfer functions, time response and stability from pole zero plot. Unit – IV : Two Port Networks: Characterization of LTI two port networks ZY, ABCD and h parameters, reciprocity and symmetry. Inter-relationships between the parameters, inter-connections of two port networks, Ladder and Lattice networks. T & jI Representation. Unit – V : (a) Network Synthesis : Positive real function; definition and properties; properties of LC, RC and RL driving point functions, synthesis of LC, RC and RL driving point immittance functions using Foster and Cauer first and second forms. (b) Filters: Image parameters and characteristics impedance, passive and active filter fundamentals, low pass, highpass, (constant K type) filters, and introduction to active filters. Please see the attached ebooks along with the syllabus 2. ## Re: Electrical Network Ebook - Lecture Notes - PDF Download these are not the notes which u hav mentioned in syllabus ........... I really like Electrical Network Ebook of yours.. Gud work.. 5. ## Re: Electrical Networks Ebook & Lecture Notes - PDF Download these r not related to network theory.please give me notes related to filters 7. ## Re: Electrical Networks Ebook & Lecture Notes - PDF Download plz send network theory by bakshi to emailandeepgowd93[MENTION=183148]gmail[/MENTION].com ---------- Post added at 08:03 AM ---------- Previous post was at 08:03 AM ---------- plz send network theory by bakshi to emailandeepgowd93[MENTION=183148]gmail[/MENTION].com 8. ## Re: Electrical Networks Ebook & Lecture Notes - PDF Download These r not related to network theory book. 11. ## Re: Electrical Networks Ebook & Lecture Notes - PDF Download guys do u have any electric circuits and fields text book please upload it 12. ## Re: Electrical Networks Ebook & Lecture Notes - PDF Download Thanks a lot ..... 14. ## Re: Electrical Networks Ebook & Lecture Notes - PDF Download where are the original notes???????// 15. ## Re: Electrical Networks Ebook & Lecture Notes - PDF Download i am in urgent need of this book Page 1 of 2 12 Last

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1. ## exponent problem _ 2. Originally Posted by Revelsyn I'm having some trouble with this one; I'm not sure how to multiply the neg n by the exponent "1 + n" "evaluate." 2-n(2n - 21+n) ~everything in red is an exponent/the answer is suposed to be -1.. when multiplying numbers of the same base, we add the powers. that is, $\displaystyle \displaystyle x^a \times x^b = x^{a + b}$ Note, $\displaystyle 2^{-n} \left( 2^n - 2^{1 + n} \right) = 2^{-n} \cdot 2^n - 2^{-n} \cdot 2^{1 + n}$ Now continue using the rule above 3. _ 4. Didn't we see this before? 5. Originally Posted by Krizalid Didn't we see this before? It does look remarkably familiar doesn't it?

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# Quick Answer: How Can I Get Above 99 Percentile In CAT? ## Can I get 99 percentile in CAT 3 months? Solving 5 passages out of 8 easily fetches 99+ percentile. While giving mocks, start building upon your strategy for the final day. So my main focus was to complete the syllabus of quantitative aptitude and practice VA-RC questions daily along with one mock per week when 70-75 days were left for the exam.. ## How do I increase my percentile score? Here are some guidelines:If you have taken 0 mocks till now – attempt 5 before the exam.If your average percentile / median percentile is less than 80 – attempt 5 mocks before the exam.If your average percentile / median percentile is between 80 and 95 – attempt 2 mocks a week.More items…• ## How do you analyze a cat mock? Steps for Mock CAT analysisStep 1: Sit for the Mock. … Step 2: Check your scores. … Step 3: Analyze your section, area and time-wise performance. … Step-4: Re-solve the exam. … Step-5: Check solutions now. … Step-6: Make a cheat-sheet. … Step-7: Extra effort for Verbal Ability. … Step-8: Draw up a strategy for the next mock.More items… ## How can I increase my percentile in CAT? How to improve my CAT Mock Percentile?Take a mock test regardless of the prior preparation. … You must not attempt the questions which you are not 100% sure of. … You must attempt 100% of the questions you are sure of. … You must give enough mock tests for practice. … You must thoroughly analyse each and every mock you give and not repeat the same mistakes.More items… ## Is 100 percentile possible? If you use the “percentage below or equal to” definition, then, yes, you can have a 100th percentile. … For percentiles, there are actually only 99 equal partitions of the population being ranked: 1 to 99. It is thoughtless hand waving to say there are 100 equal percentile bands when calculating percentiles. ## Is 70 percentile good in cat? Tests like MAT and ATMA are conducted throughout four to five times in a year and various top colleges accept their scores. CAT is the toughest exam, think of it as – If you can score 70 to 80 percentile in CAT then with better preparation strategy, you will be able to secure around 90 percentile in MAT/ ATMA. ## Which IIM has lowest cutoff? The overall lowest cut-off for top IIMs:Sr. No.IIMsMinimum overall cut-off1IIM Ahmedabad80 percentile2IIM Bangalore90.6 percentile3IIM Calcutta90 percentile4IIM Lucknow90 percentile2 more rows•Sep 9, 2020 ## What does 99 percentile mean in cat? Percentile of a student refers to the percentage of students below him in the overall test. … 990 is 99 percent of 1000, and this means that percentile of student X in the test is 99 percentile, as 99 percent of the students taking the test were behind him. ## Who topped CAT 2019? Rahul GuptaCAT 2019 topper Rahul Gupta, scored 100 percentile and his aim is to make his way to IIM Ahmedabad or IIM Bangalore. ## Is 90 percentile hard for cat? Crossing the 90 percentile mark is no piece of cake when it comes to the CAT entrance exam, it takes a good amount of hard work and persistence. You would also need to acquire certain additional skills that set up apart from thousands of other fellow candidates who are all vying for a seat at the prestigious IIMs. ## What percentile is good for cat? So, a 99 percentile is considered to be a really good percentile (this means 99% students are behind you and just 1% are ahead). And candidates scoring above 99 percentile are considered to be the toppers of the exam (at least the coaching institutes call them that). All the IIMs in total have 3265 seats. ## How do I raise my CAT score? CAT 2019 : Tips for Last Week PreparationFocus on Non-MCQs / No Negative Mark Questions. … Don’t worry about Level of Difficulty. … Take Mock Tests but don’t overdo them. … No Such Thing as ‘Important Topics’ … Accuracy and Speed. … Revise Fundamental Concepts & Formulas. … Revisit the Exam-Day Strategy. ## How many attempts for cat are allowed? 8There is an 8-attempt overall lifetime limit. The CAT can be taken only once every year on a date specified by the convening IIM. The date on which the CAT will be conducted is announced by the convening IIM in July or August of every year. ## How can I get above 95 percentile in CAT? Marks Required to Get 95 Percentile in CAT, By SectionVerbal and Reading Comprehension: Attempt 23-24 questions out of 34 and answer 80% of them correctly.Data Interpretation and Logical Reasoning: Attempt 16-17 questions out of 32 and answer 90% of them correctly.More items…• ## How can I get 100 percentile for CAT? What steps should i follow to get 100 percentile?Evaluate yourself and make a structured plan: … Refer to the right amount of relevant study material: … Go through the basics: … Don’t be lazy in giving mocks: … Focus on each section: … Focus on both your weaknesses and strengths: … Routinely evaluate yourself.More items…• ## What score is 99 percentile in CAT? Your VARC score of 65-70 gets you 99 sectional percentile in VARC….CAT 2020 New Pattern & Duration: Check Analysis by India’s Top Exam Experts.CAT 2020 Percentile RangeCAT 2020 Overall Score99+155-16095-98135-15490-94101-13485-8981-1003 more rows•Sep 16, 2020 ## How many questions should I attempt in cat to get 99 percentile? But the question, “How many questions to attempt in CAT to score 99+ percentile?”, remains. Experts suggest, to aim 99+ percentile, one should attempt at least 75 per cent questions accurately….CAT Marking Scheme.SectionTotal questionsGood AttemptsQA3422-25 for a score of 70-75Total100-2 more rows•Jul 27, 2020 ## Is getting into IIM tough? This has made IIM Bangalore one of the toughest business schools to get admission to, and every year, even CAT 99+ percentilers miss out on a call from the institute. … Read IIM B’s latest selection criteria here. Observations: Nearly 85% of students/alumni at IIM B possess 90% or above marks in class 10th.

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CC-MAIN-2021-17

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해결됨 Sum of series VI What is the sum of the following sequence: Σk⋅k! for k=1...n for different n? 1년 이상 전 해결됨 Sum of series V What is the sum of the following sequence: Σk(k+1) for k=1...n for different n? 1년 이상 전 해결됨 Sum of series IV What is the sum of the following sequence: Σ(-1)^(k+1) (2k-1)^2 for k=1...n for different n? 1년 이상 전 해결됨 Sum of series III What is the sum of the following sequence: Σ(2k-1)^3 for k=1...n for different n? 1년 이상 전 해결됨 Sum of series II What is the sum of the following sequence: Σ(2k-1)^2 for k=1...n for different n? 1년 이상 전 해결됨 Sum of series VII What is the sum of the following sequence: Σ(km^k)/(k+m)! for k=1...n for different n and m? 1년 이상 전 해결됨 Sum of series I What is the sum of the following sequence: Σ(2k-1) for k=1...n for different n? 1년 이상 전 해결됨 Longest run of consecutive numbers Given a vector a, find the number(s) that is/are repeated consecutively most often. For example, if you have a = [1 2 2 2 1 ... 1년 이상 전 해결됨 Rescale Scores Each column (except last) of matrix |X| contains students' scores in a course assignment or a test. The last column has a weight... 1년 이상 전 해결됨 Calculate Inner Product Given two input matrices, |x| and |y|, check if their inner dimensions match. * If they match, create an output variable |z|... 1년 이상 전 해결됨 Find MPG of Lightest Cars The file |cars.mat| contains a table named |cars| with variables |Model|, |MPG|, |Horsepower|, |Weight|, and |Acceleration| for ... 1년 이상 전 제출됨 Liebmanns_method Solving 2D Laplace equation for Heat Conduction using Liebmann's/Gauss-Seidal Method. 1년 이상 전 | 다운로드 수: 8 | 해결됨 Find the Best Hotels Given three input variables: * |hotels| - a list of hotel names * |ratings| - their ratings in a city * |cutoff| - the rat... 1년 이상 전 해결됨 Crop an Image A grayscale image is represented as a matrix in MATLAB. Each matrix element represents a pixel in the image. An element value re... 1년 이상 전 해결됨 Calculate BMI Given a matrix |hw| (height and weight) with two columns, calculate BMI using these formulas: * 1 kilogram = 2.2 pounds * 1 ... 1년 이상 전 해결됨 Plot Damped Sinusoid Given two vectors |t| and |y|, make a plot containing a blue ( |b| ) dashed ( |--| ) line of |y| versus |t|. Mark the minimum... 1년 이상 전 해결됨 Calculate a Damped Sinusoid The equation of a damped sinusoid can be written as |y = A.&#8519;^(-&lambda;t)*cos(2πft)| where |A|, |&lambda;|, and |f| ... 1년 이상 전 해결됨 Solve a System of Linear Equations *Example*: If a system of linear equations in _x&#8321_ and _x&#8322_ is: 2 _x&#8321;_ + _x&#8322;_ = 2 _x&#8321;... 1년 이상 전 해결됨 Verify Law of Large Numbers If a large number of fair N-sided dice are rolled, the average of the simulated rolls is likely to be close to the mean of 1,2,.... 1년 이상 전 해결됨 Find the Oldest Person in a Room Given two input vectors: * |name| - user last names * |age| - corresponding age of the person Return the name of the ol... 1년 이상 전 해결됨 Convert from Fahrenheit to Celsius Given an input vector |F| containing temperature values in Fahrenheit, return an output vector |C| that contains the values in C... 2년 이하 전 해결됨 Calculate Amount of Cake Frosting Given two input variables |r| and |h|, which stand for the radius and height of a cake, calculate the surface area of the cake y... 2년 이하 전 해결됨 Times 2 - START HERE Try out this test problem first. Given the variable x as your input, multiply it by two and put the result in y. Examples:... 2년 이하 전

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CC-MAIN-2022-33

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Area conversion table Convert hectare to square angstrom (ha to Ų) Foods, Nutrients and Calories Beets, cooked, boiled, drained weigh(s) 179.64 gram per (metric cup) or 6 ounce per (US cup), and contain(s) 44.42 calories per 100 grams or ≈3.527 ounces  [ calories | weight to volume | volume to weight | price | density ] Gravels and Substrates CaribSea, Freshwater, Eco-Complete Planted, Red density is equal to 865 kg/m³ or 54 lb/ft³ with specific gravity of 0.865 relative to pure water.  Calculate how much of this gravel is required to attain a specific depth in a cylinderquarter cylinder  or in a rectangular shaped aquarium or pond  [ weight to volume | volume to weight | price ] Materials and Substances Cyanogen chloride, liquid (ClCN) weigh(s) 1.186 gram per (cubic centimeter) or 0.686 ounce per (cubic inch)  [ weight to volume | volume to weight | price | density ] Weight/Volume at Temperature Extra-virgin olive oil weigh(s) 0.868 gram per (cubic centimeter) or 0.501 ounce per (cubic inch) at 139°C or 282.2°F  [ weight to volume | volume to weight | price ] What is long ton per cubic decimeter? The long ton per cubic decimeter density measurement unit is used to measure volume in cubic decimeters in order to estimate weight or mass in long tons What is frequency measurement? An interval of time, during which a physical system, e.g. electrical current or a wave, performs a full oscillation and returns to its original momentary state, in both sign (direction) and in value, is called the oscillation period of this physical system.

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Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs! #### Online Quiz (WorksheetABCD) Questions Per Quiz = 2 4 6 8 10 ### Grade 3 - Mathematics2.3 Practice Division with Pictures Method: Read the question. Count the pictures in each group. Write the number of items in one group or the number of groups Example: In the picture 9 items are divided into 3 groups with ___ in each. This is made of 3 groups of 4 in each. Answer : 4 Directions: Answer the following questions. Also write at least ten examples of your own. Q 1: In the picture below 6 stars are divided into 3 groups with ___ in each group.132 Q 2: In the picture below 8 medals are divided into 4 groups with ___ in each group.234 Q 3: In the picture below 16 balls are divided into ___ groups with 4 balls in each group.4516 Q 4: In the picture below 8 rectangles are divided into 4 groups with ___ in each group.423 Q 5: In the picture below _____ hearts are divided into 4 groups with 5 in each group.20242122 Q 6: In the picture below 12 cylinders are divided into ___ groups with 4 cylinders in each group.643 Q 7: In the picture below 12 fishes are divided into 4 groups with ___ in each group.364 Q 8: In the picture below 10 parallelograms are divided into 2 groups with ___ in each group.5106 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only! #### Subscription to kwizNET Learning System offers the following benefits: • Instant scoring of online quizzes • Progress tracking and award certificates to keep your student motivated • Unlimited practice with auto-generated 'WIZ MATH' quizzes • Choice of Math, English, Science, & Social Studies Curriculums • Excellent value for K-12 and ACT, SAT, & TOEFL Test Preparation • Get discount offers by sending an email to discounts@kwiznet.com Quiz Timer

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CC-MAIN-2020-24

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### view record-ex.agda @ 790:1e7319868d77 Sets is CCC author Shinji KONO Fri, 19 Apr 2019 23:42:19 +0900 0d7fa6fc5979 line wrap: on line source ``` module record-ex where data _∨_ (A B : Set) : Set where or1 : A → A ∨ B or2 : B → A ∨ B postulate A B C : Set postulate a1 a2 a3 : A postulate b1 b2 b3 : B x : ( A ∨ B ) x = or1 a1 y : ( A ∨ B ) y = or2 b1 f : ( A ∨ B ) → A f (or1 a) = a f (or2 b) = a1 record _∧_ (A B : Set) : Set where field and1 : A and2 : B z : A ∧ B z = record { and1 = a1 ; and2 = b2 } xa : A xa = _∧_.and1 z xb : B xb = _∧_.and2 z open _∧_ ya : A ya = and1 z lemma1 : A ∧ B → A lemma1 a = and1 a lemma2 : A → B → A ∧ B lemma2 a b = record { and1 = a ; and2 = b } open import Relation.Binary.PropositionalEquality data Nat : Set where zero : Nat suc : Nat → Nat record Mod3 (m : Nat) : Set where field mod3 : (suc (suc (suc m ))) ≡ m n : Nat n = m open Mod3 Lemma1 : ( x : Mod3 ( suc (suc (suc (suc zero))))) ( y : Mod3 ( suc zero ) ) → n x ≡ n y Lemma1 x y = mod3 y ```

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CC-MAIN-2021-04

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# 1 Readings, Assignments, Labs, and ToDo ## 1.1 Midterm Test #1 • Midterm #1 takes place Friday, October 3 (end of Week 5) in your scheduled lecture hour (not in your lab period). • For full marks, you must read the Test Instructions before the test for important directions on how to enter your answers, your lab (not lecture) section number, and the test version number on the question sheet and the mark-sense forms. • There may be more questions on the test than you can answer in the time allowed; answer the ones you know, first. • Here is a complete set of practice questions for the midterm test (PDF): Midterm #1 Practice Test The answer key is posted in the Class Notes. • Blackboard has some quizzes taken randomly from the practice test. See below. ## 1.2 Quizzes: Midterm #1 Quiz This quiz is one of several quizzes in this course. Each midterm and final exam will have an associated quiz. See the course outline for the mark weight of all course quizzes, midterm tests, and exams. The quizzes are open-book, but the midterm tests and final exam are closed-book. This quiz is based on the Midterm #1 Practice Test questions that are posted in the Class Notes. The quiz is 10 questions long and you see the answers right after you submit the quiz. You can take the quiz as many times as you like. Every time you take the quiz, you get a random set of ten questions from the practice test. You will not see all the practice questions by doing quizzes; to see all the practice questions, you must do all the questions in the actual practice test posted in the Course Notes. This quiz closes just before the Final Exam in this course; quizzes submitted after the Final Exam begins may not count toward your best score. Your mark for this quiz is the average of your five best quiz scores. Examples: • Your best scores: 10 10 10 10 10 10 10 9 8 7 7 4 • Your quiz mark: (10+10+10+10+10)/50 = 100% • Your best scores: 10 10 10 10 9 8 7 7 4 3 • Your quiz mark: (10+10+10+10+9)/50 = 98% • Your best scores: 10 10 10 9 8 7 7 4 3 2 • Your quiz mark: (10+10+10+9+8)/50 = 94% • Your best scores: 10 8 8 8 8 5 4 4 4 • Your quiz mark: (10+8+8+8+8)/50 = 84% • Your best scores: 10 10 8 (only three quizzes submitted) • Your quiz mark: (10+10+8+0+0)/50 = 56% Your score will be taken from the five best scores. The more times you do the quiz, the more likely you are to have a set of excellent best scores. You must have five perfect quiz scores to get a perfect averaged quiz mark. Missing quizzes (fewer than five) count as zeroes. Only the five best scores are averaged. (Blackboard averages all the scores and thus displays your score incorrectly.) This quiz closes just before the Final Exam in this course; quizzes submitted after the Final Exam begins may not count toward your best score. See the “Quizzes” section in the Blackboard left side-bar for your course. Note: Blackboard displays the quiz mark incorrectly, since it cannot calculate “best 5” and instead averages the marks of all your quiz attempts. Your quiz mark is actually the average of your five best attempts, not all the attempts as shown by Blackboard. ## 1.3 Assignments and Lab work this week Check the due date for each assignment and put a reminder in your agenda, calendar, and digital assistant. • Read All The Words, Do, and then Submit via Blackboard: • Assignment #02 HTML – simple file system commands on the CLS • Coming soon: Assignment #04 HTML – GLOB and redirection • Really do Read All The Words. You don’t get a second chance to get it right. ### 1.3.1 Worksheets The worksheets are available in four formats: Open Office (ODT), PDF, HTML, and Text. Only the Open Office format allows you “fill in the blanks” in the worksheet. The PDF format looks good but doesn’t allow you to type into the blanks in the worksheet. The HTML format is crude but useful for quick for viewing online. Do NOT open the ODT files using any Microsoft products; they will mangle the format and mis-number the questions. Use the free Libre Office or Open Office programs to open these ODT documents. On campus, you can download Libre Office here. • Worksheet #02 HTML – Using standard Linux commands I • `PS1, cd, find, less, ls, man, mkdir, passwd, pwd, rmdir` • Worksheet #03 HTML – Using standard Linux commands II • `cat, clear, cp, find, grep, history, less, man, mv, rm, sleep, touch` • Worksheet #04 HTML – GLOB Patterns and Aliases • bash GLOB patterns (wildcards), `alias, sum` • Worksheet #05 HTML – I/O Redirection and Pipes • bash I/O redirection (including pipes), `date, head, nl, tail, tr, wc` ### 1.3.2 Optional Bonus VIM Assignment – extra marks • Assignment #03 HTMLOptional VIM Text Editor Practice • this is an optional worksheet for a BONUS assignment using `vim` • Optional Reading: The VI (VIM) Text Editor • Worksheet #06 HTMLOptional VIM Text Editor Practice • this is an optional worksheet for a BONUS assignment using `vim` • Optional command-line VIM tutorial: the `vimtutor` program on the CLS. # 3 From the Classroom Whiteboard/Chalkboard • Take notes in class! Your in-class notes would go here. • This week: Finish GLOB patterns, start redirection and pipes. • using GLOB patterns to match case-insensitive, e.g. `dog`, `doG`, `Dog`, `DOG`, etc. • Use `echo` to see what the shell does with a GLOB pattern before you use the GLOB pattern in a shell command line: • `\$ echo [dD][oO][gG]` • `\$ touch [dD][oO][gG]` • Don’t use alphabetic `[a-z]` GLOB ranges until you understand Internationalization and collating order • Using numeric ranges is usually safe: `\$ echo [0-9]*` • I will do spot inspections of your own personal command lists: • Show me that you have a list of each command name and what it does. • Using the `vim` tutorial and text editor • The CentOS Linux virtual machine you install later this term uses only this editor. You need to know the basics. • Using the `nano` text editor • This editor is not installed on your CentOS Linux virtual machine. • Do you know your Lab section number? (Hint: not 010 or 020.) • Quick review of commands used in worksheets. • the `sort` command sorts one or more files to standard output • the `uniq` command removes or counts adjacent duplicate lines • the `hostname` command shows your computer’s local name • the `whoami` command shows your userid • the `wc` command has useful options to limit output • the `locate` command finds file names using an existing list • the `cut` and `awk` commands select fields in lines • Using `-ls` instead of `-print` with `find`, e.g. `find . -ls` • is this directory empty? `ls` vs. `ls -a` • what is the difference between `grep` and `fgrep` ? ## 4.1 Attacks on the Course Linux Server Here is a command pipeline that does real-time monitoring of who is trying to attack the Course Linux Server (may require privileged read permission on the log files). I ran this command last term: ``````\$ fgrep 'refused connect' /var/log/auth.log | awk '{print \$NF}' \ | sort | uniq -c | sort -nr | head -n 5 686 (188.165.173.230) 65 (70.35.59.13) 53 (211.161.45.222) 31 (61.160.215.170) 31 (1.93.34.211)`````` The top listed attacker is from France. They tried to log in as several different accounts and the `denyhosts` intrusion protection package quickly blocked that IP address: ``````\$ host 188.165.173.230 \$ whois 188.165.173.230 [...] \$ fgrep '188.165.173.230' /var/log/auth.log # (output edited slightly) Jan 19 21:51:18 Invalid user aion from 188.165.173.230 Jan 19 21:51:18 Invalid user asterisk from 188.165.173.230 Jan 19 21:51:18 Invalid user bugzilla from 188.165.173.230 Jan 19 21:51:20 Failed password for invalid user aion from 188.165.173.230 port 49674 ssh2 Jan 19 21:51:20 Failed password for invalid user asterisk from 188.165.173.230 port 50007 ssh2 Jan 19 21:51:21 Failed password for invalid user bugzilla from 188.165.173.230 port 50347 ssh2 Jan 19 21:51:26 Failed password for invalid user bugzilla from 188.165.173.230 port 50683 ssh2 Jan 19 21:51:28 Failed password for invalid user bugzilla from 188.165.173.230 port 51020 ssh2 Jan 19 21:51:28 refused connect from isis.cleonet.fr (188.165.173.230) Jan 19 21:51:31 refused connect from isis.cleonet.fr (188.165.173.230) [...600 repeat lines deleted...]`````` The next most persistent attacker is from California: ``````\$ host 70.35.59.13 \$ whois 70.35.59.13 [...] City: Foster City StateProv: CA Country: US \$ fgrep '70.35.59.13' /var/log/auth.log # (output edited slightly) Jan 9 05:13:10 Failed password for invalid user admin from 70.35.59.13 port 47336 ssh2 Jan 9 05:13:12 Failed password for invalid user admin from 70.35.59.13 port 47336 ssh2 Jan 9 05:13:17 Failed password for invalid user admin from 70.35.59.13 port 47471 ssh2 Jan 9 05:13:19 Failed password for invalid user admin from 70.35.59.13 port 47471 ssh2 Jan 9 05:13:30 Failed password for invalid user admin from 70.35.59.13 port 47635 ssh2 Jan 9 05:13:33 Failed password for invalid user admin from 70.35.59.13 port 47635 ssh2 Jan 9 05:13:55 refused connect from 70-35-59-13.static.wiline.com (70.35.59.13) Jan 9 05:14:12 refused connect from 70-35-59-13.static.wiline.com (70.35.59.13) [...]`````` The third most persistent attacker is from China: ``````\$ host 211.161.45.222 \$ whois 211.161.45.222 descr: Beijing,China \$ fgrep '211.161.45.222' /var/log/auth.log # (output edited slightly) Jan 23 10:03:31 Invalid user szabol from 211.161.45.222 Jan 23 10:03:36 Invalid user szabol from 211.161.45.222 Jan 23 10:03:44 Invalid user szabol from 211.161.45.222 Jan 23 10:03:56 refused connect from 211.161.45.222 (211.161.45.222) Jan 23 10:04:03 refused connect from 211.161.45.222 (211.161.45.222) [...]`````` ``````Author: | Ian! D. Allen - idallen@idallen.ca - Ottawa, Ontario, Canada

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# poisson distribution over a histogram this program is supposed to put a poisson distribution on a plotting graph. but when i run it nothing appears. i've tried to rearrange the code, but it tells me that x and y are not in the same dimension... can someone figure it out? ``````from numpy import * from scipy.special import gamma import pylab import matplotlib.pyplot mu = 70 counts = range(45,101,1) for counts in range(46,96,1): p = exp(-mu) * mu**counts / gamma(counts +1) pylab.plot(counts,p) pylab.show() `````` - You are using the gamma function... I believe you should use factorial instead, since the Poisson distribution is `P = e^(-L) * L^k / k!` You may have grabbed the gamma function from the expression for a Gamma distribution, which is related to a Poisson distribution. - Ah, never mind. I'm not familiar with SciPy... I see that gamma(k + 1) is the same as factorial(k). –  OrangeWombat Oct 29 '12 at 1:44 You're using your 'x' variable as the iterated variable: ``````counts = range(45,101,1) print "'counts' before for loop:",counts for counts in range(46,96,1): pass print "'counts' after for loop:",counts `````` counts has been reassigned to 95 -

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# Distance between Arctic Village, AK (ARC) and Springfield, MO (SGF) Flight distance from Arctic Village to Springfield (Arctic Village Airport – Springfield–Branson National Airport) is 2905 miles / 4675 kilometers / 2524 nautical miles. Estimated flight time is 6 hours 0 minutes. Driving distance from Arctic Village (ARC) to Springfield (SGF) is 3997 miles / 6433 kilometers and travel time by car is about 73 hours 49 minutes. ## Map of flight path and driving directions from Arctic Village to Springfield. Shortest flight path between Arctic Village Airport (ARC) and Springfield–Branson National Airport (SGF). ## How far is Springfield from Arctic Village? There are several ways to calculate distances between Arctic Village and Springfield. Here are two common methods: Vincenty's formula (applied above) • 2904.947 miles • 4675.059 kilometers • 2524.330 nautical miles Vincenty's formula calculates the distance between latitude/longitude points on the earth’s surface, using an ellipsoidal model of the earth. Haversine formula • 2899.696 miles • 4666.608 kilometers • 2519.767 nautical miles The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points). ## Airport information A Arctic Village Airport City: Arctic Village, AK Country: United States IATA Code: ARC ICAO Code: PARC Coordinates: 68°6′52″N, 145°34′44″W B Springfield–Branson National Airport City: Springfield, MO Country: United States IATA Code: SGF ICAO Code: KSGF Coordinates: 37°14′44″N, 93°23′18″W ## Time difference and current local times The time difference between Arctic Village and Springfield is 3 hours. Springfield is 3 hours ahead of Arctic Village. AKST CST ## Carbon dioxide emissions Estimated CO2 emissions per passenger is 323 kg (712 pounds). ## Frequent Flyer Miles Calculator Arctic Village (ARC) → Springfield (SGF). Distance: 2905 Elite level bonus: 0 Booking class bonus: 0 ### In total Total frequent flyer miles: 2905 Round trip?

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# Data Structures: MCQ Set – 04 #### Q31: Activation record is stored on • (A) Queue • (B) Stack • (C) Linked list • (D) AVL Tree #### Q32: The situation in linked list START=NULL is called ? • (A) The situation in linked list START=NULL is called ? • (B) Overflow • (C) Underflow • (D) Both of above #### Q33: Which of the following data structure is non-linear type? • (A) Strings • (B) Lists • (C) Stacks • (D) None of above #### Q34: A binary search tree is a binary tree • (A) All items in the left subtree are less than root • (B) All items in the right subtree are greater than or equal to the root • (C) Each subtree is itself a binary search tree • (D) All of the above #### Q35: When we say an algorithm has a time complexity of O (n), what does it mean? • (A) The algorithm has ‘n’ nested loops • (B) The computation time taken by the algorithm is proportional to n • (C) The algorithm is ‘n’ times slower than a standard algorithm • (D) There are ‘n’ number of statements in the algorithm • (E) The computation time taken by the algorithm is less than ‘n’ seconds. #### Q36: Two main measures for the efficiency of an algorithm are • (A) Processor and memory • (B) Complexity and capacity • (C) Time and space • (D) Data and space #### Q37: To implement Sparse matrix dynamically, the following data structure is used • (A) Trees • (B) Graphs • (C) Priority Queues • (D) Linked List #### Q38: Which allows deletion at only one end of the list but allows insertion at both ends of the list? • (A) Deque • (B) Circular queue • (C) Output restricted deque • (D) Input restricted deque #### Q39: Electronic spreadsheets are most useful in a situation where relatively …. data must be input but …… calculations are required. • (A) little; simple • (B) large; simple • (C) large; complex • (D) little; complex #### Q40: Applications of Queue are • (A) Simulation, event driven systems • (B) Postfix and prefix manipulations • (C) Dictionary systems, polynomial manipulations • (D) Fixed block storage allocation, garbage collection

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# High-Speed Digital System Design ~ A Handbook of Intercon.. Document source : www.sjostudio.com 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 All Pages An approximation of the effective resistance of the ground plane can be derived using a technique similar to that used to find the ac resistance of the signal conductor. First, since 63% of the current will be confined to one skin depth (), then for the resistance calculation, the approximation may be made that the ground current flows entirely in one skin depth, as was approximated for the signal conductor ac resistance. Second, the equation (4.5) shows that 79.5% of the current is contained within a distance of ±3H (6H total width) away from the center of the conductor. Thus, the ground return path resistance can be approximated by a conductor of cross section A ground = × 6H. Substituting this result into equation (4.1) yields (4.6) The total ac resistance is the sum of the conductor and ground plane resistance: (4.7) (4.8) Equation (4.8) should be considered a first-order approximation. However, since surface roughness can increase resistance by 10 to 50% (see " Effect of Conductor Surface Roughness " below), equation (4.8) will probably provide an adequate level of accuracy for most situations. A more exact formula for the ac resistance of a microstrip can be derived through conformal mapping techniques. (4.9) Equation set (4.9) was derived using conformal mapping techniques and appears to have excellent agreement with experimental results [ Collins, 1992 ]. These formulas are significantly more cumbersome than (4.8) but should yield the most accurate results. Equation (4.8) will tend to yield resistance values that are larger then those in (4.9) . Often, the slightly larger values given by (4.8) are used to roughly approximate the additional resistance gained from surface roughness. Frequency-Dependent Conductor Losses in a Stripline. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 All Pages Summary : ## An approximation of the effective resistance of the ground plane can be derived using a technique similar to that used to find the ac resistance of the signal conductor. Substituting this result into equation (4.1) yields (4.6) The total ac resistance is the sum of the conductor and ground plane resistance: (4.7) (4.8) Equation (4.8) should be considered a first-order approximation. Tags : conductor,equation,ground,deried,current,roughness,approximation,surface,mapping,skin,signal,approximated,quot Related Documents Terms    |    Link pdf-search-files.com    |    Site Map    |    Contact    All books are the property of their respective owners. Please respect the publisher and the author for their creations if their books copyrighted © 2009 pdf-search-files.com

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### Be The Class-Topper With SS 2035 Statistical Science Assignment Help Service At Affordable Prices! Home   Course   SS 2035 Statistical Science Assignment Help Previous << || >> Next SS 2035 Statistical Science This SS 2035 Statistical Science course aims to provide some basic statistical tools to help you understand the concept of "data variability". These tools will allow you to analyze this variability so that you can conclude the data. It will help you understand: • What statistical methods and tests should be used when analyzing data? • How to use these methods and tests and where they come from. • What are the main assumptions of your chosen statistical test and what happens if these assumptions turn out to be wrong? The course as well introduces breadth and unity of the field by presenting the full range of modern statistical ideas at an intermediate technical level, accessible to a wide range of practitioners, researchers and students studying statistics and probability. In addition to using statistical methods and tests to analyze data, the first third of this course will discuss the concept of probability and how it can be used to model certain phenomena that occur in science, social science, and business. This course will explore the different types of probabilistic models (discrete and continuous) and show how to use them to predict future events. Many challenges and problems are faced by students pursuing higher education at colleges/universities. Students who are accustomed to striving for victory in the whole college/university, in the faculty or any academic group face huge obstacles. These obstacles make them feel difficult and interfere with their thinking, but they also make them nervous. The main situation arises when students study complex subject topics and begin seeking help with assignments and homework. Most of the students were unable to jot down SS 2035 Statistical Science based assignments and homework as needed. The tutors of ExpertsMinds provide the finest online SS 2035 Statistical Science Assignment Help services to the students to help students fully understand the subject and guide them in their overall academic tasks by providing online lessons. Another major problem for students is the lack of time. They used to spend most of their time lecturing. Therefore, they cannot find a convenient time to allocate and seek help. In addition, students often find writing assignments and homework boring because they do not have enough data on the topic and they lose the ability to write assignments and homework. For this reason, they choose unhealthy online resources, resulting in poor grades. Students will select verified counselors to write their homework and assignments and will receive SS 2035 Statistical Science Assignment Help services to help them. These consultants provide written homework and assignments when they embark on their work, which is never below plagiarism at college/university. So even at the last minute of your application, we provide high-quality SS 2035 Statistical Science Homework Help services, covering all your academic needs and wants. We have experienced tutors to assist you with this course. Our PhDs can adapt and substantiate needs, wants and needs to meet the expectations of our students. Our counselors have a clear way of expressing students of all levels to reach a completely different solution from their grades. If you are not satisfied with our online SS 2035 Statistical Science Assignment Help services, our tutors will provide extraordinary assistance in obtaining bonuses and money-back guarantees. We, at SS 2035 Statistical Science Homework Help desk allow a partial payment process during an order, so you do not need to pay the full fees to take advantage of our online assignments assistance service. Students can purchase finest documents from well-educated and qualified consultants at any time through our online SS 2035 Statistical Science Assignment Help service. Our students can easily carry over past decisions right away for more reference material to help them while writing current assignments and homework. Below are some of the relevant courses, which are covered by the professional tutors of ExpertsMinds: • SS 1023 - Statistical Concepts Assignment Help • SS 1024 - Introduction to Statistics Assignment Help • SS 2037 - Statistics for Health Assignment Help • SS 2141 - Applied Probability and Statistics for Engineers Assignment Help • SS 2244 - Statistics for Science Assignment Help • SS 2857 - Probability and Statistics Assignment Help • SS 3859 - Regression Assignment Help • SS 4654 - Markov Chains with Applications Assignment Help • SS 4846 - Experimental Design Assignment Help • SS 4864 - Advanced Statistical Computing Assignment Help Tag This :- SS 2035 Statistical Science Assignment Help ### Are You Seeking Trusted Tutor's Advice? Get Academic Excellence with Best Skilled Tutor! Order Assignment Now!

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# For Loop Problem error 1 view (last 30 days) shalaw faraj on 15 Jul 2019 Commented: shalaw faraj on 15 Jul 2019 [n,m]=size(img); part1=img(1:n/2,1:m/2); part2=img(1:n/2,(m/2)+1:end); part3=img(n/2+1:end,1:m/2); part4=img(n/2+1:end,m/2+1:end); for i=1:4 subplot(2,2,i); end #### 1 Comment Stephen Cobeldick on 15 Jul 2019 Simply use a cell array with indexing: Putting numbers into variable names is a sign that you are doing something wrong. In most cases using indexing is simpler, neater, and much more efficient. [n,m]=size(img); part{1}=img(1:n/2,1:m/2); part{2}=img(1:n/2,(m/2)+1:end); part{3}=img(n/2+1:end,1:m/2); part{4}=img(n/2+1:end,m/2+1:end); for i=1:4 subplot(2,2,i); imshow(part{i}); end #### 1 Comment shalaw faraj on 15 Jul 2019 Andrei Bobrov on 15 Jul 2019 [n,m]=size(img); imgs = mat2cell(img,[n,n]/2,[m,m]/2)'; for ii = 1:4 subplot(2,2,ii); imshow(imgs{ii}); end shalaw faraj on 15 Jul 2019 your answre is greate, what about 4*4 and 8*8 and .... ? very thanks. Andrei Bobrov on 15 Jul 2019 k = 4; [n,m]=size(img); imgs = mat2cell(img, n/k*ones(1,k), m/k*ones(1,k))'; for ii = 1:k^2 subplot(k,k,ii); imshow(imgs{ii}); end shalaw faraj on 15 Jul 2019 I am very sorry, but I want to find (mean, max, min, std, entropy) for each block and using for but it is not working please help. thanks again. [n,m]=size(img); part{1}=img(1:n/2,1:m/2); part{2}=img(1:n/2,(m/2)+1:end); part{3}=img(n/2+1:end,1:m/2); part{4}=img(n/2+1:end,m/2+1:end); for i=1:4 subplot(2,2,i); imshow(part{i}); Xmean{i}=mean(part{i}); Xmax{i}=max(part{i}); Xmin{i}=min(part{i}); Xstd{i}=std(part{i}); Xentropy{i}=entropy(part{i}); end

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Share # NCERT solutions for Class 7 Mathematics Textbook chapter 12 - Algebraic Expressions [Latest edition] Course Textbook page ## Chapter 12: Algebraic Expressions Ex. 12.1Ex. 12.2Ex. 12.3Ex. 12.4 #### NCERT solutions for Class 7 Mathematics Textbook Chapter 12 Algebraic Expressions Exercise 12.1 [Pages 234 - 235] Ex. 12.1 | Q 1.1 | Page 234 Get the algebraic expressions in the following cases using variables, constants and arithmetic operation Subtraction of z from y Ex. 12.1 | Q 1.2 | Page 234 Get the algebraic expressions in the following cases using variables, constants and arithmetic operation One-half of the sum of numbers x and y. Ex. 12.1 | Q 1.3 | Page 234 Get the algebraic expressions in the following cases using variables, constants and arithmetic operation The number z multiplied by itself. Ex. 12.1 | Q 1.4 | Page 234 Get the algebraic expressions in the following cases using variables, constants and arithmetic operation One-fourth of the product of numbers p and q. Ex. 12.1 | Q 1.5 | Page 234 Get the algebraic expressions in the following cases using variables, constants and arithmetic operation Numbers x and y both squared and added Ex. 12.1 | Q 1.6 | Page 234 Get the algebraic expressions in the following cases using variables, constants and arithmetic operation Number 5 added to three times the product of number m and n. Ex. 12.1 | Q 1.7 | Page 234 Get the algebraic expressions in the following cases using variables, constants and arithmetic operation Product of numbers y and z subtracted from 10. Ex. 12.1 | Q 1.8 | Page 234 Get the algebraic expressions in the following cases using variables, constants and arithmetic operation Sum of numbers and b subtracted from their product Ex. 12.1 | Q 2.1 | Page 234 Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams. a) x − 3 b)1 + x + x2 c) y − y3 d) 5xy2 +   7x2y e) − ab + 2b2 − 3a2 Ex. 12.1 | Q 2.2 | Page 234 Identify terms and factors in the expressions given below: a) − 4x + 5 b) − 4x + 5y c) 5y + 3y2 d) xy + 2x2y2 e) pq + q f) 1.2 ab − 2.4 b + 3.6 a g) 3/4 x + 1/4 h) 0.1p2 + 0.2q2 Ex. 12.1 | Q 3 | Page 235 Identify the numerical coefficients of terms (other than constants) in the following expressions: 1) 5 − 3t2 2) 1 + t + t2 + t3 3) x + 2xy+ 3y 4) 100m + 1000n 5) − p2q2 + 7pq 6) 1.2a + 0.8b 7) 3.14 r2 8) 2 (l + b) 9) 0.1y + 0.01 y2 Ex. 12.1 | Q 4.1 | Page 235 Identify terms which contain x and give the coefficient of x. 1) y2x + y 2) 13y2− 8yx 3) x + y + 2 4) 5 + z + zx 5) 1 + x+ xy 6) 12xy2 + 25 7) 7x + xy2 Ex. 12.1 | Q 4.2 | Page 235 Identify terms which contain y2 and give the coefficient of y2. 1) 8 - xy2 2) 5y2 + 7x 3) 2x2y - 15xy2 + 7y2 Ex. 12.1 | Q 5.01 | Page 235 Classify into monomials, binomials and trinomials 4y − 7z Ex. 12.1 | Q 5.02 | Page 235 Classify into monomials, binomials and trinomials y2 Ex. 12.1 | Q 5.03 | Page 235 Classify into monomials, binomials and trinomials. x + y − xy Ex. 12.1 | Q 5.04 | Page 235 Classify into monomials, binomials and trinomials 100 Ex. 12.1 | Q 5.05 | Page 235 Classify into monomials, binomials and trinomials ab − a − b Ex. 12.1 | Q 5.06 | Page 235 Classify into monomials, binomials and trinomials 5 − 3t Ex. 12.1 | Q 5.07 | Page 235 Classify into monomials, binomials and trinomials 4p2q − 4pq2 Ex. 12.1 | Q 5.08 | Page 235 Classify into monomials, binomials and trinomials 7mn Ex. 12.1 | Q 5.09 | Page 235 Classify into monomials, binomials and trinomials z2 − 3z + 8 Ex. 12.1 | Q 5.1 | Page 235 Classify into monomials, binomials and trinomials a2 + b2 Ex. 12.1 | Q 5.11 | Page 235 Classify into monomials, binomials and trinomials z2 + z Ex. 12.1 | Q 5.12 | Page 235 Classify into monomials, binomials and trinomials 1 + x + x2 Ex. 12.1 | Q 6.1 | Page 235 State whether a given pair of terms is of like or unlike term 1, 100 Ex. 12.1 | Q 6.2 | Page 235 State whether a given pair of terms is of like or unlike term -7x, 5/2 x Ex. 12.1 | Q 6.3 | Page 235 State whether a given pair of terms is of like or unlike terms. − 29x, − 29y Ex. 12.1 | Q 6.4 | Page 235 State whether a given pair of terms is of like or unlike terms. 14xy, 42yx Ex. 12.1 | Q 6.5 | Page 235 State whether a given pair of terms is of like or unlike terms. 4m2p, 4mp2 Ex. 12.1 | Q 6.6 | Page 235 State whether a given pair of terms is of like or unlike terms. 12xz, 12 x2z2 Ex. 12.1 | Q 7.1 | Page 235 Identify like terms in the following: −xy2, − 4yx2, 8x2, 2xy2, 7y, − 11x2, − 100x, −11yx, 20x2y, −6x2, y, 2xy,3x Ex. 12.1 | Q 7.2 | Page 235 Identify like terms in the following: 10pq, 7p, 8q, − p2q2, − 7qp, − 100q, − 23, 12q2p2, − 5p2, 41, 2405p, 78qp, 13p2q, qp2, 701p2 #### NCERT solutions for Class 7 Mathematics Textbook Chapter 12 Algebraic Expressions Exercise 12.2 [Pages 239 - 240] Ex. 12.2 | Q 1.1 | Page 239 Simplify combining like terms: 21b − 32 + 7b − 20b Ex. 12.2 | Q 1.2 | Page 239 Simplify combining like terms: - z2 + 13z2 − 5z + 7z3 − 15z Ex. 12.2 | Q 1.3 | Page 239 Simplify combining like terms: p − (p − q) − q − (− p) Ex. 12.2 | Q 1.4 | Page 239 Simplify combining like terms: 3a - 2b - ab - (a - b + ab) + 3ab + b - a Ex. 12.2 | Q 1.5 | Page 239 Simplify combining like terms: 5x2y − 5x2 + 3y x2 − 3y2 + x2 − y2 + 8xy2 −3y2 Ex. 12.2 | Q 1.6 | Page 239 Simplify combining like terms: (3y2 + 5y - 4) - (8y - y2 - 4) Ex. 12.2 | Q 2.01 | Page 239 Add: 3mn, − 5mn, 8mn, −4mn Ex. 12.2 | Q 2.02 | Page 239 Add: t - 8tz, 3tz - z, z - t Ex. 12.2 | Q 2.03 | Page 239 Add: -7mn + 5, 12mn + 2, 9mn - 8, -2mn - 3 Ex. 12.2 | Q 2.04 | Page 239 Add: a + b - 3, b - a + 3, a - b + 3 Ex. 12.2 | Q 2.05 | Page 239 Add: 14x + 10y - 12xy - 13, 18 - 7x - 10y + 8xy, 4xy Ex. 12.2 | Q 2.06 | Page 239 Add: 5m - 7n, 3n - 4m + 2, 2m - 3mn - 5 Ex. 12.2 | Q 2.07 | Page 239 Add: 4x2y, - 3xy2, - 5xy2, 5x2y Ex. 12.2 | Q 2.08 | Page 239 Add: 3p2q2 - 4pq + 5, - 10p2q2, 15 + 9pq + 7p2q2 Ex. 12.2 | Q 2.09 | Page 239 Add:ab - 4a, 4b - ab, 4a - 4b Ex. 12.2 | Q 2.1 | Page 239 Add: x2 - y2 - 1 , y2 - 1 - x2, 1- x2 - y2 Ex. 12.2 | Q 3.1 | Page 240 Subtract: - 5y2 from y2 Ex. 12.2 | Q 3.2 | Page 240 Subtract: 6xy from − 12xy Ex. 12.2 | Q 3.3 | Page 240 Subtract: (a - b) from (a + b) Ex. 12.2 | Q 3.4 | Page 240 Subtract: a (b - 5) from b (5 - a) Ex. 12.2 | Q 3.5 | Page 240 Subtract: -m2 + 5mn from 4m2 - 3mn + 8 Ex. 12.2 | Q 3.6 | Page 240 Subtract: -x2 + 10x - 5 from 5x - 10 Ex. 12.2 | Q 3.7 | Page 240 Subtract: 5a2 - 7ab + 5b2 from 3ab - 2a2 -2b2 Ex. 12.2 | Q 3.8 | Page 240 Subtract: 4pq - 5q2 - 3p2 from 5p2 + 3q2 - pq Ex. 12.2 | Q 4.1 | Page 240 What should be added to x2 + xy + y2 to obtain 2x2 + 3xy? Ex. 12.2 | Q 4.2 | Page 240 What should be subtracted from 2a + 8b + 10 to get - 3a + 7b + 16? Ex. 12.2 | Q 5 | Page 240 What should be taken away from 3x2 - 4y2 + 5xy + 20 to obtain - x2 - y2 + 6xy + 20? Ex. 12.2 | Q 6.1 | Page 240 From the sum of 3x - y + 11 and - y - 11, subtract 3x - y - 11. Ex. 12.2 | Q 6.2 | Page 240 From the sum of 4 + 3x and 5 - 4x + 2x2, subtract the sum of 3x2 - 5x and -x2 + 2x + 5. #### NCERT solutions for Class 7 Mathematics Textbook Chapter 12 Algebraic Expressions Exercise 12.3 [Page 242] Ex. 12.3 | Q 1.1 | Page 242 If m = 2, find the value of m − 2 Ex. 12.3 | Q 1.2 | Page 242 If m = 2, find the value of 3m − 5 Ex. 12.3 | Q 1.3 | Page 242 If m = 2, find the value of 9 - 5m Ex. 12.3 | Q 1.4 | Page 242 If m = 2, find the value of: 3m2 − 2m − 7 Ex. 12.3 | Q 1.5 | Page 242 If m = 2, find the value of: "5m"/2 - 4 Ex. 12.3 | Q 2.1 | Page 242 If p = −2, find the value of: 4p + 7 Ex. 12.3 | Q 2.2 | Page 242 If p = -2, find the value of −3p2 + 4p + 7 Ex. 12.3 | Q 2.3 | Page 242 If p = -2, find the value of -2p3 - 3p2 + 4p + 7 Ex. 12.3 | Q 3.1 | Page 242 Find the value of the following expressions, when x = − 1: 2x - 7 Ex. 12.3 | Q 3.2 | Page 242 Find the value of the following expressions, when x = - 1: -x + 2 Ex. 12.3 | Q 3.3 | Page 242 Find the value of the following expressions, when x = -1: x2 + 2x + 1 Ex. 12.3 | Q 3.4 | Page 242 Find the value of the following expressions, when x = − 1: 2x2 − x − 2 Ex. 12.3 | Q 4.1 | Page 242 If a = 2, b = − 2, find the value of a2 + b2 Ex. 12.3 | Q 4.2 | Page 242 If a = 2, b = − 2, find the value of a2 + ab + b2 Ex. 12.3 | Q 4.3 | Page 242 If a = 2, b = − 2, find the value of a2 − b2 Ex. 12.3 | Q 5.1 | Page 242 When a = 0, b = − 1, find the value of the given expressions 2a + 2b Ex. 12.3 | Q 5.2 | Page 242 When a = 0, b = − 1, find the value of the given expressions 2a2 + b2 + 1 Ex. 12.3 | Q 5.3 | Page 242 When a = 0, b = − 1, find the value of the given expressions 2a2 b + 2ab2 + ab Ex. 12.3 | Q 5.4 | Page 242 When a = 0, b = − 1, find the value of the given expressions a2 + ab + 2 Ex. 12.3 | Q 6.1 | Page 242 Simplify the expressions and find the value if x is equal to 2: x + 7 + 4 (x - 5) Ex. 12.3 | Q 6.2 | Page 242 Simplify the expressions and find the value if x is equal to 2 : 3 (x + 2) + 5x - 7 Ex. 12.3 | Q 6.3 | Page 242 Simplify the expressions and find the value if x is equal to 2: 6x + 5 (x − 2) Ex. 12.3 | Q 6.4 | Page 242 Simplify the expressions and find the value if x is equal to 2: 4 (2x - 1) + 3+ 11 Ex. 12.3 | Q 7.1 | Page 242 Simplify these expressions and find their values if x = 3, a = − 1, b = − 2. 3x - 5 - x + 9 Ex. 12.3 | Q 7.2 | Page 242 Simplify these expressions and find their values if x = 3, a = − 1, b = − 2 2 - 8x + 4x + 4 Ex. 12.3 | Q 7.3 | Page 242 Simplify these expressions and find their values if x = 3, a = − 1, b = − 2 3a + 5 - 8a + 1 Ex. 12.3 | Q 7.4 | Page 242 Simplify these expressions and find their values if x = 3, a = − 1, b = − 2 10 - 3b - 4 - 5b Ex. 12.3 | Q 7.5 | Page 242 Simplify these expressions and find their values if x = 3, a = − 1, b = − 2. 2a - 2b - 4 - 5 + a Ex. 12.3 | Q 8.1 | Page 242 if z = 10, find the value of z3 − 3 (z − 10). Ex. 12.3 | Q 8.2 | Page 242 If p = − 10, find the value of p2 − 2p − 100 Ex. 12.3 | Q 9 | Page 242 What should be the value of a if the value of 2x2 + x − a equals to 5, when x = 0? Ex. 12.3 | Q 10 | Page 242 Simplify the expression and find its value when a = 5 and b = −3. 2 (a2 + ab) + 3 − ab #### NCERT solutions for Class 7 Mathematics Textbook Chapter 12 Algebraic Expressions Exercise 12.4 [Pages 246 - 247] Ex. 12.4 | Q 1.1 | Page 246 Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators. If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form 5, 10, 100 digits of the kind − Ex. 12.4 | Q 1.2 | Page 246 Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators. If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form 5, 10, 100 digits of the kind − Ex. 12.4 | Q 1.3 | Page 246 Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators. If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form 5, 10, 100 digits of the kind − Ex. 12.4 | Q 2 | Page 247 Use the given algebraic expression to complete the table of number patterns. S. No Expression Terms 1st 2nd 3rd 4th 5th ... 10th ... 100th ... 1 2n - 1 1 3 5 7 9 - 19 - - - 2 3n + 2 2 5 8 11 - - - - - - 3 4n + 1 5 9 13 17 - - - - - - 4 7n + 20 27 34 41 48 - - - - - - 5 n2 + 1 2 5 10 17 - - - - 10001 - ## Chapter 12: Algebraic Expressions Ex. 12.1Ex. 12.2Ex. 12.3Ex. 12.4 ## NCERT solutions for Class 7 Mathematics Textbook chapter 12 - Algebraic Expressions NCERT solutions for Class 7 Mathematics Textbook chapter 12 (Algebraic Expressions) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 7 Mathematics Textbook solutions in a manner that help students grasp basic concepts better and faster. Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students. Concepts covered in Class 7 Mathematics Textbook chapter 12 Algebraic Expressions are Concept of Expressions Formed, Terms of an Expression, Like and Unlike Terms, Monomials, Binomials, Trinomials and Polynomials, Addition and Subtraction of Algebraic Expressions, Finding the Value of an Expression, Using Algebraic Expressions – Formulas and Rules. Using NCERT Class 7 solutions Algebraic Expressions exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 7 prefer NCERT Textbook Solutions to score more in exam. Get the free view of chapter 12 Algebraic Expressions Class 7 extra questions for Class 7 Mathematics Textbook and can use Shaalaa.com to keep it handy for your exam preparation S

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This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A199884 Number of compositions of n such that the number of parts is not divisible by the greatest part. 2 0, 1, 1, 6, 8, 19, 43, 90, 167, 339, 722, 1503, 2987, 5883, 11820, 24167, 49348, 99707, 199626, 398475, 797457, 1604029, 3237867, 6534327, 13143278, 26336266, 52664325, 105349525, 211135006, 423949168, 851981311, 1711365899, 3433202397, 6878160656, 13768314357 (list; graph; refs; listen; history; text; internal format) OFFSET 1,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..250 FORMULA G.f.: Sum_{n>0} (2^(n-1)*x^n -Sum_{d|n} ((x^(d+1)-x)^n-(x^d-x)^n)/(x-1)^n). a(n) = A000079(n-1) - A171634(n). EXAMPLE a(5) = 8: [1,2,2], [1,4], [2,1,2], [2,2,1], [2,3], [3,2], [4,1], [5]. MAPLE b:= proc(n, t, g) option remember; `if`(n=0, `if`(irem(t, g)=0, 0, 1), add(b(n-i, t+1, max(i, g)), i=1..n)) end: a:= n-> b(n, 0, 0): seq(a(n), n=1..40); MATHEMATICA b[n_, t_, g_] := b[n, t, g] = If[n == 0, If[Mod[t, g] == 0, 0, 1], Sum [b[n-i, t+1, Max[i, g]], {i, 1, n}]]; a[n_] := b[n, 0, 0]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Nov 05 2014, after Alois P. Heinz *) CROSSREFS Cf. A000079, A171634, A200727. Sequence in context: A086913 A108341 A173975 * A028331 A279729 A309653 Adjacent sequences:  A199881 A199882 A199883 * A199885 A199886 A199887 KEYWORD nonn AUTHOR Alois P. Heinz, Nov 11 2011 STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)

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My Math Forum Sorting n real numbers in O(n), when number of digits is bounded Applied Math Applied Math Forum April 10th, 2016, 01:55 AM #1 Member   Joined: Mar 2015 From: USA Posts: 34 Thanks: 1 Sorting n real numbers in O(n), when number of digits is bounded I need to explain how to modify radix sort, in order to sort n real numbers, when every number has O(1) digits. General and short description is enough. I thought of making the numbers to have same number of digits left and right to the decimal point, then sort with radix sort only the negative numbers and make sure they will be afterwards in the beginning of the array (before the non-negative numbers, can be implmented at O(n)). Finally- sort the rest of the numbers with radix sort. Is there anything wrong with that? Tags bounded, digits, number, numbers, real, sorting Thread Tools Display Modes Linear Mode Similar Threads Thread Thread Starter Forum Replies Last Post karanv10111 Advanced Statistics 2 June 2nd, 2014 12:45 PM grangeeducation Elementary Math 2 May 29th, 2014 01:35 AM ricsi046 Number Theory 2 November 10th, 2013 05:31 AM Albert.Teng Algebra 2 July 15th, 2012 08:14 PM brangelito Algebra 1 June 13th, 2010 08:29 AM Contact - Home - Forums - Cryptocurrency Forum - Top

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IIT-JEE Apne doubts clear karein ab Whatsapp (8 400 400 400) par bhi. Try it now. Click Question to Get Free Answers Watch 1 minute video This browser does not support the video element. Question From class 14 Chapter RATIO & PROPORTION 27 को दो भागो मे इस प्रकार विभाजित करे कि पहले भाग का 5 गुणा और दूसरे भाग का 11 गुना दोनों मिलाकर 195 के बराबर हो, तो पहले और दूसरे भाग का अनुपात है B Solution : Let the first part is =x <br> second part is =y <br> प्रश्ननुसार <br> 5x+11y=195 <br> x+y=27 <br> Solve equation (i) and (ii) <br> x=17 <br> y=10 <br> Divide 80 into two parts such that the product of the cube of the part and the fifth power of the second part is the greatest. 4:36 Divide 8 into two positive parts such that the sum of the squares of one part and the cube of the other part is inferior. 3:09 Who is responsible for sending sensations from one part of the body to another? 2:04 The radius of a solid sphere of iron is r. Its two equal parts are divided. Of the same diameter after melting the first part Length wire is made. Putting the other part of the same diameter Length wire is made. Prove that the ratio of resistances of these stars will be equal to the ratio of the square of their length. 3:29 If the sum of one half of a number and one fifth of that number is one third of that number If there are more numbers A company manufactures bicycles in two plants. 60% cycles are made in the first plant and 40% cycles in the second plant. 80% of the bicycles of the first plant and 90% of the other plants get standard grade in quality. A cycle is chosen randomly and is found to be of standard grade. Find the probability that it is made in the second plant. 3:49 The wire of R resistance is cut into n equal parts. These parts are added in parallel order. The equivalent resistance of a combination is - 3:25 The two evenly charged bodies are placed 5 cm away from each other in the air. If the second body is displaced 5 cm from the first body, its repulsion force 2:49 Which system of the body of high-grade animals that carries oxygen, carbon dioxide, nutrients and substances produced as a result of metabolic activities from one part of the body to another? 1:56 A progressive wave whose equation Is reflected on the boundary page of two mediums. Part of it is reflected in the first medium and some part is transmitted in the second medium. If the amplitude of the reflected and transverse wave respectively And If, write their equation if the second medium is (i) rare, (ii) dense. 3:56 A body of m mass A falls under gravity, breaking down into two parts - Part B of the mass and Part of mass C | How will the mass center of the body of parts B and C move compared to the center of mass of A? 5:15 How to divide a charge Q into two parts to keep them at a fixed distance but have maximum repulsion force between them (both part points are charges)? 5:34 At a point, velocities of 4,3,2 and 1 km / hour are such that between the first and second , Between the second and third And between the third and fourth Is the angle of. Find the resultant velocity. Is a two-digit number. When this number is divided by the sum of its digits, the quotient is 7. If 27 is subtracted from this number, then 27 is subtracted from the number, then the place of the digits of the number changes among themselves. Then find the number. 2:17 50% of a first-class process is finished in 10 minutes. In how much time 99% of this reaction will be completed? 3:30 Latest Blog Post AP SSC Result 2020 for Class 10 Declared, All Students Promoted AP SSC result 2020 for class 10 declared, all students promoted. Know how to check BSEAP result 2020 & complete details related to AP class 10 result 2020.

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{[ promptMessage ]} Bookmark it {[ promptMessage ]} Ch4 HW4 S2008 # Ch4 HW4 S2008 - Ch4 HW4 S2008 10:28 AM Web Assign Ch4 HW4... This preview shows pages 1–3. Sign up to view the full content. 4/25/08 10:28 AM Ch4 HW4 S2008 Page 1 of 13 http://www.webassign.net/[email protected]/[email protected] Ch4 HW4 S2008 (Homework) KRISTIN SEILOFF PHYS 2211 M & N Spring 08, section N05, Spring 2008 Instructor: Jennifer Curtis Description More on curving motion Instructions Reading: Sec. 4.13. Additional examples of curving motion are found in Sec. 4.18. Web Assign Current Score: 76.5 out of 77 Due: Wednesday, February 13, 200812:00 PM EST 1. 7/7 points | 1/4 submissions A child of mass 20 kg swings at the end of an elastic cord. At the bottom of the swing, the child's velocity is horizontal, and the speed is 12 m/s. At this instant the cord is 3.60 m long. (a) At this instant, what is the parallel component of the rate of change of the child's momentum? = < 0 0 , 0 0 , 0 0 > (kg·m/s)/s (b) At this instant, what is the perpendicular component of the rate of change of the child's momentum? = < 0 0 , 800 800 , 0 0 > (kg·m/s)/s (c) At this instant, what is the net force acting on the child? net = < 0 0 , 800 800 This preview has intentionally blurred sections. Sign up to view the full version. View Full Document 4/25/08 10:28 AM Ch4 HW4 S2008 Page 2 of 13 http://www.webassign.net/[email protected]/[email protected] , 0 0 > N (d) What is the magnitude of the force that the elastic cord exerts on the child? (It helps to draw a diagram of the forces.) | due to cord | = 996 996 N (e) The relaxed length of the elastic cord is 3.56 m. What is the stiffness of the cord? (You will be given credit for this part if it is consistent with your answer to part d, even if the answer to part d is incorrect.) k s = 24900 24900 N/m Solution or Explanation (a) At this instant the magnitude of the momentum isn't changing, so the rate of change of the parallel component of momentum is zero. (b) There is a rate of change of the perpendicular component of momentum, upward. (c) The momentum principle says that the net force is equal in magnitude and direction to the rate of change of momentum, and the direction is upward (+y), directed toward the center of the kissing circle. The x and z components of the net force are zero. (d) If you draw a diagram of the forces, you'll see that the y component of the net force has two contributions, the upward force of magnitude F of the elastic cord and the downward force of the Earth of magnitude mg. So the y component of the net force found in part (c) is equal to F-mg; solve for F. (e) Now that you know from part (c) the force exerted by the elastic cord, you can determine the stiffness from |F| = k s |s|, where s is the stretch (change in length of the cord). 2. 6.5/7 points | 4/4 submissions A Ferris wheel is a vertical, circular amusement ride with radius 9 m. Riders sit on seats that swivel to remain horizontal. The Ferris wheel rotates at a constant rate, going around once in 9 s. Consider a rider whose mass is 58 kg. At the bottom of the ride, what is the parallel component of the rate of change of the rider's momentum? = < 0 0 , 0 0 , 0 > kg·m/s/s At the bottom of the ride, what is the perpendicular component of the rate of change of the rider's momentum? This is the end of the preview. Sign up to access the rest of the document. {[ snackBarMessage ]} ### Page1 / 13 Ch4 HW4 S2008 - Ch4 HW4 S2008 10:28 AM Web Assign Ch4 HW4... This preview shows document pages 1 - 3. Sign up to view the full document. View Full Document Ask a homework question - tutors are online

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# Risk Equations and Formulas Calculator ## Toxicology and Risk Assessment Solving for number of cancer cases in individuals not exposed to carcinogen #### Inputs: number of cancer cases in individuals exposed to carcinogen (XC) total number of individuals not exposed to carcinogen (NN) standard mortality ratio or relative risk (SMR) total number of individuals exposed to carcinogen (NC) #### Conversions: number of cancer cases in individuals exposed to carcinogen (XC)= 0 = 0 total number of individuals not exposed to carcinogen (NN)= 0 = 0 standard mortality ratio or relative risk (SMR)= 0 = 0 total number of individuals exposed to carcinogen (NC)= 0 = 0 #### Solution: number of cancer cases in individuals not exposed to carcinogen (XN)= NOT CALCULATED #### Other Units: Change Equation Select to solve for a different unknown probability adverse health effects number individuals in the population number standard mortality ratio or relative risk probability of fatal cancer cases of individuals exposed to carcinogen probability of fatal cancer cases of individuals not exposed to carcinogen standard mortality ratio or relative risk number of cancer cases in individuals exposed to carcinogen total number of individuals not exposed to carcinogen number of cancer cases in individuals not exposed to carcinogen total number of individuals exposed to carcinogen standard mortality ratio or relative risk number of cancer deaths in a population from exposure to carcinogen number of cancer deaths in a same size population not exposed to carcinogen carcinogenic risk chronic daily intake carcinogen slope factor hazard index chronic daily intake reference dose administered dose exposure point concentration contact rate exposure frequency exposure duration body weight averaging time fugitive dust inhalation pathway intake dose exposure point concentration contact rate exposure frequency exposure duration retention rate bloodstream absorption body weight averaging time References - Books: 1) P. Aarne Vesilind, J. Jeffrey Peirce and Ruth F. Weiner. 1994. Environmental Engineering. Butterworth Heinemann. 3rd ed. 2) Michael D. LaGrega, Phillip L. Buckingham and Jeffery C. Evan. 1994. Hazardous Waste Management. McGraw Hill, Inc. Online Web Apps, Rich Internet Application, Technical Tools, Specifications, How to Guides, Training, Applications, Examples, Tutorials, Reviews, Answers, Test Review Resources, Analysis, Homework Solutions, Worksheets, Help, Data and Information for Engineers, Technicians, Teachers, Tutors, Researchers, K-12 Education, College and High School Students, Science Fair Projects and Scientists By Jimmy Raymond Contact: aj@ajdesigner.com

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# ttest2 with a group describing independent values (statistics) 19 views (last 30 days) Pedro Gomis on 5 Jan 2021 Edited: Jeff Miller on 9 Jan 2021 Hi, I use Matlab ttest2 function to assess if observations from vectors x and y come from populations with different means. The function works fine if vectors are passed as arguments: [h, p] = ttest2(x, y) My data includes biomarker (as blood pressure) in x and y during day and night, respectively. Therefore, we assess paired groups into a matrix [x y], where: x = [120, 110.5, 123, 140, 142, 151, 121, 119, 110, 115, 130]' % there are more observations y = [118, 110, 120, 135, 134, 140, 120, 116, 110, 113 ,127]' % there are more observations m = [x y]; The point is that we also want to compare unpaired or independent groups (males vs. females), at day and night. For this, a third column is included defining the group (male=0, female=1) in matrix [x y g], where g = [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1]' % there are more observations m = [x y g]; Function anova1() has the functionality of including a group as second argument for each observation in x or y. I wonder if it is possible to use ttest2 function in anova1() fashion, something like [h, p] = ttest2(x, g) % where x contains the observation and g contains categorical values To compare the biomarker, e.g. during night, between male and female, without rearrenge vectors Thanks Jeff Miller on 5 Jan 2021 Edited: Jeff Miller on 9 Jan 2021 No, it is not possible to use ttest2 as you suggest. Your design has 2 factors: gender and time (day/night) with repeated measures on the time factor, and you can conveniently analyze it with 'fitlm' and 'ranova', something like this (note the categorical conversions added on edit): x = [120, 110.5, 123, 140, 142, 151, 121, 119, 110, 115, 130]'; % there are more observations y = [118, 110, 120, 135, 134, 140, 120, 116, 110, 113 ,127]'; % there are more observations g = [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1]'; % there are more observations m = [x y g]; t = array2table(m,'VariableNames',{'x','y','gender'}); t.gender = categorical(t.gender); timeDesign = table([1 2]','VariableNames',{'time'}); timeDesign.time = categorical(timeDesign.time); rm = fitrm(t,'x-y~gender','WithinDesign',timeDesign); ranova(rm,'WithinModel','time') Pedro Gomis on 5 Jan 2021 I will try fitrm and repeated measures anova.

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# 1 tonne per cubic centimeter in milligrams per cubic millimeter ## tonnes/centimeter³ to milligram/millimeter³ unit converter of density 1 tonne per cubic centimeter [t/cm³] = 1 000 000 milligrams per cubic millimeter [mg/mm³] ### tonnes per cubic centimeter to milligrams per cubic millimeter density conversion cards • 1 through 25 tonnes per cubic centimeter • 1 t/cm³ to mg/mm³ = 1 000 000 mg/mm³ • 2 t/cm³ to mg/mm³ = 2 000 000 mg/mm³ • 3 t/cm³ to mg/mm³ = 3 000 000 mg/mm³ • 4 t/cm³ to mg/mm³ = 4 000 000 mg/mm³ • 5 t/cm³ to mg/mm³ = 5 000 000 mg/mm³ • 6 t/cm³ to mg/mm³ = 6 000 000 mg/mm³ • 7 t/cm³ to mg/mm³ = 7 000 000 mg/mm³ • 8 t/cm³ to mg/mm³ = 8 000 000 mg/mm³ • 9 t/cm³ to mg/mm³ = 9 000 000 mg/mm³ • 10 t/cm³ to mg/mm³ = 10 000 000 mg/mm³ • 11 t/cm³ to mg/mm³ = 11 000 000 mg/mm³ • 12 t/cm³ to mg/mm³ = 12 000 000 mg/mm³ • 13 t/cm³ to mg/mm³ = 13 000 000 mg/mm³ • 14 t/cm³ to mg/mm³ = 14 000 000 mg/mm³ • 15 t/cm³ to mg/mm³ = 15 000 000 mg/mm³ • 16 t/cm³ to mg/mm³ = 16 000 000 mg/mm³ • 17 t/cm³ to mg/mm³ = 17 000 000 mg/mm³ • 18 t/cm³ to mg/mm³ = 18 000 000 mg/mm³ • 19 t/cm³ to mg/mm³ = 19 000 000 mg/mm³ • 20 t/cm³ to mg/mm³ = 20 000 000 mg/mm³ • 21 t/cm³ to mg/mm³ = 21 000 000 mg/mm³ • 22 t/cm³ to mg/mm³ = 22 000 000 mg/mm³ • 23 t/cm³ to mg/mm³ = 23 000 000 mg/mm³ • 24 t/cm³ to mg/mm³ = 24 000 000 mg/mm³ • 25 t/cm³ to mg/mm³ = 25 000 000 mg/mm³ • 26 through 50 tonnes per cubic centimeter • 26 t/cm³ to mg/mm³ = 26 000 000 mg/mm³ • 27 t/cm³ to mg/mm³ = 27 000 000 mg/mm³ • 28 t/cm³ to mg/mm³ = 28 000 000 mg/mm³ • 29 t/cm³ to mg/mm³ = 29 000 000 mg/mm³ • 30 t/cm³ to mg/mm³ = 30 000 000 mg/mm³ • 31 t/cm³ to mg/mm³ = 31 000 000 mg/mm³ • 32 t/cm³ to mg/mm³ = 32 000 000 mg/mm³ • 33 t/cm³ to mg/mm³ = 33 000 000 mg/mm³ • 34 t/cm³ to mg/mm³ = 34 000 000 mg/mm³ • 35 t/cm³ to mg/mm³ = 35 000 000 mg/mm³ • 36 t/cm³ to mg/mm³ = 36 000 000 mg/mm³ • 37 t/cm³ to mg/mm³ = 37 000 000 mg/mm³ • 38 t/cm³ to mg/mm³ = 38 000 000 mg/mm³ • 39 t/cm³ to mg/mm³ = 39 000 000 mg/mm³ • 40 t/cm³ to mg/mm³ = 40 000 000 mg/mm³ • 41 t/cm³ to mg/mm³ = 41 000 000 mg/mm³ • 42 t/cm³ to mg/mm³ = 42 000 000 mg/mm³ • 43 t/cm³ to mg/mm³ = 43 000 000 mg/mm³ • 44 t/cm³ to mg/mm³ = 44 000 000 mg/mm³ • 45 t/cm³ to mg/mm³ = 45 000 000 mg/mm³ • 46 t/cm³ to mg/mm³ = 46 000 000 mg/mm³ • 47 t/cm³ to mg/mm³ = 47 000 000 mg/mm³ • 48 t/cm³ to mg/mm³ = 48 000 000 mg/mm³ • 49 t/cm³ to mg/mm³ = 49 000 000 mg/mm³ • 50 t/cm³ to mg/mm³ = 50 000 000 mg/mm³ • 51 through 75 tonnes per cubic centimeter • 51 t/cm³ to mg/mm³ = 51 000 000 mg/mm³ • 52 t/cm³ to mg/mm³ = 52 000 000 mg/mm³ • 53 t/cm³ to mg/mm³ = 53 000 000 mg/mm³ • 54 t/cm³ to mg/mm³ = 54 000 000 mg/mm³ • 55 t/cm³ to mg/mm³ = 55 000 000 mg/mm³ • 56 t/cm³ to mg/mm³ = 56 000 000 mg/mm³ • 57 t/cm³ to mg/mm³ = 57 000 000 mg/mm³ • 58 t/cm³ to mg/mm³ = 58 000 000 mg/mm³ • 59 t/cm³ to mg/mm³ = 59 000 000 mg/mm³ • 60 t/cm³ to mg/mm³ = 60 000 000 mg/mm³ • 61 t/cm³ to mg/mm³ = 61 000 000 mg/mm³ • 62 t/cm³ to mg/mm³ = 62 000 000 mg/mm³ • 63 t/cm³ to mg/mm³ = 63 000 000 mg/mm³ • 64 t/cm³ to mg/mm³ = 64 000 000 mg/mm³ • 65 t/cm³ to mg/mm³ = 65 000 000 mg/mm³ • 66 t/cm³ to mg/mm³ = 66 000 000 mg/mm³ • 67 t/cm³ to mg/mm³ = 67 000 000 mg/mm³ • 68 t/cm³ to mg/mm³ = 68 000 000 mg/mm³ • 69 t/cm³ to mg/mm³ = 69 000 000 mg/mm³ • 70 t/cm³ to mg/mm³ = 70 000 000 mg/mm³ • 71 t/cm³ to mg/mm³ = 71 000 000 mg/mm³ • 72 t/cm³ to mg/mm³ = 72 000 000 mg/mm³ • 73 t/cm³ to mg/mm³ = 73 000 000 mg/mm³ • 74 t/cm³ to mg/mm³ = 74 000 000 mg/mm³ • 75 t/cm³ to mg/mm³ = 75 000 000 mg/mm³ • 76 through 100 tonnes per cubic centimeter • 76 t/cm³ to mg/mm³ = 76 000 000 mg/mm³ • 77 t/cm³ to mg/mm³ = 77 000 000 mg/mm³ • 78 t/cm³ to mg/mm³ = 78 000 000 mg/mm³ • 79 t/cm³ to mg/mm³ = 79 000 000 mg/mm³ • 80 t/cm³ to mg/mm³ = 80 000 000 mg/mm³ • 81 t/cm³ to mg/mm³ = 81 000 000 mg/mm³ • 82 t/cm³ to mg/mm³ = 82 000 000 mg/mm³ • 83 t/cm³ to mg/mm³ = 83 000 000 mg/mm³ • 84 t/cm³ to mg/mm³ = 84 000 000 mg/mm³ • 85 t/cm³ to mg/mm³ = 85 000 000 mg/mm³ • 86 t/cm³ to mg/mm³ = 86 000 000 mg/mm³ • 87 t/cm³ to mg/mm³ = 87 000 000 mg/mm³ • 88 t/cm³ to mg/mm³ = 88 000 000 mg/mm³ • 89 t/cm³ to mg/mm³ = 89 000 000 mg/mm³ • 90 t/cm³ to mg/mm³ = 90 000 000 mg/mm³ • 91 t/cm³ to mg/mm³ = 91 000 000 mg/mm³ • 92 t/cm³ to mg/mm³ = 92 000 000 mg/mm³ • 93 t/cm³ to mg/mm³ = 93 000 000 mg/mm³ • 94 t/cm³ to mg/mm³ = 94 000 000 mg/mm³ • 95 t/cm³ to mg/mm³ = 95 000 000 mg/mm³ • 96 t/cm³ to mg/mm³ = 96 000 000 mg/mm³ • 97 t/cm³ to mg/mm³ = 97 000 000 mg/mm³ • 98 t/cm³ to mg/mm³ = 98 000 000 mg/mm³ • 99 t/cm³ to mg/mm³ = 99 000 000 mg/mm³ • 100 t/cm³ to mg/mm³ = 100 000 000 mg/mm³ #### Foods, Nutrients and Calories DELI MILD MUSTARD BLEND, UPC: 041500882260 weigh(s) 304.33 gram per (metric cup) or 10.16 ounce per (US cup), and contain(s) 167 calories per 100 grams or ≈3.527 ounces  [ weight to volume | volume to weight | price | density ] #### Gravels, Substances and Oils CaribSea, Freshwater, Super Naturals, Sunset Gold weighs 1 505.74 kg/m³ (94.00028 lb/ft³) with specific gravity of 1.50574 relative to pure water.  Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical  or in a rectangular shaped aquarium or pond  [ weight to volume | volume to weight | price ] Thiosulfuric acid, disodium salt, pentahydrate [Na2S2O3 ⋅ 5H2O] weighs 1 690 kg/m³ (105.50325 lb/ft³)  [ weight to volume | volume to weight | price | mole to volume and weight | mass and molar concentration | density ] Volume to weightweight to volume and cost conversions for Refrigerant R-403B, liquid (R403B) with temperature in the range of -56.67°C (-70.006°F) to 48.89°C (120.002°F) #### Weights and Measurements The ounce per US quart density measurement unit is used to measure volume in US quarts in order to estimate weight or mass in ounces Magnetic flux is a scalar quantity that measures the magnetic flux density (induction) through a surface in a magnetic field. s/ft to s/km conversion table, s/ft to s/km unit converter or convert between all units of speed measurement. #### Calculators Calculate area of a trapezoid, its median, perimeter and sides

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1. ## Sin 2A=... If I know the value and quadrant of Sin (A+B) and Cos (A-B), how would I find Sin2A and Cos2A? Btw, 2A would equal (A+B)+(A-B). Thanks! 2. Originally Posted by JasonW If I know the value and quadrant of Sin (A+B) and Cos (A-B), how would I find Sin2A and Cos2A? Btw, 2A would equal (A+B)+(A-B). Thanks! nope, think of 2A as A + A so sin(2A) = sin(A + A) and cos(2A) = cos(A + A) and you can find each of those using the addition formulas 3. Maybe I should have explained that better. I know the formula for Sin2A and Cos2A, I'm asked for the exact value of them, given that sin (A+B)=3/5 and is in Q1, and that cos (A-B)=12/13 and is in Q4. 4. Originally Posted by JasonW If I know the value and quadrant of Sin (A+B) and Cos (A-B), how would I find Sin2A and Cos2A? Btw, 2A would equal (A+B)+(A-B). Thanks! Originally Posted by JasonW Maybe I should have explained that better. I know the formula for Sin2A and Cos2A, I'm asked for the exact value of them, given that sin (A+B)=3/5 and is in Q1, and that cos (A-B)=12/13 and is in Q4. Let's try this: We know that $sin(A + B) = \frac{3}{5}$ and A + B is in QI. Thus $cos(A + B) = \frac{4}{5}$. Similarly $sin(A - B) = -\frac{5}{13}$. So $sin(2A) = sin([A + B] + [A - B]) = sin(A + B)cos(A - B) + sin(A - B)cos(A + B)$ $= \frac{3}{5} \cdot \frac{12}{13} - \frac{5}{13} \cdot \frac{4}{5}$ etc. -Dan 5. Ah, ok, that makes sense. Thanks!

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## Monday, 31 August 2015 ### Problem Solving-Week 7 WALT: Multiply and Divide decimals numbers. In Problem Solving this week I have learnt about dividing decimal numbers. I have already learnt different ways to solve this sort of questions, and tried to find the right one that I can use every time. My buddy who helped me (Presayus) also did a question and I think that she has some very good solutions. ### Problem Solving-Week 6 WALT: Multiply and divide decimal numbers. In maths Problem Solving this week, I learnt that it is very very important to look at the last number before answering. I had to do a whole lot of decimals question and the way that I worked it out was by looking at the number on the right. For example: 1893-546=?, before I answer I am going to look at the last two numbers. So 13-16=7, after that we solve the rest of the question. The end result would be 1347. So all I'm saying is to always look at the number on the right. ### What Am I? WALT: Use our inferencing skills to find meaning in the text. Here is my poem that sounds like something but is something else. I wrote this with the help of Rosalina. Hope you like it and guess it right. For a little writing/reading activity, we wrote poems that explained something when it sounded like something else. We paired up and wrote a poem that was like an example that we saw. I tried this to some people and they guessed it in the end. I hope that you can try to guess it and get it right ## Sunday, 30 August 2015 ### Loofah Review WALT: Learn and use new Vocabulary. This Week in reading, we have learnt new vocabulary. We have also have learnt about Loofahs and how to use them. We also learnt about one more thing which is, how to write a Custom Review. If you can see at the bottom it says if this helped you. If it did or did not, please could you tell me. ## Saturday, 29 August 2015 ### Team Four's Trade Fair WALT: Use language that paints a picture in the mind of our reader. This Terms topic is Trade and Enterprise and in team four we have our own business’, money and online banking accounts. Some of us have a job, which we had to write an application for. Because of all of this, we (team four) had our very own trade fair to advertise and sell our own products, I will tell you about this later in my writing. Our topic Trade and Enterprise, focuses on the two important words. I thought about the words Trade and Enterprise and what they mean during the trade fair. In the Trade Fair, we had to take orders from  our customers, make orders for our product, gain interest from our customers, explain what the product was and say what they would have to trade for the product. In our six business’ which are Toys, Kitchen, Custom Stationery, Jewellery, Musical Instruments and Homeware we had to prepare for the Trade Fair. I am in Toys, we had to take orders unlike the business Kitchen. We prepared in week one, two and three by making order forms, making example products and getting the price sorted. My product is squishy balls which sold very successfully at the Trade Fair. At the Trade Fair we had turns with our work buddy, one of us had to go trading well the other had to stay at the stall. Our turns lasted for half of the whole time. I was the first to go trading with my earned 10 PT and I bought a lot of stuff, but I forgot to buy three things. They were an orange candle, mini loom band headphones and some food. At the our stall, my partner was supposed to be making orders but she gave two squishy balls from hand. From all of this, I have learnt to always make more orders than we had in the Trade Fair or make it online. I cannot wait till week eight when we have our market. At the market we will give the orders to people and trading our products and giving by hand like my partner.  If you want to know what PT and Pieces are, click on the words. In writing this week, we had a really good writing session. Each paragraph we had to write and in between them, we all came to the mat and our teacher talked to us. It was a really good season and I hope to do it next time. ### Vocabulary WALT: Learn and use new Vocabulary. This week, our teacher gave us a little test and this was included. We learnt about new Vocabulary like employer and salary. Even our teacher learnt something new about Salary and Wages. I hope to learn more about things like this in the future. ## Wednesday, 19 August 2015 ### Maths Teacher Lesson-Week 4 WALT: Work with decimals. In Maths Teacher Lesson this week I have learnt to add when subtracting. For example: 3.364 - 5.597=?. When adding, you will take the second number and round it to the nearest whole number. Look underneath to see the whole solution. ### Auxiliary Verbs - Ms Tito WALA(we are learning about): Auxiliary verbs and using them in sentences. This week with Ms Tito, we have learnt about the Auxiliary Verbs. The verbs that we learnt were the basic, am, will, have and was. The Auxiliary Verbs are another word for helping verb, the help explain what is happening. I hope I will learn more of these in the future. ## Tuesday, 18 August 2015 ### Problem Solving-Week 5 WALT: Multiply and divide whole numbers. This week in Problem Solving I have learnt to divid and multiple in whole numbers. If you were to do this, you would have to know you multiplication and division. For example: 67 x 34 = 1828. I know the answer because I know my multiplication and I could solve it fast. So all I have to do know is to find other ways to solve question like these. ### Maths Teacher Lesson-Week 3 WALT: Subtract decimals. In Maths Teacher Lesson this week, I have learnt an easier way to subtract decimals. The way is to split the numbers into their place values and then subtract from there. For example: 16.63-8.51=8.12. This is the way I worked it out is by this. This is the some times the way I find the answer to subtraction questions. ### Maths Teacher Lesson-Week 2 WALT: Add and Subtract. This week in Maths teacher lesson always to look at the number on the right before answering. The reason why to do this is so that you know if the number is going to end up in the next column. For example: 273+183=?. The way that I solve this is by doing this, 3+3=6, 170+180=350 then add the other hundred. The answer that I ended up with in the end is, 456. So my advice for you is to use this way to solve addition and subtraction questions. ### New Cadbury Gem WALT: Use language that paints a picture in the mind of our reader. The new Cadbury Jaffa’s Chocolate is a win win in my book of chocolate. The Cadbury Jaffa’s Chocolate is a basic milk chocolate with Jaffa's inside. It’s the shape of a  square like a normal chocolate. Cadbury Jaffa’s Chocolate king size is \$3.50 at the supermarket. When I first saw the Jaffa’s Chocolate, I thought it was going to have to much orange in it and it was bumpy so I thought it was going to be to crunchy. But it only had a pinch of orange in it and the bumpiness made no difference but it was a tiny bit crunchy . The taste of the chocolate was semi-sweet and perfect, so it was too rich and not too bitter. The chocolate smelt like the Cadbury milk chocolate and it felt like every other chocolate because of the shape. The Cadbury Jaffa’s Chocolate is in my top five of Chocolate’ s, so in my opinion it is delicious! I think they could improve by cutting the Jaffa’s into smaller pieces and then putting it into the chocolate.  It would make it easier to eat it and easier to store in little containers. Except from that, I think that it is great the way it is. I recommend the new Cadbury Jaffa’s Chocolate because it taste, smells, looks great. So if you think milk chocolate and orange together makes a great mix, this is the chocolate for you. If you do think that or do not think that, I think that you should still taste it. In Writing this week, I have learnt about and how to paint a picture in the readers head. I have learnt different ways to say things. For example: I went to the shop and bought bread. I could change this a lot, I walked down to the shop (not in a hurry) to buy some fresh wheat meal bread. As you can see I have given you more information and changed it up a little bit. If you could image a person walking to the shop, then I have reached my goal. But if yiu did not, I have not reached my goal. ## Thursday, 13 August 2015 ### Advice Blog-Fitness Watch WALT: Think critically about what we read. In Reading this week, I have learnt how to make decisions when it comes to advertisements. I have learnt to always look at the custom reviews. Once I looked at the ad for the product and it made it look great. Then I looked at the reviews and I thought again about the product. So my advice for you is to look at the reviews before buying something. ## Wednesday, 12 August 2015 ### Problem Solving-Week 4 WALT: Add and Subtract. In Problem Solving this week, I have learnt to look at the number in the right. For example:1893-546=?, before I answer I am going to look at the last two numbers. So 13-16=7, after that we solve the rest of the question. The end result would be 1347.(if you did not know, Moi means me in French) ## Monday, 10 August 2015 ### Superb Window Cleaners WALT: Put our self into the text. Task: You are offering advice to someone who is looking at buying one of the two watches. You will need to review the watches and explain why you would suggest buying one or the other. Remember to use FREE TO USE images. In reading we have been learning about putting our self into the text. So we are trying to get the message from the text (well that's what I have done). My message from this text is to keep my widows clean and window cleaning would be an awesome job. It would be very dangerous job but if you are careful I think you will be okay. If you have not notice, this is not real. ## Wednesday, 5 August 2015 ### Maths Teacher Lesson-Week 2 WALT: Add and subtract. Last week in maths teacher lesson, we learnt how to add and subtract. We mostly looked at decimals and then we made them into fractions. For example; 2.4. The way I solve the question is by doing this; there is 2 and there 4/10, so if we add those together, it would equal to 2 and 4/10. So 2.4 in fractions would equal to 2 and 4/10's. ## Monday, 3 August 2015 ### PT's and Pieces WALT: Write two paragraphs about PT's and Pieces. This term our topic is trade and enterprise. So in team four, we have our own money that we can earn and spend. Instead of cent, we have pieces and instead of dollars, we have Pt's. We can earn pieces and Pt's by sitting up in class, cleaning up, doing jobs, coming to school and by lots of other things too. Everybody has a bank account (kids one) of their own where they keep there money of course. There are lots of ways we can spend our money, we could hire a bean bag or something else, we can also buy things at the auction that we have most weeks. We can also get a fine for either 3 PT's or 5 PT's. For example; you can get a fine for not being at school, not giving the right amount of money in the auction, standing up at eating time when a teacher has not said anything and loads more. We also have six business's that we are all in. There is Toys, Kitchen, Custom Stationary, Homeware, Jewels and Accessory's and Musical Instruments. In these business's we have projects that we work on and then we can sell it at the market where everybody in our team can buy it. We have a teacher and a group of students in each business. Our team also have partners of two or three in those business's who make the projects. My project that I am working on is squishy balls made from balloons and flour. It is only the start of the term and this has been really cool. So when we get into the middle of the term I might even have more than my goal. I wonder how much money I will have at the end of the term. Well until then, I should focus on my project. ### Biodiversity Animation WALT: Create an animation with detail about biodiversity. Last term in extension, I learnt about a bit about biodiversity. Our task was to create an animation that has detail about biodiversity. I have learnt what biodiversity is and what it means to our planet. I have made this animation to show what it is, what it is about, how we can help, how it is important to our planet and compare and contrast. ### Maths Problem Solving-Week 3 WALT: Add and subtract decimals. Start Writing Here: In Problem Solving I have been learning how to solve questions on my own. I have learnt that sometimes it is okay to solve questions with the simple solution. For example; 0.87-0.64=?. The simple way to work this out is by spiting them and then subtracting. It looks like this 0.8-0.6=0.2 and then we do 0.07-0.04=0.03. Once I have done this I will have the answer, 0.2+0.03=0.23. So the answer would be 0.23. ### Bean Bags for Hire-3pt Whole Day WALT:pursued the reader to agree with our message. Bean bags are like a squishy comfortable cushion to relax on. During class time the bean bags are available for hire to sit on for the whole day. Instead of sitting on the tough stiff floor or on a flat plastic chair, you will be able to sit on the comfortable squishy bean bag to do your work. The bean bags are filled with soft beans which make it comfy and are covered in a rubber skin (which is not very rough so it is still comfy). They can be moulded into the shape of your choice. You can choose to sit on the bean bag, or use it to lean back to be relax, or you could use it as a soft chair or cushion. The bean bags come in two different colors and sizes. A big dark lime green one, and a smaller daylight blue one. It’s your choice which one you want to sit or lean on, . The price to hire the bean bag is 3pt. You pay once at the beginning of the day and then you can enjoy relaxing in the beanbag for the rest of the day. Remember for 3pt you can enjoy working on the bean bag during class the whole day. (These are not the real ones) In reading this week, we had to re crafted a piece of writing about hiring bean bags in our class. I have learnt that whenever you are writing another sentence, you should always look back and read it again of the paragraph. I have use Thesaurus to get better words to re craft. This is supposed to be an advertisement in our class so we had to write like we writing a real advertisement.

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https://docs.w3cub.com/numpy~1.17/generated/numpy.ma.stack

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/NumPy 1.17 # numpy.ma.stack `numpy.ma.stack(*args, **kwargs) = <numpy.ma.extras._fromnxfunction_seq object>` Join a sequence of arrays along a new axis. The `axis` parameter specifies the index of the new axis in the dimensions of the result. For example, if `axis=0` it will be the first dimension and if `axis=-1` it will be the last dimension. New in version 1.10.0. Parameters: `arrays : sequence of array_like` Each array must have the same shape. `axis : int, optional` The axis in the result array along which the input arrays are stacked. `out : ndarray, optional` If provided, the destination to place the result. The shape must be correct, matching that of what stack would have returned if no out argument were specified. `stacked : ndarray` The stacked array has one more dimension than the input arrays. `concatenate` Join a sequence of arrays along an existing axis. `split` Split array into a list of multiple sub-arrays of equal size. `block` Assemble arrays from blocks. #### Notes The function is applied to both the _data and the _mask, if any. #### Examples ```>>> arrays = [np.random.randn(3, 4) for _ in range(10)] >>> np.stack(arrays, axis=0).shape (10, 3, 4) ``` ```>>> np.stack(arrays, axis=1).shape (3, 10, 4) ``` ```>>> np.stack(arrays, axis=2).shape (3, 4, 10) ``` ```>>> a = np.array([1, 2, 3]) >>> b = np.array([2, 3, 4]) >>> np.stack((a, b)) array([[1, 2, 3], [2, 3, 4]]) ``` ```>>> np.stack((a, b), axis=-1) array([[1, 2], [2, 3], [3, 4]]) ```

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How many is Conversion between units of measurement Rating 5.00 (3 Votes) You can easily convert 1 hectare into square kilometers using each unit definition: Hectare hectoare = 1e2 are = 10000 m² Square kilometers 1000000 m² With this information, you can calculate the quantity of square kilometers 1 hectare is equal to. ## ¿How many sq km are there in 1 ha? In 1 ha there are 0.01 sq km. Which is the same to say that 1 hectare is 0.01 square kilometers. One hectare equals to zero square kilometers. *Approximation ### ¿What is the inverse calculation between 1 square kilometer and 1 hectare? Performing the inverse calculation of the relationship between units, we obtain that 1 square kilometer is 100 times 1 hectare. A square kilometer is one hundred times one hectare. *Approximation

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Smartick is a fun way to learn math! Jul01 # Working with Decimals: Addition and Subtraction In this post we are going to see some addition and subtraction calculations with decimals. In order to add or subtract decimals, we need to stack the numbers that have a decimal point one on top of the other, making sure to line up the values in the same columns. By doing so, the tens, and even hundredths, places will be lined up. Let’s look at some examples: We are going to subtract 8.27 from 9.756. So, we’ll have to line up the values. That’s to say, tens place under tens place, hundredths place under hundredths place, and so on, just like you can see in the picture. The number 8.27 doesn’t have a number in the millionths place so we can put a 0 there and it’ll be easier for us to go on with the calculation. Now, we can move on to subtracting the numbers, making sure to write the decimal point in the same place. The final answer is 1.486. Now, we have to add 6.654 and 20.4. Just like we saw in the prior example and in the picture above, we have to line all of the place values up—the tens, hundredths and thousandths places—so that they fall in the same column. The number 20.4 doesn’t have a hundredths or thousandths place, so we can put 0s in these spots to make the calculation simpler. Now, we can add the two numbers, making sure to maintain the decimal point in the same spot in the final answer. The final answer is 27.054

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up previous next MinPolyQuot, MinPolyQuotDef, MinPolyQuotElim, MinPolyQuotMat compute a minimal polynomial Syntax ```MinPolyQuot(f: RINGELEM, I: IDEAL, z: RINGELEM): RINGELEM MinPolyQuot(f: RINGELEM, I: IDEAL, z: RINGELEM, VerificationLevel: INT): RINGELEM MinPolyQuotDef(f: RINGELEM, I: IDEAL, z: RINGELEM): RINGELEM MinPolyQuotElim(f: RINGELEM, I: IDEAL, z: RINGELEM): RINGELEM MinPolyQuotMat(f: RINGELEM, I: IDEAL, z: RINGELEM): RINGELEM``` Description These functions return the minimal polynomial (in the indeterminate z ) of the element f modulo the 0-dimensional ideal I . See article Abbott, Bigatti, Palezzato, Robbiano "Computing and Using Minimal Polynomials" ( https://arxiv.org/abs/1702.07262 ) When coefficients are in QQ , MinPolyQuot uses modular methods. If called with VerificationLevel equal to n>=0 the result polynomial is verified over FF_p , with n different primes (if n=0, not verified). Verbosity: At level 80 it lists all primes used, indicating any which are bad. Example ```/**/ use P ::= QQ[x,y]; /**/ I := IdealOfPoints(P, mat([[1,2], [3,4], [5,6]])); /**/ MinPolyQuot(x,I,x); -- the smallest x-univariate poly in I x^3 -9*x^2 +23*x -15 /**/ indent(factor(It)); record[ RemainingFactor := 1, factors := [x -1, x -3, x -5], multiplicities := [1, 1, 1] ] /**/ f := x+y; /**/ I := ideal(x^2, y^2); /**/ MinPolyQuot(f,I,x); x^3 /**/ subst(It, x, f) isin I; true /**/ use QQ[x,y]; /**/ I := ideal(x^3-5,y^2-3); /**/ f := x+y; /**/ SetVerbosityLevel(80); /**/ MinPolyQuot(f, I, x); 1: prime is 32009 2: prime is 32027 x^6 -9*x^4 -10*x^3 +27*x^2 -90*x -2 ---- this is how to use an indet in another ring: /**/ QQt := RingQQt(1); /**/ MinPolyQuot(f, I, indet(RingQQt(1),1)); t^3 ```

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# Diff of /misc/bool.ml revision 272 by abate, Tue Jul 10 17:21:20 2007 UTC revision 275 by abate, Tue Jul 10 17:21:31 2007 UTC # Line 51  Line 51 51      match (a,b) with      match (a,b) with 52        | Split (h1,x1, p1,i1,n1), Split (h2,x2, p2,i2,n2) ->        | Split (h1,x1, p1,i1,n1), Split (h2,x2, p2,i2,n2) -> 53            (h1 == h2) &&            (h1 == h2) && 54            (X.equal x1 x2) && (equal p1 p2) & (equal i1 i2) &&            (equal p1 p2) && (equal i1 i2) && 55            (equal n1 n2)            (equal n1 n2) && (X.equal x1 x2) 56        | _ -> false        | _ -> false 57 58    (* Idea: add a mutable "unique" identifier and set it to 59       the minimum of the two when egality ... *) 60 61 62    let rec compare a b =    let rec compare a b = 63      if (a == b) then 0      if (a == b) then 0 64      else match (a,b) with      else match (a,b) with # Line 133  Line 137 137      | True -> (pos,neg) :: accu      | True -> (pos,neg) :: accu 138      | False -> accu      | False -> accu 139      | Split (_,x, p,i,n) ->      | Split (_,x, p,i,n) -> 140            (*OPT: can avoid creating this list cell when pos or neg =False *) 141          let accu = get accu (x::pos) neg p in          let accu = get accu (x::pos) neg p in 142          let accu = get accu pos (x::neg) n in          let accu = get accu pos (x::neg) n in 143          let accu = get accu pos neg i in          let accu = get accu pos neg i in # Line 175  Line 180 180     - no ``subsumption'     - no ``subsumption' 181  *)  *) 182 183      let rec simplify a b = 184        if equal a b then False 185        else match (a,b) with 186          | False,_ | _, True -> False 187          | a, False -> a 188          | True, _ -> True 189          | Split (_,x1,p1,i1,n1), Split (_,x2,p2,i2,n2) -> 190              let c = X.compare x1 x2 in 191              if c = 0 then 192                let p1' = simplify (simplify p1 i2) p2 193                and i1' = simplify i1 i2 194                and n1' = simplify (simplify n1 i2) n2 in 195                if (p1 != p1') || (n1 != n1') || (i1 != i1') 196                then split x1 p1' i1' n1' 197                else a 198              else if c > 0 then 199                simplify a i2 200              else 201                let p1' = simplify p1 b 202                and i1' = simplify i1 b 203                and n1' = simplify n1 b in 204                if (p1 != p1') || (n1 != n1') || (i1 != i1') 205                then split x1 p1' i1' n1' 206                else a 207    (* 208    let rec simplify a l =    let rec simplify a l = 209      if (a = False) then False else simpl_aux1 a [] l      if (a = False) then False else simpl_aux1 a [] l 210    and simpl_aux1 a accu = function    and simpl_aux1 a accu = function # Line 209  Line 239 239            simpl_aux2 x p i n (b :: ap) (b :: ai) (b :: an) l            simpl_aux2 x p i n (b :: ap) (b :: ai) (b :: an) l 240          else          else 241            simpl_aux2 x p i n (p2 :: i2 :: ap) (i2 :: ai) (n2 :: i2 :: an) l            simpl_aux2 x p i n (p2 :: i2 :: ap) (i2 :: ai) (n2 :: i2 :: an) l 242    *) 243 244    let split x p i n =    let split x p i n = 245      split x (simplify p [i]) i (simplify n [i])      split x (simplify p i) i (simplify n i) 246 247    let rec ( ++ ) a b =    let rec ( ++ ) a b = 248  (*    if equal a b then a *)  (*    if equal a b then a *) Legend: Removed from v.272 changed lines Added in v.275

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Dear IBPS Clerk Aspirants, Reasoning Questions for IBPS Clerk Mains 2017 The reasoning is a game of wits and presence of mind! Yes, it is true and it might seem as the greatest of the challenge after English Section’s surprises but yet this one can easily be dealt with. You just need correct practice and hardwire your brain to quickly make decisions about what to attempt and what to leave. And for same we are providing you questions of Reasoning Question and Answers. Solve these to Practice latest pattern reasoning question for bank exams. Directions (1-5): Study the information and answer the following questions: In a certain code language " you had leave India " is coded as " L2%   Z19%   V15%   M18% " " one hand press your " is coded as " M12%   Z19*   I11%   L2*" " should come for event " is coded as " S8*  L24*   L21%  E22% " Q1.What is the code for ‘enhance’ in the given code language? (a) N22% (b) M2% (c) M22* (d) M22% (e)None of these Q2.What is the code for ‘former’ in the given code language? (a) L21* (b) M21* (c) L2* (d) L21% (e)None of these Q3.What is the code for ‘country’ in the given code language? (a) M24% (b) K24% (c) L24% (d) J24% (e)None of these Q4.What is the code for ‘introduce’ in the given code language? (a) M18* (b) N18% (c) M1% (d) M18% (e)None of these Q5.What is the code for ‘arrived’ in the given code language? (a) J26% (b) I2% (c) I26% (d) K26% (e)None of these Directions (6-10): Study the following information carefully and answer the given questions. Eight people J, K, L, M, N, O, P and Q are member of family. Among them four are males and four are females. There are three husbands, three wives, two daughters, and two sons in the family. Each member of the family likes different sweet i.e. Barfi, Peda, Halva, Ladoo, Jalebi, Imarti, Tilpatti and Petha. They all are sitting around a circular table facing the centre. No male like Halva. Q likes Jalebi and married to the one who like Imarti. J is father of L and O, who is a male and likes Imarti. J and K cannot sit adjacent to each other. All females sit together. M likes Petha and is sitting second to the left of her father. M is daughter of L, who is second to the right of her son. The one who like Tilpatti is married to the one who like Ladoo and neither J nor K likes Ladoo. N likes Halva and is sitting between the one who like Peda and the one who like Tilpatti. P is father of K and is sitting between two male members. Q6. How is O related to K? (a) Mother (b) Father (c) Maternal Uncle (d) Grandfather (e) None of these Q7. J likes which of the following sweet? (a) Petha (b) Imarti (c) Peda (d) Barfi (e) None of these Q8. Which of the following pairs is not correctly matched? (b) K – Peda (c) N – Halva (d) J – Tilpatti (e) None of these Q9. Four of the following five are alike in a certain way and hence they form a group. Which one of the following does not belong to that group? (a) Halva (b) Tilpatti (c) Jalebi (d) Peda (e) Petha (a) J (b) K (c) L (d) P (e) None of these Directions (11-15): In each of the questions below are given four statements (a), (b), (c) and (d) followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts. Give answer (a) if only conclusion I follows. (b) if only conclusion II follows. (c) if either conclusion I or II follows. (d) if neither conclusion I nor II follows. (e) if both conclusion I and II follow. Q11. Statements: a. All flowers are buses. b. Some buses are cats. c. All cats are tigers. Conclusions: I. Some tigers are buses. II. Some tigers are flowers. III. Some cats are flowers. IV. Some buses are tigers. (a) None follows (b) Only I and II follow (c) Only III and IV follow (d) Only I and IV follow (e) Only II and III follow Q12. Statements: a. All fans are rooms. b. No room is green. c. Some windows are green. Conclusions: I. Some windows are fans. II. Some windows are rooms. III. Some fans are green. IV. No green is fan. (a) Only I follows (b) Only III follows (c) Only IV follows (d) Only II and IV follow (e) All follow Q13. Statements: a. Some tablets are rains. b. All dogs are rains. c. All rains are chairs. Conclusions: I. Some chairs are tablets. II. All dogs are chairs. III. Some tablets are dogs. IV. Some tablets are chairs. (a) All follow (b) Only I, II and III follow (c) Only II, III and IV follow (d) Only III and IV follow (e) None of these Q14. Statements: a. No man is sky. Conclusions: III. Some skies are men. (a) None follows (b) Only I follows (c) Only I and III follow (d) Only II and III follow (e) None of these Q15. Statements: a. Some candles are houses. b. Some houses are trains. Conclusions:

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Cody # Problem 149. Is my wife right? Solution 1999775 Submitted on 2 Nov 2019 by Angus Wong This solution is locked. To view this solution, you need to provide a solution of the same size or smaller. ### Test Suite Test Status Code Input and Output 1   Pass x = 'But I''m actually right this time'; y_correct = 'yes'; assert(isequal(wiferight(x),y_correct)) 2   Pass x = 'But you just said that 2+2=3'; y_correct = 'yes'; assert(isequal(wiferight(x),y_correct))

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# Wikijunior:Programming for Kids/Designing Your Solution Wikijunior:Programming for Kids Knowing Your Problem Designing Your Solution Top-Down or Bottom-Up? Once we've figured out our problem, we need to design a way to solve our problem. At this stage, we do not write any code yet. We are only drawing up a framework which we will follow during the algorithm design stage. ## Divide and Conquer Divide and conquer (D&C) comes from the Latin saying divide et impera. It refers to the breaking up of a large problem into smaller subproblems. The subproblems can be further divided into smaller subsubproblems, which become subsubsubproblems and, well, you get the idea. Divide and conquer is a systematic way to obtain a blueprint for your solution. After each subproblem has been tackled, we merge them together to form the 'big picture'. Divide and conquer can be applied to both real-life problems and programming problems. We will look at one notable application, array sorting, in the next section. For now, let's try something simpler. Let's say you want to measure the area of a stadium. There is no formula for calculating the stadium's size directly, so let's try doing it this way: This diagram is a structure diagram. A structured diagram is a way of mapping the structure of our solution. (Surprise, surprise!) Let's try a more difficult problem. Suppose you have a squared flower bed and a path around it. You need to pave the path, and want to calculate the total cost of this project. How will you do that? Note that this problem involves division into smaller subproblems. ## The Modular Approach By using D&C with our problem, we are taking the modular approach to programming. In the diagrams above, each block represents a module. In the second diagram, the subsubproblems can be said to be submodules. Dividing a problem into different modules is a common programming practice. Data and information flow in the structured diagram in some way. For example, in the flowerbed example, the 'Find the difference between the two areas' module needs to know the data in the 'Find the area of the flowerbed' and the 'Find the area of the path plus the flowerbed' modules. To represent this clearly, each module has a module specification which clearly documents the inputs, outputs and processes of the module. We can also use an I-P-O chart for this purpose. Let's look at the module specifications for our flowerbed project. (Don't worry if you don't understand everything completely; we'll look at them soon.) Module: 'Find the total cost of the project' Inputs Processes Outputs • Width of the flowerbed • Length of the flowerbed • Width of the whole area • Length of the whole area • Cost per unit • Prompt the user to input the dimensions of the flowerbed, the dimensions of the whole area and the cost per unit • Get the dimensions of the flowerbed, the dimensions of the cost per unit • Validate the input data • Find the area of the path • Multiply the area and the per-unit path • Output the total cost of the project to the screen • The total cost of the project Module: 'Find the area of the path' Inputs Processes Outputs • Width of the flowerbed • Length of the flowerbed • Width of the whole area • Length of the whole area • Read the dimensions of the flowerbed, the dimensions of the whole area • Find the area of the flowerbed • Find the area of the path plus the area of the flowerbed • Find the difference between the two areas • Output the area of the path • The area of the flowerbed Module: 'Multiply the area with the per-unit cost' Inputs Processes Outputs • Area of the path • Per-unit cost • Read the area of the path and the per-unit cost • Convert the units of the path and the cost if needed • Multiply the area of the path with the per-unit cost • Output the cost of the project • The total cost of the project Module: 'Find the area of the flowerbed' Inputs Processes Outputs • Length of the flowerbed • Width of the flowerbed • Read the dimensions of the flowerbed • Multiply the length and width of the path together • Output the area of the flowerbed • The area of the flowerbed Module: 'Find the area of the path plus the flowerbed' Inputs Processes Outputs • Length of the whole area • Width of the flowerbed • Read the dimensions of the whole area • Multiply the length and width of the path together • Output the whole area • The area of the flowerbed Module: 'Find the difference between the two areas' Inputs Processes Outputs • Area of the flowerbed • The whole area • Find the difference between the two areas • Output the area of the path • The area of the path The modular approach has many advantages. • It allows more flexibility in programming. The modular approach facilitates code reuse. Sometimes, one module may be used more than once in a program. For example, in a geometry program, it would be desirable to have one single module for Pythagoras' theorem which can be used anytime in a program. This saves us from having to copy-and-paste (and probably make a mistake in the process). Moreover, a change in one module may not have significant changes on the whole program. • It is easier to tackle one small problem at a time. It is easier to see the structure of a program if we divide it into various modules. A very large piece of code would be hard to read and debug. Dividing it into smaller parts helps identify and rectify mistakes. • It encourages collaboration between programmers. A team of programmers can divide up the work by assigning certain modules to each person. It also facilitates specialisation: for example, one programmer who is familiar with the XML DOM may choose to work on XML, while another who is familiar with SQL may choose to work on the databases and PHP. It also facilitates management and control. The modular approach also has disadvantages. For example, it may not be clear to each team member how the program works as a whole. As such, they may be ignorant of the full picture. This may cause problems with the linkage between different modules. It also requires extensive and in-depth documentation for other programmers, which increases the time-frame and costs. ## Hang on... We've designed the framework of the program with the modular approach, but how should we start? Should we work on the smallest programs first, then work our way to the top? or should we deal with the top parts first, then work our way to the bottom? Read the next chapter to find out!

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octave-patch-tracker [Top][All Lists] ## [Octave-patch-tracker] [patch #9958] [octave forge](mapping) gcxgc From: Philip Nienhuis Subject: [Octave-patch-tracker] [patch #9958] [octave forge](mapping) gcxgc Date: Mon, 10 Aug 2020 08:00:06 -0400 (EDT) User-agent: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:51.0) Gecko/20100101 Firefox/51.0 SeaMonkey/2.48 ```Follow-up Comment #18, patch #9958 (project octave): It occurred to me that finding the polar axis for any great circle defined by a (Lat, Lon, Azimuth) trio is actually very easy, but involved. 0 Find intersection with the equator (Lat 0, Lon 0, azi = 90). 0 Get Lon values halfway between the intersections, and define great circle through those points and the N- an S-poles. 0 Find intersection point between original great circle and the last great circle found in step 2; that's where the azimuth of the orig. great circle = exactly 90 degress, or E-W. Add 90 degrees to found Lat (wrap around 180 degrees or pi if needed & also wrap Lon around 360 or 2.pi), then the resulting (Lat, Lon) = coordinates of intersection of polar axis with sphere. 0 Convert that to ECEF if needed. 0 But, computing inner products may not even be needed, a simple comparison of (Lat, Lon) values + antipodes would do. There are probably several optimizations and shortcuts possible. If your original gcxgc is more accurate than the one based on converting to ECEF (XYZ), see comment #8, it might be worth pursuing this way; at least to know how much more accurate the answers would be; obviously there's a trade-off as regards overall performance. If you want/agree I'll give it a try when I find a spell. _______________________________________________________ <https://savannah.gnu.org/patch/?9958> _______________________________________________ Message sent via Savannah https://savannah.gnu.org/ ```

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cancel Showing results for Search instead for Did you mean: Highlighted Frequent Visitor ## Need Help in DAX ! :) Hello everybody, I'm a beginner on Power Bi and actually I have some difficulties with DAX language. Since I still can't find a solution to my problem, I've decided to post my question here. I have a database with a list of bugs of an application. Each bug has a status (new, assigned, resolved, closed…) and we have the date of the status modification. Here are a sample of my data: We would like to have a graphical representation like this : For each day, we would like to know the number of bugs for each status. In our database, we do not have data one row per day per bug, but only one row when the status modification has been done. We try to display the cumulative result of bug ID per date and per StatusName but it’s not what we want We try many other things without success Thank you for your help. 1 ACCEPTED SOLUTION Accepted Solutions Super Contributor ## Re: Need Help in DAX ! :) Hi @pira, Based on my test, the formula below should work in your scenario. Measure = VAR currentStatus = FIRSTNONBLANK ( Table1[NewStatusName], 1 ) VAR currentDate = MAX ( Table1[ModifyDate] ) RETURN COUNTROWS ( FILTER ( SUMMARIZE ( FILTER ( ALL ( Table1 ), Table1[ModifyDate] <= currentDate ), Table1[bug_id], "MaxDate", MAX ( Table1[ModifyDate] ), "LastStatus", CALCULATE ( FIRSTNONBLANK ( Table1[NewStatusName], 1 ), FILTER ( Table1, Table1[ModifyDate] = MAX ( Table1[ModifyDate] ) && Table1[Index] = MAX ( Table1[Index] ) ) ) ), [LastStatus] = currentStatus ) ) Note: You need to add an Index Column to your table under Query Editor > Add Column tab > Index Column first. Regards 6 REPLIES 6 Super Contributor ## Re: Need Help in DAX ! :) you need to create a date table that has all the dates and then link that to your transaction table on the date and that should sort out your issue Did I answer your question? Mark my post as a solution. Proud a to be a Datanaut! Frequent Visitor ## Re: Need Help in DAX ! :) I've already tried it but  it does not solve the problem. When the status of a bug is changed from New to Assigned for example, the number of bugs in the status New doesn't decreased (as it is a cumulative result). Super Contributor ## Re: Need Help in DAX ! :) @pira you will probably have to create a separate calculated measure for each status and plot them separately i am thinking? Did I answer your question? Mark my post as a solution. Proud a to be a Datanaut! Super Contributor ## Re: Need Help in DAX ! :) Hi @pira, Based on my test, the formula below should work in your scenario. Measure = VAR currentStatus = FIRSTNONBLANK ( Table1[NewStatusName], 1 ) VAR currentDate = MAX ( Table1[ModifyDate] ) RETURN COUNTROWS ( FILTER ( SUMMARIZE ( FILTER ( ALL ( Table1 ), Table1[ModifyDate] <= currentDate ), Table1[bug_id], "MaxDate", MAX ( Table1[ModifyDate] ), "LastStatus", CALCULATE ( FIRSTNONBLANK ( Table1[NewStatusName], 1 ), FILTER ( Table1, Table1[ModifyDate] = MAX ( Table1[ModifyDate] ) && Table1[Index] = MAX ( Table1[Index] ) ) ) ), [LastStatus] = currentStatus ) ) Note: You need to add an Index Column to your table under Query Editor > Add Column tab > Index Column first. Regards Frequent Visitor ## Re: Need Help in DAX ! :) Hi @vanessafvg, Sorry for my late response. I don't think that is the best solution ... Frequent Visitor ## Re: Need Help in DAX ! :) Thank you so much for your help. It works perfectly well ! ## Helpful resources Announcements #### Microsoft Business Applications October Virtual Launch Event Join us for an in-depth look at the new innovations across Dynamics 365 and the Microsoft Power Platform. #### Power BI Helps Homeless and Trouble Youth We spoke with Power BI Super User, Greg Deckler, about his charity work #### Watch Sessions On Demand! Continue your learning in our online communities. Top Kudoed Authors Users Online Currently online: 129 members 2,072 guests Recent signins: Please welcome our newest community members:

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# Homework Help: RMS displacement of a diatomic atom 1. Apr 4, 2013 ### Erubus 1. The problem statement, all variables and given/known data A hypothetical atom is diatomic containing two identical atoms separated by an equilibrium distance. About this distance the atoms vibrate with the electric forces providing an effective spring constant of k = 4.0×10^−3 N/m. As the temperature of the sample is increased the amplitude of the vibration increases. At what temperature will the rms displacement of the atoms be x= 5.0×10−10m? (Answer: 72 K) 2. Relevant equations <E> = 7kT/2 U = 7nRT/2 3. The attempt at a solution I assumed that because of spring like nature of the atoms, this atom was a diatomic non rigid rotator, which is how I have those relevent equations. I am unsure if this initial assumption is even correct. Even if it was, I still don't have an idea of how to proceed from there. 2. Apr 5, 2013 ### Staff: Mentor It seems that you need to be modelling the bond as a harmonic oscillator. I imagine also that this should be considered as a classical oscillator, and not quantum mechanical. Then, you need to take out your classical mechanics textbook and figure out the relation between the energy of the oscillator and the amplitude of the oscillation, which will be related to the rms displacement $\sqrt{\langle x^2 \rangle}$. 3. Apr 6, 2013 ### Erubus Got it, thanks.

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 aggregate belt conveyor speed # aggregate belt conveyor speed ##### aggregate conveyor belt speed calculator - Hitlers 2021-5-19  Aggregate Conveyor Belt Speed Calculator Conveyor Belt Calculations Brighthub Engineering Calculations include conveyor capacity belt speed conveyor height and length mass of idlers and idler spacing belt tension load due to belt inclination angle of the conveyor coefficient of friction power at the drive pulley starting belt ##### Aggregate Conveyor Belt Speed And Inclined Angle Aggregate belt conveyor speed - mehraseducationcoin caculate aggregate belt conveyor capicity how to calculate belt conveyor speed with motor rpm and ger rastioc , dec 1, 2015 , to calculate an accurate value of power required by the conveyor online server material handling systems47 online aggregate conveyor belt speed and inclined angle. ##### Aggregate Conveyor Belt Feet Per Minute Formula What is the formula for calculating conveyor belt length. ... speed for most unit handling conveyors is 65 FPM (Feet Per Minute). ... speed powder aggregate conveyor calculate conveyor speed conveying system fpm formula ##### Belt Conveyors for Bulk Materials Calculations by CEMA 5 ... 2014-1-21  4. 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During the turning of a $20$ mm- diameter steel bar at a spindle speed of $400$ rpm, a tool life of $20$ minute is obtained. When the same bar is turned at $200$ rpm, the tool life becomes $60$ minute. Assume that Taylor's tool life equation is valid. When the bar is turned at $300$ rpm, the tool life (in minute) is approximately. 1. $25$ 2. $32$ 3. $40$ 4. $50$

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🎉 Exercism Research is now launched. Help Exercism, help science and have some fun at research.exercism.io 🎉 # ataetgi's solution ## to Sum Of Multiples in the Swift Track Published at Apr 24 2021 · 0 comments Instructions Test suite Solution Given a number, find the sum of all the unique multiples of particular numbers up to but not including that number. If we list all the natural numbers below 20 that are multiples of 3 or 5, we get 3, 5, 6, 9, 10, 12, 15, and 18. The sum of these multiples is 78. ## Setup Go through the project setup instructions for Xcode using Swift: http://exercism.io/languages/swift http://exercism.io/languages/swift/tests Notably from the source directory: `swift test` runs tests `swift package generate-xcodeproj` creates an Xcode project ## Source A variation on Problem 1 at Project Euler http://projecteuler.net/problem=1 ## Submitting Incomplete Solutions It's possible to submit an incomplete solution so you can see how others have completed the exercise. ### LinuxMain.swift ``````import XCTest @testable import SumOfMultiplesTests XCTMain([ testCase(SumOfMultiplesTests.allTests), ])`````` ### SumOfMultiplesTests.swift ``````import XCTest @testable import SumOfMultiples class SumOfMultiplesTests: XCTestCase { func testSumTo1() { XCTAssertEqual(0, SumOfMultiples.toLimit(1, inMultiples: [3, 5])) } func testSumTo3() { XCTAssertEqual(3, SumOfMultiples.toLimit(4, inMultiples: [3, 5])) } func testSumTo10() { XCTAssertEqual(23, SumOfMultiples.toLimit(10, inMultiples: [3, 5])) } func testSumTo100() { XCTAssertEqual(2318, SumOfMultiples.toLimit(100, inMultiples: [3, 5])) } func testSumTo1000() { XCTAssertEqual(233168, SumOfMultiples.toLimit(1000, inMultiples: [3, 5])) } func testConfigurable_7_13_17_to_20() { XCTAssertEqual(51, SumOfMultiples.toLimit(20, inMultiples: [7, 13, 17])) } func testConfigurable_4_6_to_15() { XCTAssertEqual(30, SumOfMultiples.toLimit(15, inMultiples: [4, 6])) } func testConfigurable_5_6_8_to_150() { XCTAssertEqual(4419, SumOfMultiples.toLimit(150, inMultiples: [5, 6, 8])) } func testConfigurable_43_47_to_10000() { XCTAssertEqual(2203160, SumOfMultiples.toLimit(10000, inMultiples: [43, 47])) } func testConfigurable_0_to_10() { XCTAssertEqual(0, SumOfMultiples.toLimit(10, inMultiples: [0])) } func testConfigurable_0_1_to_10() { XCTAssertEqual(45, SumOfMultiples.toLimit(10, inMultiples: [0, 1])) } func testConfigurable_0_27_to_0() { XCTAssertEqual(0, SumOfMultiples.toLimit(0, inMultiples: [0, 27])) } static var allTests: [(String, (SumOfMultiplesTests) -> () throws -> Void)] { return [ ("testSumTo1", testSumTo1), ("testSumTo3", testSumTo3), ("testSumTo10", testSumTo10), ("testSumTo100", testSumTo100), ("testSumTo1000", testSumTo1000), ("testConfigurable_7_13_17_to_20", testConfigurable_7_13_17_to_20), ("testConfigurable_4_6_to_15", testConfigurable_4_6_to_15), ("testConfigurable_5_6_8_to_150", testConfigurable_5_6_8_to_150), ("testConfigurable_43_47_to_10000", testConfigurable_43_47_to_10000), ("testConfigurable_0_to_10", testConfigurable_0_to_10), ("testConfigurable_0_1_to_10", testConfigurable_0_1_to_10), ("testConfigurable_0_27_to_0", testConfigurable_0_27_to_0) ] } }`````` ``````//Solution goes in Sources import Foundation struct SumOfMultiples { static func toLimit(_ limit: Int, inMultiples: [Int]) -> Int { guard limit > 0 else { return 0 } var allValidNumbers = Set<Int>() for i in 1..<limit { inMultiples.forEach { (num) in if i.isMultiple(of: num) { allValidNumbers.insert(i) print(i) } } } return allValidNumbers.reduce(0, +) } }``````

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9.5_practice # 9.5_practice - Mat120- Homework Practice - Section 9.5 This preview shows page 1. Sign up to view the full content. This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: Mat120- Homework Practice - Section 9.5 Name___________________________________ Class Hour:______________________________ Decide whether the relation defines a function. 1) {(-5, -1), (-2, 8), (4, 2), (5, 6)} 1) B) Not a function A) Function Determine whether the relation is a function. 2) x -9 -9 1 3 7 y 2 1 8 -2 7 2) B) Not a function A) Function Given the function, find the indicated value. 3) Find f(-2) when f(x) = 4x2 + 3x + 4. 3) C) 14 D) 6 A) 26 B) 2 Decide whether the relation is a function, and give the domain and range. 4) y 10 4) 5 -10 -5 -5 5 10 x -10 A) Function; domain: [-2, 8]; range: [3, 5] B) Not a function; domain: [-2, 8]; range: [3, 5] Page 1 of 2 Use the graph to find the indicated function value. 5) y = f(x). Find f(2). y 4 3 2 1 -4 -3 -2 -1 -1 -2 -3 -4 1 2 3 4 x 5) A) -2 Find the domain of the function. 6) f(x) = -9x x+3 B) 1.25 C) 2 D) 5 6) A) {xx is a real number and x < -3} C) {xx is a real number and x -3} Solve the problem. 7) Find (f + g)(4) when f(x) = x - 2 and g(x) = x + 1. B) {xx is a real number} D) {xx is a real number and x 0} 7) C) (f + g)(4) = 5 D) (f + g)(4) = 11 8) A) (f + g)(4) = 7 B) (f + g)(4) = 9 8) Find ( f )(-3) when f(x) = 4x - 3 and g(x) = 5x2 + 14x + 4. g A) ( f )(-3) = - 5 g g 9 B) ( f )(-3) = - 15 g g 7 C) ( f )(-3) = 5 7 D) ( f )(-3) = 4 7 Page 2 of 2 Answer Key Testname: 9.5_PRACTICE 1) 2) 3) 4) 5) 6) 7) 8) A B C B B C A B Page 3 of 2 ... View Full Document ## This note was uploaded on 05/05/2008 for the course MAT 120/222/10 taught by Professor None during the Spring '08 term at ASU. Ask a homework question - tutors are online

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Вы находитесь на странице: 1из 6 # EE1401 - POWER SYSTEM OPERATION AND CONTROL ## KINGS COLLEGE OF ENGINEERING, - PUNALKULAM 1 KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING ACADEMIC YEAR 2011- 2012 / ODD SEMESTER QUESTION BANK SUBJECT CODE/NAME: EE 1401 - POWER SYSTEM OPERATION AND CONTROL YEAR/SEM : IV / VII UNIT I - GENERAL BACKGROUND AND SPEED GOVERNORS PART A (2 Marks) 1. What is the objective of power system control? 2. Why the frequency and voltage are to be regulated in power system? 3. What happens to frequency if the load on the generator increases? 4. Define per unit droop. 5. State the difference between P-f, and Q-lVl. 7. What is the duty of the power system operator? 8. What are the problems associated with the interconnected power system? PART B 1. Explain the need for voltage and frequency regulation in power system. (16) 2. What are the components of speed governor system of an alternator? Derive a transfer function and sketch a block diagram. (16) 3. Draw and explain the basic P-f and Q-V control loops. (16) 4. Briefly explain about the plant level and the system level controls. (16) 5. Briefly discuss the classification of loads and list out the important characteristics of 6. i) Briefly explain the overview of system operation. (8) UNIT II - FREQUENCY CONTROL AND AUTOMATIC GENERATION CONTROL PART A 1. What is the function of Load Frequency Control? 2. Explain the Principle of Tie-line Bias control. 3. What is the purpose pf primary ALFC? 4. How is the real power in a power system controlled? 5. What is meant by control area? EE1401 - POWER SYSTEM OPERATION AND CONTROL KINGS COLLEGE OF ENGINEERING, - PUNALKULAM 2 6. Define area control error. 7. Write the tie line power deviation equation in terms of frequency? 8. List the advantage of multi area operation. 9. List out the various needs for frequency regulation in power system. 10. What is the purpose of a speed changer? PART B 1. Discuss in detail the dynamic response of a single area system, without integral control, following a step load disturbance. (16) 2. Derive the transfer function of an uncontrolled load frequency control of a single area system and derive the expression for static error following a step load change. (16) 3. Draw the transfer function block diagram for a two area system provided with governor control and obtain the steady state frequency error following a step load change in both the areas. (16) 4. A 210 MVA, 50 Hz Turbo Alternator operates at no load at 3000 rpm. A load of 75 MW is suddenly applied to the machine and the steam valves to the turbine commence to open after 1 sec due to the time lag in the governor system. Assuming Inertia Constant H of 5Kw-sec per kVA of generator capacity. Calculate the frequency to which the generated voltage drops before the steam flow commences to increase to meet the 5. The data pertaining to a single area power system with linear load-frequency characteristics are as follows: Rated Capacity = 2000 MW System Load = 1000 MW Inertia Constant = 5 sec Speed regulation = 0.03 pu Load damping factor = 1 pu Nominal Frequency = 50 Hz Governor Time constant = 0 sec Turbine time constant = 0 sec For a sudden change in load of 20 MW, determine the steady state frequency deviation and the change in generation in MW and reduction in original load in MW (16) 6. The data pertaining to a single area power system with linear load-frequency characteristics are as follows: Rated Capacity = 1200 MW System Load = 600 MW Inertia Constant = 4 sec Speed regulation = 4% Load damping factor = 0.85 pu Nominal Frequency = 50 Hz Governor Time constant = 0 sec Turbine time constant = 0 sec For a sudden change in load of 40 MW, determine the steady state frequency deviation (16) 7. A two area power system has two identical areas with parameters are given below: Rated Capacity of the area = 3000 MW Nominal Operating load = 1500 MW Inertia Constant = 4 sec Speed regulation = 4% Load damping factor = 1 pu Nominal Frequency = 50 Hz Governor Time constant = 0.06 sec Turbine time constant = 0.3 sec A load increase M2 = 30 MW, occurs in area 2 Determine i) the steady state frequency deviation ii) P 12s (16) EE1401 - POWER SYSTEM OPERATION AND CONTROL KINGS COLLEGE OF ENGINEERING, - PUNALKULAM 3 8. A two area system connected by a tie-line has the following parameters: AREA 1 2 Turbine output Power (MW) Nominal Frequency (Hz) Inertia Constant speed regulation Power system Gain ( k p ) Governor Time Constant Turbine Time Constant 4000 50 4% 50 0.2 0.3 2000 50 5% 125 0.1 0.25 A load change of 80 MW occurs in area 1. Determine the steady state frequency and the change in the tie-line flow. UNIT III REACTIVE POWER AND VOLTAGE CONTROL PART A 1. What are the methods of Voltage control? 2. List the various components in AVR loop. 3. Where are synchronous condensers installed? 4. What are the methods of increasing response in AVR? 5. What are the different types of static VAR compensators? 7. Compare series and shunt capacitors 8. How is voltage control obtained by using tap changing transformer? 9. What is booster transformer? Where it is used? 10. What is SVC? PART B 1. i) Discuss generation and absorption of Reactive Power (8) ii) Explain how voltage control can be effected by injection of Reactive Power (8) 2. i) Draw the composite SVS power system characteristics (8) ii) What are the applications of SVS (8) 3. Explain different types of static VAR compensators with a phasor diagram (16) 4. A 3, 230 kV transmission line having the following parameters operates at no-load. R=20, X= 80 , B= 4x10 -4 mho. If the receiving end voltage is 210kV find the sending end voltage representing the transmission line as model. (16) 5. The load at receiving end of a 3 overhead line is 30 MW, 0.8 pf lag at the line voltage of 66kV. A synchronous compensator is situated at sending end and the voltage at both ends of the line is maintained at 66kV. Calculate the MVAR of compensator. The line has a resistance and reactance of 6/ph, 24 /ph, respectively. (16) 6. A 415 kV line is fed through an 132/415kVtransformer from a constant 132kV supply. At the load end of the line, the voltage is reduced by another transformer of ratio 415/132kV. The total impedance of the line is (30+j60). Both transformers are equipped with tap- changing, the product of the two off-nominal setting is unity. If the load on the system is EE1401 - POWER SYSTEM OPERATION AND CONTROL KINGS COLLEGE OF ENGINEERING, - PUNALKULAM 4 200 MW at 0.8of lagging. Calculate the settings of the tap-changer required to maintain the voltage at 132kV. (16) 7. Two sub-station are connected by two lines in parallel with negligible impedance, but each containing a tap-changing transformer of reactance 0.22pu on the basis of its rating of 200 MVA. Find the net absorption of reactive power when the transformer, taps are set to 1:1.08, and 1:0.95 respectively. Assume pu voltages to be equal at the two ends. (16) UNIT IV - ECONOMIC OPERATION OF POWER SYSTEMS PART - A 2. What are the needs for load forecasting? 3. What is daily, Weekly, Annual load curve? 5. Define diversity factor. 6. What is demand factor? 7. What is meant by incremental cost curve? 8. Define spinning reserve. 9. What are cold reserves and hot reserves? 10. When do discontinuities occur in the fuel cost curve and the incremental cot curve? 11. What is plant use factor? 12. What is the purpose of economic dispatch? 13. What is meant by unit Commitment? 14. Compare unit commitment and economic dispatch 15. What do you mean by priority list method? 16. What are all the points to be noted for a economic load dispatch including transmission losses? PART B 1. i) Explain briefly the constraints on unit commitment problem. (8) ii) What is spinning reserve and does this reserve help in operating a power system efficiently? (8) 2. Explain Priority list method using full load average production cost. State the merits and demerits. (16) 3. Explain with a neat flowchart the procedure for finding the solution for unit commitment problems using forward DP method. (16) 4. There are three thermal generating units which can be committed to take the system load. The fuel cost data and generation operating unit data are given below: F1 = 392.7 + 5.544 P 1 + 0.001093 P 1 2 F2 = 217 + 5.495 P 2 + 0.001358 P 2 2 F3 = 65.5 + 6.695 P 3 + 0.004049 P 3 2 , P 1 , P 2 , P 3 in MW Generation limits : 150 P 1 600 MW 100 P 2 400 MW 50 P 3 200 MW EE1401 - POWER SYSTEM OPERATION AND CONTROL KINGS COLLEGE OF ENGINEERING, - PUNALKULAM 5 There are no other constraints on system operation. Obtain an optimum unit commitment table. Adopt Brute force enumeration technique. Show the details of economic schedule and the component and total costs of operation for each feasible combination of units for the load level of 900 MW. 5. The input output curve characteristics of three units are: F1=750+6.49 P G1 +0.0035P 2 G1 F2=870+5.75 P G2 +0. 0015P 2 G2 F3=620+8.56 P G3 +0. 001P 2 G3 The fuel cost of unit 1, 2, 3 is 1.0 Rs / Mbtu. Total load is 800 MW. Use participation factor method to calculate the dispatch for a load is increased to 880 MW? (16) 6. Obtain the priority list of unit commitment using full load average production cost for the given data for the load level of 900 MW. F1 = 392.7 + 5.544 P 1 + 0.001093 P 1 2 F2 = 217 + 5.495 P 2 + 0.001358 P 2 2 F3 = 65.5 + 6.695 P 3 + 0.004049 P 3 2 , P 1 , P 2 , P 3 in MW Generation limits : 150 P 1 600 MW 100 P 2 400 MW 50 P 3 200 MW There are no other constraints on system operation. Obtain an optimum unit commitment table. (16) 7. Derive the expression for base point and participation method. (16) 8. Give iteration algorithm for solving economic scheduling problem, without transmission loss. (16) 9. Derive coordination equation for economic dispatch including losses, in the power system. Give steps for economic dispatch calculation. Neglecting losses (16) 10. Consider the following three units: I C1 = 7.92 + 0.003124 P G1 I C2 = 7.85 + 0.00388 P G2 I C3 = 7.97 + 0.00964 P G3 P D = 850 MW P G1 = 392.2 MW, P G2 = 334.6 MW, P G3 = 122.2 MW Determine the optimum schedule if the load is increased to 900 MW by using Participation Factor method. (16) EE1401 - POWER SYSTEM OPERATION AND CONTROL KINGS COLLEGE OF ENGINEERING, - PUNALKULAM 6 UNIT V - CONTROL CENTERS AND POWER SYSTEM SECURITY PART A 1. What are the major functions that are carried out in an operations control center? 2. What are the EMS functions? 3. Define Energy control centre. 4. What is contingency analysis program? 6. What are the functions of SCADA? 7. What are the different operating states of a power system? 8. What is emergency state? 9. Write importance of state estimation in power system. 10. What is security monitoring and control? 11. List the factors that affect the power system security. 12. What are the important types of relays used for protection? 13. What do you understand power system stability? 14. Distinguish between reliability and security of a power system. PART B 1. Explain the different system operating states . (16)

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# Search: Tag: dates Page 1 of 19 1 ## Search: Replies Views Search took 0.00 seconds; generated 57 minute(s) ago. 1. ### conditional formatting- before today, another after today passes • 86 Last Post: 05-25-2022 09:15 AM by ecConnect 2. ### Formula for end-of-year holiday week • 112 Last Post: 05-17-2022 03:58 PM by Bernie Deitrick 3. ### Help link data to new page using date range that can be changed easily • 128 Last Post: 05-15-2022 04:34 PM by Tonzplace 4. ### [SOLVED] Count dates greater than today based on other date criteria • 123 Last Post: 04-21-2022 10:44 AM by AliGW 5. ### Data Validation list and Month display • 89 Last Post: 04-12-2022 12:09 PM by Fluff13 6. ### Project management formula Help for prepopulating dates. • 132 Last Post: 04-04-2022 03:29 PM by TheDatoz 7. ### [SOLVED] Percent progress with future dates • 166 Last Post: 03-29-2022 06:03 PM by Palagi9 8. ### [SOLVED] Convert Formula to Function | PercentBetweenDates • 158 Last Post: 03-01-2022 11:36 AM by TMS 9. ### Excel assumes date is 1st when sorting mm format - how to change? • 136 Last Post: 02-11-2022 10:24 AM by MrShorty 10. ### Generate Historical Seasonality Curve and apply to annual data being converted to monthly • 140 Last Post: 02-07-2022 12:41 PM by Dapper10 11. ### Ramp up calculation of sales depending on staff hire date • 260 Last Post: 02-01-2022 05:16 AM by JohnTopley 12. ### [SOLVED] Conditional format : Highlight row if column F has a date that is 60 days past or more • 174 Last Post: 01-14-2022 12:37 PM by DarkPurpleInk 13. ### Gantt Chart with 4 dates instead of usual 2 • 179 Last Post: 01-11-2022 01:09 PM by Pete_UK 14. ### Count Overlapping Minutes from two ranges with multiple criteria • 211 Last Post: 01-07-2022 11:26 AM by kvsrinivasamurthy 15. ### Excel cost us few thousands dollar for changing SKUs to dates • 482 Last Post: 12-09-2021 07:44 PM by TMS 16. ### [SOLVED] Show 1 day instead 0 days between dates • 210 Last Post: 12-01-2021 05:12 AM by JohnTopley 17. ### Numbers changing to dates • 220 Last Post: 11-22-2021 06:07 PM by DJunqueira 18. ### Automating each days date in Google Sheets • 282 Last Post: 11-10-2021 10:17 AM by janmorris 19. ### Using If statements with multiple dates and hiding rows • 167 Last Post: 10-29-2021 06:14 AM by mehmetcik 20. ### Conditionally format multiple dates in a single row • 259 Last Post: 10-31-2021 08:56 PM by Henz 21. ### [SOLVED] How To Auto Fill The Dates • 206 Last Post: 10-04-2021 04:02 PM 22. ### [SOLVED] Date formatting • 267 Last Post: 09-29-2021 09:21 AM by AliGW 23. ### [SOLVED] can I use SUMIFs and the "AND" function to return based on date values? • 188 Last Post: 09-27-2021 12:12 PM by rcane 24. ### [SOLVED] Autofill networking days dates with variable start and end date • 266 Last Post: 08-03-2021 05:39 AM by AliGW 25. ### [SOLVED] formula that only takes into account date but has a capped value • 305 Last Post: 07-26-2021 11:00 AM by AliGW 26. ### [SOLVED] Display text dependent upon today's date • 432 Last Post: 07-16-2021 07:39 AM by rayted 27. ### Pivot Table from Date Range • 229 Last Post: 07-14-2021 05:10 AM by AliGW 28. ### Help with Find when dates exceed 6 digits • 335 Last Post: 07-12-2021 11:17 AM by 6StringJazzer 29. ### [SOLVED] Errors when switching date from long format back to short format • 202 Last Post: 07-01-2021 10:20 PM by Tyla99 30. ### Index, Match & Indirect Reference to Dates and Values • 338 Last Post: 06-22-2021 10:31 AM by Estevaoba 31. ### Formula to insert multiple dates • 418 Last Post: 05-21-2021 10:23 AM by Bo_Ry 32. ### [SOLVED] Help! Calculating stock levels with short expiry, regular deliveries and demand • 634 Last Post: 05-21-2021 05:49 PM by JeteMc 33. ### Find slope where changes in X are dates • 305 Last Post: 05-07-2021 06:22 AM by lilybickel 34. ### [SOLVED] Find earliest and latest date • 352 Last Post: 05-20-2021 03:05 AM by etaf 35. ### Return value based on two project dates: Completed, Ongoing, Upcoming • 327 Last Post: 04-27-2021 01:40 PM by FlameRetired Results 1 to 35 of 641 Page 1 of 19 1 Search Engine Friendly URLs by vBSEO 3.6.0 RC 1

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# What are other strategies for a 7 year old for addition and subtraction besides counting fingers? We recently received feedback from our 7 year old daugther's school teacher. One of the things mentioned was that our daughter still counts her fingers when she does addition and subtraction. The teacher said that it is important to find other strategies which will save time and effort. She doesn't have any trouble identifying ones, tens, hundreds, thousands, and she does addition and subtraction on paper when we stack the numbers on top of each other. So, the understanding of numbers and positions are in place. Although I understand that counting fingers may not be the fastest way to do addition or subtraction, I'm not quite sure which / if other strategies are available to her / us? Answers to a similar post on this site, although about younger children, seems to agree that using fingers are perfectly fine. However, I'm curious to know if there are any "standard" ways out there to teach our daughter to do subtraction and addition in her head - without inventing our own system for that. • "The teacher said that it is important to find other strategies which will save time and effort." "I'm not quite sure which / if other strategies are available to her / us." Did the teacher only identify a "problem" and offer no possible solutions? – Nick C Jun 4 at 13:59 • @Nick C, no alternative strategies were offered in the written feedback. I haven't responded to that feedback, but wanted to be a little prepared and investigate some on my own as well before i did that. – sbrattla Jun 4 at 16:21 • For numbers, written or imagined visually, can count points on the numbers, up for addition and down for subtraction. I saw this for numbers 1 - 4 in the 60's. A reference is touchmath.com/index.cfm?fuseaction=about.how – Tom Jun 7 at 21:09 I have no problem with her counting on her fingers but here are 2 other strategies that she may find useful. These 2 strategies assume she can add 1 or subtract 1 without her fingers. If not she should learn that adding or subtracting 1 is just counting up or down. 1. If she knows her doubles e.g. 3 + 3 or 8 + 8, then when she adds 3 + 4 or 8 + 9, she could realize that the new equations are just doubles plus one. Even if she doesn't know a lot of doubles, she probably knows that 5 + 5 is 10. 2. When adding 10 + 7, she should recognize that you just have to put 7 in the ones place (although) she may not call it that) to get 17. Once she knows the trick for adding 10's, she can add 9's by adding 10 and taking away 1. There may be other strategies listed in her book - it is worth looking or asking the teacher to suggest strategies. She should also know some of her facts by heart. In particular it is good to learn doubles and sums to 10 by heart. When counting on her fingers, encourage her to start from one of the numbers and count up, so that if she is adding 3 + 9, she shouldn't count 3 and then another 9. Instead she should start at 9 and then count up 3 more using her fingers (10, 11, 12). This is faster and shows a greater understanding. In short: a standard expectation is that children of about your daughter's age should have memorized all sums of one-digit numbers. For example, here's the language from the Common Core Standards for Grade 2: CCSS.Math.Content.2.OA.B.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Nowadays this memorized, instant-recall knowledge is often referred to as "addition facts". It's a fundamental expectation to how our base-10 number system is designed to support operations like adding and multiplying large numbers. When I was your daughter's age, the customary way of learning this was to get a set of flash cards with all of the combinations of one-digits addends and practice with those daily. Nowadays there are many more options (such as online games, phone apps, etc.) Here's one site with suggestions. You can internet search for the phrase "learn addition facts" for many more. Typical strategies include: • Memorizing sums to 10, e.g. $$7 + 3 = 10$$, then using that equation to determine $$6 + 3 = \_\_$$ or $$7+4=\_\_$$ • Memorizing the doubles, e.g. $$7 + 7 = 14$$, then using that to determine $$8+7=\_\_$$ • Decomposing/Recomposing. e.g. $$9+8=10+7=17$$ • Using single digit facts to determine sums within 20. e.g. Since $$3+6=9$$, then we can easily figure out $$13+6=\_\_$$. If these strategies do not seem obvious to your daughter after seeing them in symbolic form, then you should use ten-frames, linking cubes, and number tracks to help her visualize them. Auction games are a fun way to practice a lot of this. • Small addition to this: Switching up the format makes the student learn subtraction without them knowing that they are learning something new, e.g. $7 + ___ = 10$ – Chris Cunningham Jun 12 at 14:15 Play games: dice, board games, card games. So many of them include counting and "adding on". Or an online game like this one. Play store, where you pretend to buy things. Draw a circle numbered 1 to 10, and draw lines between the pairs that add to 10. Then decorate it. If she likes this, do a circle numbered 1 to 12, and connect the pairs that add to 12. Make up your own rules. The idea is to make friends with the numbers, so it's not tedious. As Montessori said, "Play is children's work." • Nice drawing! A similar one gets rainbows on the number line. For a seven color version, draw arcs joining pairs of numbers that add to 14. – Jaume Oliver Lafont Jun 15 at 6:26

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# Comparing Lengths Worksheet 2nd In Free Printable Worksheets174 views 4.07 / 5 ( 162votes ) Top Suggestions Comparing Lengths Worksheet 2nd : Comparing Lengths Worksheet 2nd Students practice measuring everyday objects in both inches and centimeters in this measure and compare worksheet inches and centimeters this second grade math worksheet supports kids as they In this lesson you will learn to compare lengths measured in centimetres and metres in this lesson we will think carefully about comparing lengths you will also learn to compare lengths that Learn how to compare lengths and heights by using particular words to define the differences for more help and advice with using words to compare length and height watch this teacher talk video. 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The worksheet is an assortment of 4 intriguing pursuits that will enhance your kid's knowledge and abilities. The worksheets are offered in developmentally appropriate versions for kids of different ages. Adding and subtracting integers worksheets in many ranges including a number of choices for parentheses use. You can begin with the uppercase cursives and after that move forward with the lowercase cursives. Handwriting for kids will also be rather simple to develop in such a fashion. If you're an adult and wish to increase your handwriting, it can be accomplished. As a result, in the event that you really wish to enhance handwriting of your kid, hurry to explore the advantages of an intelligent learning tool now! Consider how you wish to compose your private faith statement. Sometimes letters have to be adjusted to fit in a particular space. When a letter does not have any verticals like a capital A or V, the very first diagonal stroke is regarded as the stem. 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Know that whatever life you want, the grades you want, the job you want, the reputation you want, friends you want, that it's possible. Top

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Problem 1451. Symmetry of vector Determine whether the vector is symmetric or not (vector could be even or odd in length). For example: x = [1 2 3 3 2 1] is symmetric x = [1 2 3 4 3 2 1] is symmetric as well! x = [-1 -2 -3 3 2 1] is not symmetric Solution Stats 43.64% Correct | 56.36% Incorrect Last Solution submitted on Aug 09, 2024 Community Treasure Hunt Find the treasures in MATLAB Central and discover how the community can help you! Start Hunting!

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## The Other Kind of Bypass Capacitor January 3, 20173 comments There’s a type of bypass capacitor I’d like to talk about today. It’s not the usual power supply bypass capacitor, aka decoupling capacitor, which is used to provide local charge storage to an integrated circuit, so that the high-frequency supply currents to the IC can bypass (hence the name) all the series resistance and inductance from the power supply. This reduces the noise on a DC voltage supply. I’ve... October 4, 201618 comments I thought it would take me a day or two to implement, it took almost two weeks... But here it is, the new comments systems for blogs, heavily inspired by the forum system I developed earlier this year. Which means that: • You can easily add images, either by drag and drop or through the 'Insert Image' button • You can add MathML, TeX and ASCIImath equations and they will be rendered with Mathjax • You can add code snippets and they will be highlighted with highlights.js • You can edit... ## Use DPLL to Lock Digital Oscillator to 1PPS Signal July 24, 20168 comments Introduction There are occasions where it is desirable to lock a digital oscillator to an external time reference such as the 1PPS (One Pulse Per Second) signal output from a GPS receiver. One approach would be to synchronize a fixed frequency oscillator on the leading edge of the 1PPS signal. In many cases, this will result in adequate performance. However, in situations where simple synchronization does not provide adequate performance, digital phase-lock techniques can be applied to a... ## Digital PLL's -- Part 2 June 15, 20165 comments In Part 1, we found the time response of a 2nd order PLL with a proportional + integral (lead-lag) loop filter.  Now let’s look at this PLL in the Z-domain [1, 2].  We will find that the response is characterized by a loop natural frequency ωn and damping coefficient ζ. Having a Z-domain model of the DPLL will allow us to do three things: Compute the values of loop filter proportional gain KL and integrator gain KI that give the desired loop natural... ## Digital PLL's -- Part 1 June 7, 201626 comments 1. Introduction Figure 1.1 is a block diagram of a digital PLL (DPLL).  The purpose of the DPLL is to lock the phase of a numerically controlled oscillator (NCO) to a reference signal.  The loop includes a phase detector to compute phase error and a loop filter to set loop dynamic performance.  The output of the loop filter controls the frequency and phase of the NCO, driving the phase error to zero. One application of the DPLL is to recover the timing in a digital... ## Stability or insanity May 17, 20161 comment I've just spent over two weeks getting ready to do my next video.  It was a combination of one of those vast underestimations one occasionally makes, combined with falling into a bit of an obsession. I am, at this point, not only wondering if it was worth it, but questioning my sanity in carrying on even when the going went beyond tough to just plain crazy. At any rate, a good video needs a visual aid, and I decided that my video needed to demonstrate stability with a pendulum.... ## PID Without a PhD April 26, 201614 comments I both consult and teach in the area of digital control. Through both of these efforts, I have found that while there certainly are control problems that require all the expertise I can bring to bear, there are a great number of control problems that can be solved with the most basic knowledge of simple controllers, without resort to any formal control theory at all. This article will tell you how to implement a simple controller in software and how to tune it without getting into heavy... ## 3 Good News March 9, 20161 comment Good News #1 Last week, I announced a new and ambitious reward program that will be funded by the new Vendors Directory. This week, I am happy to announce that we have our firsts two sponsors!  Quantum Leaps & Abelon Systems have agreed to pay the sponsorship fee to be listed in the new Vendors Directory.  Because of their support, there is now some money in the reward pool (\$1,000) and enough to pay for the firsts 500 'beers' awarded.  Please... ## The New Forum is LIVE! February 18, 20161 comment After months of hard word, I am very excited to introduce to you the new forum interface. Here are the key features: 1- Easily add images to a post by drag & dropping the images in the editor 2- Easily attach files to a post by drag & dropping the files in the editor 3- Add latex equations to a post and they will be rendered with Mathjax (tutorial) 4- Add a code snippet and surround the code with ## Ancient History January 18, 201612 comments The other day I was downloading an IDE for a new (to me) OS.  When I went to compile some sample code, it failed.  I went onto a forum, where I was told "if you read the release notes you'd know that the peripheral libraries are in a legacy download".  Well damn!  Looking back at my previous versions I realized I must have done that and forgotten about it.  Everything changes, and keeping up with it takes time and effort. When I first started with microprocessors we... ## Basic hand tools for electronics assembly November 20, 20153 comments Though the software tools vary with different microcontrollers, many hardware tools are the same. ## Complexity in Consumer Electronics Considered Harmful October 1, 20111 comment I recently returned from a visit to my grandmother, who lives in an assisted living community, and got to observe both her and my frustration first-hand with a new TV. This was a Vizio flatscreen TV that was fairly easy to set up, and the picture quality was good. But here's what the remote control looks like: You will note: • the small lettering (the number buttons are just under 1/4 inch in diameter) • a typeface chosen for marketing purposes (matching Vizio's "futuristic" corporate... ## Two jobs December 5, 201223 comments For those of you following closely embeddedrelated and the other related sites, you might have noticed that I have been less active for the last couple of months, and I will use this blog post to explain why. The main reason is that I got myself involved into a project that ended up using a better part of my cpu than I originally thought it would. edit - video of the event: I currently have two jobs: one as an electrical/dsp engineer recycled as a web publisher and the other... ## Optimizing Optoisolators, and Other Stories of Making Do With Less December 14, 20144 comments It’s been a few months since I’ve rolled up my sleeves here and dug into some good old circuit design issues. I started out with circuit design articles, and I’ve missed it. Today’s topic will be showing you some tricks for how to get more performance out of an optoisolator. These devices — and I’m tempted to be lazy and call them “optos”, but that sounds more like a cereal with Greek yogurt-covered raisins — are essentially just an LED... ## The DSP Online Conference - Right Around the Corner! September 20, 20201 comment It is Sunday night as I write this blog post with a few days to go before the virtual doors of the very first DSP Online Conference open.. It all started with a post in the DSPRelated forum about three months ago.  We had just had a blast running the 2020 Embedded Online Conference and we thought it could be fun to organize a smaller event dedicated to the DSP community.  So my goal with the post in the forum was to see if... ## Sensors Expo - Trip Report & My Best Video Yet! August 3, 20183 comments This was my first time at Sensors Expo and my second time in Silicon Valley and I must say I had a great time. Before I share with you what I find to be, by far, my best 'highlights' video yet for a conference/trade show, let me try to entertain you with a few anecdotes from this trip.  If you are not interested by my stories or maybe don't have the extra minutes needed to read them, please feel free to skip to the end of this blog post to watch the... October 4, 201618 comments I thought it would take me a day or two to implement, it took almost two weeks... But here it is, the new comments systems for blogs, heavily inspired by the forum system I developed earlier this year. Which means that: • You can easily add images, either by drag and drop or through the 'Insert Image' button • You can add MathML, TeX and ASCIImath equations and they will be rendered with Mathjax • You can add code snippets and they will be highlighted with highlights.js • You can edit... ## A New Related Site! September 22, 20222 comments We are delighted to announce the launch of the very first new Related site in 15 years!  The new site will be dedicated to the trendy and quickly growing field of Machine Learning and will be called - drum roll please - MLRelated.com. We think MLRelated fits perfectly well within the “Related” family, with: • the fast growth of TinyML, which is a topic of great interest to the EmbeddedRelated community • the use of Machine/Deep Learning in Signal Processing applications, which is of... ## Linear Feedback Shift Registers for the Uninitiated, Part II: libgf2 and Primitive Polynomials July 17, 2017 Last time, we looked at the basics of LFSRs and finite fields formed by the quotient ring $GF(2)[x]/p(x)$. LFSRs can be described by a list of binary coefficients, sometimes referred as the polynomial, since they correspond directly to the characteristic polynomial of the quotient ring. Today we’re going to look at how to perform certain practical calculations in these finite fields. I maintain a Python library on bitbucket called... ## March is Oscilloscope Month — and at Tim Scale! March 6, 2014 I got my oscilloscope today. Maybe that was a bit of an understatement; I'll have to resort to gratuitous typography: I GOT MY OSCILLOSCOPE TODAY!!!! Those of you who are reading this blog may remember I made a post about two years ago about searching for the right oscilloscope for me. Since then, I changed jobs and have been getting situated in the world of applications engineering, working on motor control projects. I've been gradually working to fill in gaps in the infrastructure...

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# The length of the rectangle is 3 m and the width is 1 cm. What is the perimeter of the rectangle? First, let’s bring all units of measurement to a single one. 3 m = 300 cm. Next, we write down the formula for finding the perimeter of a rectangle: P = 2a + 2b, where a – length, b – width. Let us find the perimeter of the rectangle if the length and width are known by the problem statement: P = 2 * 300 + 2 * 1 = 600 + 2 = 602 cm. Answer: The perimeter of the rectangle is 602 cm. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.

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http://physics.stackexchange.com/questions/6792/is-weyl-invariance-absolutely-necessary-for-string-worldsheets

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# Is Weyl invariance absolutely necessary for string worldsheets? The Polyakov action for a string worldsheet has Weyl invariance. In the conformal gauge augmented with Weyl gauge-fixing, we can always impose a flat worldsheet metric in Minkowski coordinates. The residual gauge symmetries take on the form of conformal Virasoro and anti-Virasoro algebras. This is equivalent to a two dimensional conformal field theory. Later, we impose the Virasoro constraints. However, can't we come up with more general worldsheet actions which are invariant under diffeomorphisms but not Weyl transformations? The conformal gauge is still possible, but the worldsheet volume factor is dynamical. Residual diffeomorphisms taking on the same form as conformal transformations, minus the compensating Weyl transformation, still exist. They still take on the form of Virasoro algebras and Virasoro constraints. This is no longer a conformal field theory because we have a characteristic length scale on the worldsheet. Some of these theories are also modular invariant. Do they describe valid string theories? - Dear Jenkins, the theories you want to construct are "noncritical string theories" and they're less interesting and less consistent than the "critical string theories". First, the Nambu-Goto action - the proper area of the world sheet - is nonlinear. It includes square roots etc. It's much better to introduce an auxiliary metric tensor on the world sheet and the action for the coordinates $X$ becomes nice and bilinear - a free theory. However, we don't want new degrees of freedom to be added. The 2D metric tensor has three independent components. Two of them may be set to a standard form by the 2 degrees of freedom in the 2D coordinate reparameterization symmetry; and the third by the Weyl symmetry if it exists. If it doesn't exist, it's too bad. The auxiliary world sheet metric may only be brought to the form of $e^\phi \eta_{ab}$. That means that $\phi$, determining the overall scaling, becomes another function of the world sheet coordinates $(\sigma,\tau)$, very analogously to the spacetime coordinates $X(\sigma,\tau)$. In fact, it is really valid to say that the parameter determining the overall scaling of the metric is another spacetime coordinate. If this coordinate were totally identical to the other coordinates, then there would also be a translation symmetry in the $\phi$ direction - but that's equivalent to the Weyl symmetry (multiplicative scaling of $e^\phi$ is the same thing as additive shifts to $\phi$). Because by assumption, the Weyl symmetry doesn't hold in your theory, the new spacetime coordinate $\phi$ can't have quite the same properties as the other spacetime coordinates. However, in normal circumstances, you obtain the violations of the Weyl invariance as a disease. In particular, if you try to study string theory in a non-critical dimension, i.e. $D\neq 26$ or $D\neq 10$, you will find out that the field $\phi$ doesn't decouple and the path integral, when calculated including the one-loop accuracy, still depends on $\phi$. So the Weyl symmetry, equivalent to an additive shift of $\phi$ by a function of the world sheet, is not a symmetry. As I said, this can be interpreted as $\phi$'s becoming a new spacetime coordinate. But if you try to calculate the effective action in the new spacetime that has an additional dimension $\phi$, you will find out that the laws of physics are not invariant under translations in $\phi$ - that's nothing else than the failure of the theory to be Weyl-invariant. In particular, you will find out that the dilaton linearly depends on $\phi$: search for papers about "linear dilaton". The squared gradient of the dilaton is related to the surplus or excess (if it is time-like or space-like) of the spacetime coordinates, relatively to the critical dimension. If the spacetime has two dimensions, one may choose the dilaton to depend on the (only) spacelike coordinate $\phi=X^1$ in such a way that the theory including $\phi$ is Weyl-invariant again. In this case, it's useful to consider not only the right linear dilaton - solving the equations of motion - but also a non-trivial background for the tachyon. One ends up with the so-called "Liouville theory" - a "linear dilaton" theory with some extra tachyonic profile in a non-critical stringy $D=2$ spacetime - which is slightly more consistent than other noncritical string theories. The Liouville theory may also be described by a quantum mechanical model with a large matrix - the old matrix theory. -

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# DoITPoMS TLP Library Teaching and learning packages (TLPs) are self-contained, interactive resources, each focusing on one area of Materials Science. Introduction To Anisotropy It is common in basic analysis to treat bulk materials as isotropic - their properties are independent of the direction in which they are measured. However the atomic scale structure can result in properties that vary with direction. This teaching and learning package (TLP) looks into typical examples of such anisotropy and gives a brief mathematical look into modelling the behaviour. Atomic Scale Structure of Materials This teaching and learning package provides an introduction to crystalline, polycrystalline and amorphous solids, and how the atomic-level structure has radical consequences for some of the properties of the material. It introduces the use of polarised light to examine the optical properties of materials, and shows how a variety of simple models can be used to visualise important features of the microstructure of materials. Casting This TLP introduces a number of important processes through which metallic items can be fabricated from molten metal. As well as detailing the practical aspects of these manufacturing processes, attention is given to the important parameters which determine the microstructure of the finished items. Creep Deformation of Metals Creep is a major concern in engineering, since it can cause materials to fail well below their yield stress. This package outlines the mechanisms of creep and the associated equations. It is largely based around a first year Materials Science practical at the University of Cambridge, which is concerned with the creep of solder at different temperatures. It also includes a case study of a creep-resistant material to illustrate how materials can be designed to prevent creep. Crystallinity in Polymers An understanding of polymer crystallinity is important because the mechanical properties of crystalline polymers are different from those of amorphous polymers. Polymer crystals are much stiffer and stronger than amorphous regions of polymer. Crystallography Crystalline materials are characterised by a regular atomic structure that repeats itself in all three dimensions. In other words the structure displays translational symmetry. Dielectric Materials This teaching and learning package will introduce you to the properties and uses of dielectric materials. Diffusion An introduction to the mechanisms and driving forces of diffusion, and some of the processes in which it is observed. Elasticity in Biological Materials This teaching and learning package (TLP) discusses the elasticity of biological materials. Whilst some show Hookean elasticity, the vast majority do not. Non-linear elasticity is considered, in particular J-shaped and S-shaped curves. Viscoelasticity is also discussed, using hair and spiders' silk as examples. Electromigration Electromigration is an ever-increasing problem as integrated circuits are pushed towards further miniaturization. The theory of the phenomenon is explained, including electromigration-induced failure and how it has been and can be minimized. Epitaxial Growth This TLP enables you to explore the way in which perfect thin crystalline layers are deposited epitaxially (i.e. in the same crystal orientation) on semiconductor substrates. This is the way many electronic and opto-electronic devices are now fabricated using techniques such as molecular beam epitaxy (MBE). Examination of a Manufactured Article This TLP provides an introduction to the deconstruction and investigation of the materials and processes used in an everyday item or article. Ferroelectric Materials Ferroelectrics are an important device in today's world. They are useful both as capacitors, for example in camera flashes, or as non-volatile memory storage. The memory use of which you are most likely to be aware is in the Playstation 2. Ferromagnetic Materials How many ferromagnets do you think you own? Maybe many more than you realise. Ferromagnetic materials lie at the heart not just of the humble compass, but also of many loudspeakers and of computer memory. This teaching and learning package outlines the microscopic basis of magnetism and some of the conquences of ferromagnetic order in real materials. The Glass Transition in Polymers This teaching and learning package is based on a lecture demonstrations used within the Department of Materials Science and Metallurgy at the University of Cambridge. The package is aimed at first year undergraduate Materials Science students and focuses on the glass transition in polymers. Liquid Crystals This Teaching and Learning Package provides an introduction to liquid crystals, their physical properties and their modern-day applications. Introduction To Photoelasticity This tutorial is based on lab work within the Department of Materials Science and Metallurgy at the University of Cambridge. The tutorial provides an introduction to the topic of photoelasticity and preparation for lab work. Photographs illustrate many features of birefringence in polymers under polarised light. Piezoelectric Materials This teaching and learning package (TLP) provides an introduction to piezoelectric materials. Polymer Basics This teaching and learning package is an introduction to the basic concepts of polymer science. It includes molecular structure, synthesis and tests for identification. Pyroelectric Materials Pyroelectric materials are found in almost every home, in the form of intrusion detectors and other devices, and this TLP will consider how they work, and what the most common ones are made of. Introduction To Semiconductors This teaching and learning package provides a very basic introduction to semiconductors. These materials are essential to the operation of solid state electronic devices. Solidification of Alloys This teaching and learning package (TLP) is an introduction to how solute affects the solidification of metallic alloys. The Stereographic Projection This TLP covers the use of the Stereographic projection and Wulff nets. The Stiffness of Rubber This teaching and learning package is based on two experiments which demonstrate the behaviour of rubber under tension. The first displays the unusual behaviour of a rubber strip when heated under tension; the second considers the behaviour of a rubber membrane under tension. In both cases the behaviour is considered theoretically in terms of the molecular structure of rubber and the thermodynamic entropy changes involved. Superconductivity Electrons in pairs? Levitating trains? Superconductivity - the combination of lossless electrical conduction and the ability of a material to expel a magnetic field - is a property that excites interest in fundamental science whilst offering tantalising prospects for a range of applications. In this teaching and learning package (TLP), we trace the history of superconductivity, outline some fundamental properties of superconductors, and describe current and potential applications of materials with this unusual property. Tensors This TLP offers an introduction to the mathematics of tensors rather than the intricacies of their applications. Its aims are to familiarise the learner with tensor notation, how they can be constructed and how they can be manipulated to give numerical answers to problems.

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