id
stringlengths
9
10
abstract
stringlengths
13
3.93k
embedding
sequence
1001.0112
The complete supersymmetric action for eleven-dimensional supergravity is presented. The action is polynomial in the scalar fermionic pure spinor superfield, and contains only a minor modification to the recently proposed three-point coupling.
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1001.0113
A new method for determining whether or not a mitrochondrial DNA (mtDNA) sequence belongs to a vertebrate is described and tested. This method only needs the mtDNA sequence of the organism in question, and unlike alignment based methods, it does not require it to be compared with anything else. The method is tested on all 1877 mtDNA sequences that were on NCBI's nucleotide database on August 12, 2009, and works in 94.57% of the cases. Furthermore, all organisms on which this method failed are closely related phylogenetically in comparison to all other organisms included in the study. A list of potential extensions to this method and open problems that emerge out of this study is presented at the end.
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1001.0114
In this article, we study topological properties of Voisin's punctual Hilbert schemes of an almost-complex fourfold $X$. In this setting, we compute their Betti numbers and construct Nakajima operators. We also define tautological bundles associated with any complex bundle on $X$, which are shown to be canonical in $K$-theory.
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1001.0115
This paper gives an overview of a proposed strategy for the "Cows and Herders" scenario given in the Multi-Agent Programming Contest 2009. The strategy is to be implemented using the Jason platform, based on the agent-oriented programming language Agent-Speak. The paper describes the agents, their goals and the strategies they should follow. The basis for the paper and for participating in the contest is a new course given in spring 2009 and our main objective is to show that we are able to implement complex multi-agent systems with the knowledge gained in an introductory course on multi-agent systems.
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1001.0116
With Girardeau's Fermi-Bose mapping, we have constructed the eigenstates of a TG gas in an external magnetic field. When the number of bosons $N$ is commensurate with the number of potential cycles $M$, the probability of this TG gas in the ground state is bigger than the TG gas raised by Girardeau in 1960. Through the comparison of properties between this TG gas and Fermi gas, we find that the following issues are always of the same: their average value of particle's coordinate and potential energy, system's total momentum, single-particle density and the pair distribution function. But the reduced single-particle matrices and their momentum distributions between them are different.
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1001.0117
This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing reductions that are computed by polynomial-size circuits. 2. If there is a problem in coNP that cannot be solved by polynomial-size nondeterministic circuits, then every many-one complete set is complete under length-increasing reductions that are computed by polynomial-size circuits. 3. If there exist a one-way permutation that is secure against subexponential-size circuits and there is a hard tally language in NP intersect coNP, then there is a Turing complete language for NP that is not many-one complete. Our first two results use worst-case hardness hypotheses whereas earlier work that showed similar results relied on average-case or almost-everywhere hardness assumptions. The use of average-case and worst-case hypotheses in the last result is unique as previous results obtaining the same consequence relied on almost-everywhere hardness results.
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1001.0118
We explore two-dimensional sigma models with (0,2) supersymmetry through their chiral algebras. Perturbatively, the chiral algebras of (0,2) models have a rich infinite-dimensional structure described by the cohomology of a sheaf of chiral differential operators. Nonperturbatively, instantons can deform this structure drastically. We show that under some conditions they even annihilate the whole algebra, thereby triggering the spontaneous breaking of supersymmetry. For a certain class of K\"ahler manifolds, this suggests that there are no harmonic spinors on their loop spaces and gives a physical proof of the H\"ohn-Stolz conjecture.
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1001.0119
In this article, we study the rational cohomology rings of Voisin's punctual Hilbert schemes $X^{[n]}$ associated to a symplectic compact fourfold $X$. We prove that these rings can be universally constructed from $H^*(X,\mathbb{Q})$ and $c_1(X)$, and that Ruan's crepant resolution conjecture holds if $c_1(X)$ is a torsion class. Next, we prove that for any almost-complex compact fourfold $X$, the complex cobordism class of $X^{[n]}$ depends only on the cobordism class of $X$.
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1001.0121
Using Landau-Ginzburg-Devonshire approach we calculated the equilibrium distributions of electric field, polarization and space charge in the ferroelectric-semiconductor heterostructures containing proper or incipient ferroelectric thin films. The role of the polarization gradient and intrinsic surface energy, interface dipoles and free charges on polarization dynamics are specifically explored. The intrinsic field effects, which originated at the ferroelectric-semiconductor interface, lead to the surface band bending and result into the formation of depletion space-charge layer near the semiconductor surface. During the local polarization reversal (caused by the inhomogeneous electric field induced by the nanosized tip of the Scanning Probe Microscope (SPM) probe) the thickness and charge of the interface layer drastically changes, it particular the sign of the screening carriers is determined by the polarization direction. Obtained analytical solutions could be extended to analyze polarization-mediated electronic transport.
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1001.0122
Demonstrating the quantum-confined Stark effect (QCSE) in silicon nanocrystals (NCs) embedded in oxide has been rather elusive, unlike the other materials. Here, the recent experimental data from ion-implanted Si NCs is unambiguously explained within the context of QCSE using an atomistic pseudopotential theory. This further reveals that the majority of the Stark shift comes from the valence states which undergo a level crossing that leads to a nonmonotonic radiative recombination behavior with respect to the applied field. The polarizability of embedded Si NCs including the excitonic effects is extracted over a diameter range of 2.5--6.5 nm, which displays a cubic scaling, $\alpha=c D^3$, with $c=2.436\times 10^{-11}$ C/(Vm), where $D$ is the NC diameter. Finally, based on intraband electroabsorption analysis, it is predicted that p-doped Si NCs will show substantial voltage tunability, whereas n-doped samples should be almost insensitive. Given the fact that bulk silicon lacks the linear electro-optic effect as being a centrosymmetric crystal, this may offer a viable alternative for electrical modulation using p-doped Si NCs.
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1001.0123
We explore electron transport properties in honeycomb lattice ribbons with zigzag edges coupled to two semi-infinite one-dimensional metallic electrodes. The calculations are based on the tight-binding model and the Green's function method, which numerically compute the conductance-energy and current-voltage characteristics as functions of the lengths and widths of the ribbons. Our numerical results predict that for such a ribbon an energy gap always appears in the conductance spectrum across the energy E=0. With the increase of the size of the ribbon, the gap gradually decreases but it never vanishes. This clearly manifests that a honeycomb lattice ribbon with zigzag edges always exhibits the semiconducting behavior, and it becomes much more clearly visible from our presented current-voltage characteristics.
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1001.0124
Black hole spacetimes that are topological geons in the sense of Sorkin can be constructed by taking a quotient of a stationary black hole that has a bifurcate Killing horizon. We discuss the geometric properties of these geon black holes and the Hawking-Unruh effect on them. We in particular show how correlations in the Hawking-Unruh effect reveal to an exterior observer features of the geometry that are classically confined to the regions behind the horizons.
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1001.0125
We consider an undirected graph $G = (VG, EG)$ with a set $T \subseteq VG$ of terminals, and with nonnegative integer capacities $c(v)$ and costs $a(v)$ of nodes $v\in VG$. A path in $G$ is a \emph{$T$-path} if its ends are distinct terminals. By a \emph{multiflow} we mean a function $F$ assigning to each $T$-path $P$ a nonnegative rational \emph{weight} $F(P)$, and a multiflow is called \emph{feasible} if the sum of weights of $T$-paths through each node $v$ does not exceed $c(v)$. The \emph{value} of $F$ is the sum of weights $F(P)$, and the \emph{cost} of $F$ is the sum of $F(P)$ times the cost of $P$ w.r.t. $a$, over all $T$-paths $P$. Generalizing known results on edge-capacitated multiflows, we show that the problem of finding a minimum cost multiflow among the feasible multiflows of maximum possible value admits \emph{half-integer} optimal primal and dual solutions. Moreover, we devise a strongly polynomial algorithm for finding such optimal solutions.
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1001.0126
Squeezed correlations of particle-antiparticle pairs were predicted to exist if the hadron masses were modified in the hot and dense medium formed in high energy heavy ion collisions. Although well-established theoretically, they have not yet been observed experimentally. We suggest here a clear method to search for such signal, by analyzing the squeezed correlation functions in terms of measurable quantities. We illustrate this suggestion for simulated phi-phi pairs at RHIC energies.
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1001.0127
A multidimensional cosmological type model with 1-component anisotropic fluid is considered. An exact solution is obtained. This solution is defined on a product manifold containing n Ricci-flat factor spaces. We singled out a special solution governed by the function cosh. It is shown that this special solution has Kasner-like asymptotics in the limits \tau \to + 0 and \tau \to + \infty, where \tau is a synchronous time variable. A relation between two sets of Kasner parameters \alpha_{\infty} and \alpha_{0} is found. This formula (of "scattering law") is coinciding with that obtained earlier for the S-brane solution (when scalar fields are absent).
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1001.0128
First-principles electronic structure calculations have been performed for the double perovskite Bi$_2$CoMnO$_6$ in its non-centrosymmetric polar state using generalized gradient approximation plus Hubbard U approach. We find that while Co is in a high spin state, Mn is in an intermediate spin state. The calculated dynamical charge tensors are anisotropic reflecting a low-symmetry structure of the compound. Magnetic structure dependent phonon frequencies indicate the presence of spin-phonon coupling. Using Berry phase method, we obtain a spontaneous electronic polarization of 5.88 ${\mu}C/cm^2$ which is close to the experimental value observed for a similar compound, Bi$_2$NiMnO$_6$.
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1001.0129
We study beta-extensions in a p-adic classical group and we produce a relation between some beta-extensions by means of a Weil representation. We apply this to the study of reducibility points of some parabolically induced representations.
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1001.0131
This paper briefly summarizes previous work on complex classical mechanics and its relation to quantum mechanics. It then introduces a previously unstudied area of research involving the complex particle trajectories associated with elliptic potentials.
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1001.0132
In a series of papers the authors proved that twisted Alexander polynomials detect fibered 3-manifolds, and they showed that this implies that a closed 3-manifold N is fibered if and only if S^1 x N is symplectic. In this note we summarize some of the key ideas of the proofs. We also give new evidence to the conjecture that if $ is a symplectic 4-manifold with a free S^1-action, then the orbit space is fibered.
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1001.0133
Using a bidifferential graded algebra approach to integrable partial differential or difference equations, a unified treatment of continuous, semi-discrete (Ablowitz-Ladik) and fully discrete matrix NLS systems is presented. These equations originate from a universal equation within this framework, by specifying a representation of the bidifferential graded algebra and imposing a reduction. By application of a general result, corresponding families of exact solutions are obtained that in particular comprise the matrix soliton solutions in the focusing NLS case. The solutions are parametrised in terms of constant matrix data subject to a Sylvester equation (which previously appeared as a rank condition in the integrable systems literature). These data exhibit a certain redundancy, which we diminish to a large extent. More precisely, we first consider more general AKNS-type systems from which two different matrix NLS systems emerge via reductions. In the continuous case, the familiar Hermitian conjugation reduction leads to a continuous matrix (including vector) NLS equation, but it is well-known that this does not work as well in the discrete cases. On the other hand there is a complex conjugation reduction, which apparently has not been studied previously. It leads to square matrix NLS systems, but works in all three cases (continuous, semi- and fully-discrete). A large part of this work is devoted to an exploration of the corresponding solutions, in particular regularity and asymptotic behaviour of matrix soliton solutions.
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1001.0134
We derive expressions for the time integrated spectrum of Cosmic Rays (CRs) that are accelerated in a decelerating relativistic shock wave and escape ahead of the shock. It is assumed that at any given time the CRs have a power law form, carry a constant fraction of the energy E_tot of the shocked plasma, and escape continuously at the maximal energy attainable. The spectrum of escaping particles is highly sensitive to the instantaneous spectral index due to the fact that the minimal energy, E_min ~ \Gamma^2 m_pc^2 where \Gamma is the shock Lorentz factor, changes with time. In particular, the escaping spectrum may be considerably harder than the canonical N(E)\propto E^-2 spectrum. For a shock expanding into a plasma of density n, a spectral break is expected at the maximal energy attainable at the transition to non relativistic velocities, E ~ 10^19 (\epsilon_B/0.1)(n/1 cm^-3)^(1/6)(E_tot/10^51 erg)^(1/3) eV where \epsilon_B is the fraction of the energy flux carried by the magnetic field. If ultra-high energy CRs are generated in decelerating relativistic blast waves arising from the explosion of stellar mass objects, their generation spectrum may therefore be different than the canonical N(E)\propto E^-2.
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1001.0135
(abridged) We present a comprehensive study of stellar stratification in young star clusters in the Large Magellanic Cloud (LMC). We apply our recently developed effective radius method for the assessment of stellar stratification on imaging data obtained with the Advanced Camera for Surveys of three young LMC clusters to characterize the phenomenon and develop a comparative scheme for its assessment in such clusters. The clusters of our sample, NGC 1983, NGC 2002 and NGC 2010, are selected on the basis of their youthfulness, and their variety in appearance, structure, stellar content, and surrounding stellar ambient. Our photometry is complete for magnitudes down to m_814 ~ 23 mag, allowing the calculation of the structural parameters of the clusters, the estimation of their ages and the determination of their stellar content. Our study shows that each cluster in our sample demonstrates stellar stratification in a quite different manner and at different degree from the others. Specifically, NGC 1983 shows to be partially segregated only for the faintest stars of the cluster, NGC 2002 shows evidence of strong stellar stratification for both bright and faint stars, and NGC 2010 is found not to be segregated. For the parametrization of the phenomenon of stellar stratification and its quantitative comparison among these clusters, we propose the slope derived from the change in the effective radius over the corresponding magnitude range as indicative parameter of the degree of stratification in the clusters. A positive value of this slope indicates mass segregation in the cluster, while a negative or zero value signifies the lack of the phenomenon.
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1001.0136
We study the spectral distribution of the threshold network model.The results contain an explicit description and its asymptotic behaviour.
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1001.0137
In \cite{Mul} one-parameter planar motion was first introduced and the relations between absolute, relative, sliding velocities (and accelerations) in the Euclidean plane $\mathbb{E}^2$ were obtained. Moreover, the relations between the Complex velocities one-parameter motion in the Complex plane were provided by \cite{Mul}. One-parameter planar homothetic motion was defined in the Complex plane, \cite{Kur}. In this paper, analogous to homothetic motion in the Complex plane given by \cite{Kur}, one-parameter planar homothetic motion is defined in the Hyperbolic plane. Some characteristic properties about the velocity vectors, the acceleration vectors and the pole curves are given. Moreover, in the case of homothetic scale $h$ identically equal to 1, the results given in \cite{Yuc} are obtained as a special case. In addition, three hyperbolic planes, of which two are moving and the other one is fixed, are taken into consideration and a canonical relative system for one-parameter planar hyperbolic homothetic motion is defined. Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, is obtained with the help of this relative system.
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1001.0138
One-parameter hyperbolic planar motion was first studied by S. Y$\ddot{\texttt{u}}$ce and N. Kuruo$\tilde{\texttt{g}}$lu. Moreover, they analyzed the relationships between the absolute, relative and sliding velocities of one-parameter hyperbolic planar motion as well as the related pole curves, \cite{Yuc}. One-parameter planar motions in the Euclidean plane $\mathbb{E}^2$ and the Euler-Savary formula in one-parameter planar motions were given by M$\ddot{\texttt{u}}$ller, \cite{Mul}. In the present article, one hyperbolic plane moving relative to two other hyperbolic planes, one moving and the other fixed, was taken into consideration and the relation between the absolute, relative and sliding velocities of this movement was obtained. In addition, a canonical relative system for one-parameter hyperbolic planar motion was defined. Euler-Savary formula, which gives the relationship between the curvature of trajectory curves, was obtained with the help of this relative system.
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1001.0139
Asteroseismology involves probing the interiors of stars and quantifying their global properties, such as radius and age, through observationsof normal modes of oscillation. The technical requirements for conducting asteroseismology include ultra-high precision measured in photometry in parts per million, as well as nearly continuous time series over weeks to years, and cadences rapid enough to sample oscillations with periods as shortas a few minutes. We report on results from the first 43 days of observations in which the unique capabilities of Kepler in providing a revolutionary advance in asteroseismology are already well in evidence. The Kepler asteroseismology program holds intrinsic importance in supporting the core planetary search program through greatly enhanced knowledge of host star properties, and extends well beyond this to rich applications in stellar astrophysics.
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1001.0141
73 broadband optical spectra of dwarf stars later than F0 have been obtained from the Nearby Stars Project website. The number of absorption lines is computed for each spectrum between 6000 and 6200 Angstrom. A correlation is found between the density of lines K$\lambda$ and the spectral type. This method is independent of calibration process, does not require high resolution or high signal to noise data and does not make use of a large library of standard spectra.
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1001.0142
The Kepler Mission offers two options for observations -- either Long Cadence (LC) used for the bulk of core mission science, or Short Cadence (SC) which is used for applications such as asteroseismology of solar-like stars and transit timing measurements of exoplanets where the 1-minute sampling is critical. We discuss the characteristics of SC data obtained in the 33.5-day long Quarter 1 (Q1) observations with Kepler which completed on 15 June 2009. The truly excellent time series precisions are nearly Poisson limited at 11th magnitude providing per-point measurement errors of 200 parts-per-million per minute. For extremely saturated stars near 7th magnitude precisions of 40 ppm are reached, while for background limited measurements at 17th magnitude precisions of 7 mmag are maintained. We note the presence of two additive artifacts, one that generates regularly spaced peaks in frequency, and one that involves additive offsets in the time domain inversely proportional to stellar brightness. The difference between LC and SC sampling is illustrated for transit observations of TrES-2.
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1001.0143
A new approach to the design of massively parallel and interactive programming languages has been recently proposed using rv-systems (interactive systems with registers and voices) and Agapia programming. In this paper we present a few theoretical results on FISs (finite interactive systems), the underlying mechanism used for specifying control and interaction in these systems. First, we give a proof for the undecidability of the emptiness problem for FISs, by reduction to the Post Correspondence Problem. Next, we use the construction in this proof to get other undecidability results, e.g., for the accessibility of a transition in a FIS, or for the finiteness of the language recognized by a FIS. Finally, we present a simple proof of the equivalence between FISs and tile systems, making explicit that they precisely capture recognizable two-dimensional languages.
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1001.0144
We propose a new method to derive certain higher order estimates in quantum electrodynamics. Our method is particularly convenient in the application to the non-local semi-relativistic models of quantum electrodynamics as it avoids the use of iterated commutator expansions. We re-derive higher order estimates obtained earlier by Fr\"ohlich, Griesemer, and Schlein and prove new estimates for a non-local molecular no-pair operator.
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1001.0145
We calculate nucleosynthesis of proton-rich isotopes in the carbon-deflagration model for Type Ia supernovae (SNe Ia). The seed abundances are obtained by calculating the s-process nucleosynthesis that is expected to occur in the repeating helium shell flashes on the carbon-oxygen (CO) white dwarf (WD) during mass accretion from a binary companion. When the deflagration wave passes through the outer layer of the CO WD, p-nuclei are produced by photodisintegration reactions on s-nuclei in a region with the peak temperature ranging from 1.9 to 3.6 x10^9 K. We confirm the sensitivity of the p-process on the initial distribution of s-nuclei. We show that the initial C/O ratio in the WD does not much affect the yield of p-nuclei. On the other hand, the abundance of 22Ne left after the s-processing has a large influence on the p-process via 22Ne(alpha,n) reaction. We find that about 50% of p-nuclides are co-produced when normalized to their solar abundances in all adopted cases of seed distribution. Mo and Ru, which are largely underproduced in Type II supernovae (SNe II), are produced more than in SNe II although they are underproduced with respect to the yield levels of other p-nuclides. The ratios between p-nuclei and iron in the ejecta are larger than the solar ratios by a factor of 1.2. We also compare the yields of oxygen, iron, and p-nuclides in SNe Ia and SNe II and suggest that SNe Ia could make a larger contribution than SNe II to the solar system content of p-nuclei.
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1001.0146
We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a mathematical answer for the long standing problem of existence of Planetary Sistems around stars.
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1001.0147
We classify all negatively curved $\R^n \rtimes \R$ up to quasiisometry. We show that all quasiisometries between such manifolds (except when they are biLipschitz to the real hyperbolic spaces) are almost similarities. We prove these results by studying the quasisymmetric maps on the ideal boundary of these manifolds.
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1001.0148
We describe all the self quasisymmetric maps on the ideal boundary of a particular negatively curved solvable Lie group. As applications, we prove a Liouville type theorem, and derive some rigidity properties for quasiisometries of the solvable Lie group.
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1001.0149
We develop a hierarchical matrix construction algorithm using matrix-vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorithm uses $\mathcal{O}(\log n)$ applications of the matrix on structured random test vectors and $\mathcal{O}(n \log n)$ extra computational cost, where $n$ is the dimension of the unknown matrix. Numerical examples on constructing Green's functions for elliptic operators in two dimensions show efficiency and accuracy of the proposed algorithm.
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1001.0151
The two-dimensional ideal (Euler) fluids can be described by the classical fields of streamfunction, velocity and vorticity and, in an equivalent manner, by a model of discrete point-like vortices interacting in plane by a self-generated long-range potential. This latter model can be formalized, in the continuum limit, as a field theory of scalar matter in interaction with a gauge field, in the $su(2) $ algebra. This description has already offered the analytical derivation of the \emph{sinh}-Poisson equation, which was known to govern the stationary coherent structures reached by the Euler fluid at relaxation. In order this formalism to become a familiar theoretical instrument it is necessary to have a better understanding of the physical meaning of the variables and of the operations used by the field theory. Several problems will be investigated below in this respect.
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1001.0152
Reissner--Nordstr\"om black holes have two static regions: $r > \ro$ and $0 < r < \ri$, where $\ri$ and $\ro$ are the inner and outer horizon radii. The stability of the exterior static region has been established long time ago. In this work we prove that the interior static region is unstable under linear gravitational perturbations, by showing that field perturbations compactly supported within this region will generically excite a mode that grows exponentially in time. This result gives an alternative reason to mass inflation to consider the space time extension beyond the Cauchy horizon as physically irrelevant, and thus provides support to the strong cosmic censorship conjecture, which is also backed by recent evidence of a linear gravitational instability in the interior region of Kerr black holes found by the authors. The use of intertwiners to solve for the evolution of initial data plays a key role, and adapts without change to the case of super-extremal \rn black holes, allowing to complete the proof of the linear instability of this naked singularity. A particular intertwiner is found such that the intertwined Zerilli field has a geometrical meaning -it is the first order variation of a particular Riemann tensor invariant-. Using this, calculations can be carried out explicitely for every harmonic number.
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1001.0153
A theorem of N. Katz \cite{Ka} p.45, states that an irreducible differential operator $L$ over a suitable differential field $k$, which has an isotypical decomposition over the algebraic closure of $k$, is a tensor product $L=M\otimes_k N$ of an absolutely irreducible operator $M$ over $k$ and an irreducible operator $N$ over $k$ having a finite differential Galois group. Using the existence of the tensor decomposition $L=M\otimes N$, an algorithm is given in \cite{C-W}, which computes an absolutely irreducible factor $F$ of $L$ over a finite extension of $k$. Here, an algorithmic approach to finding $M$ and $N$ is given, based on the knowledge of $F$. This involves a subtle descent problem for differential operators which can be solved for explicit differential fields $k$ which are $C_1$-fields.
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1001.0154
Let $\mathbb K$ be a field and suppose $p, q\in\mathbb K^*$ are not roots of unity. We prove that the two quantum groups $U_q(\mathfrak {sl}_{n+1})$ and $U_p(\mathfrak{sl}_{n+1})$ are isomorphic as $\mathbb K$-algebras implies that $p=\pm q^{\pm 1}$ when $n$ is even. This new result answers a classical question of Jimbo.
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1001.0155
Singularities in $(3+1)$-dimensional Horava-Lifshitz (HL) theory of gravity are studied. These singularities can be divided into scalar, non-scalar curvature, and coordinate singularities. Because of the foliation-preserving diffeomorphisms of the theory, the number of scalars that can be constructed from the extrinsic curvature tensor $K_{ij}$, the 3-dimensional Riemann tensor and their derivatives is much large than that constructed from the 4-dimesnional Riemann tensor and its derivatives in general relativity (GR). As a result, even for the same spacetime, it may be singular in the HL theory but not in GR. Two representative families of solutions with projectability condition are studied, one is the (anti-) de Sitter Schwarzschild solutions, and the other is the Lu-Mei-Pope (LMP) solutions written in a form satisfying the projectability condition - the generalized LMP solutions. The (anti-) de Sitter Schwarzschild solutions are vacuum solutions of both HL theory and GR, while the LMP solutions with projectability condition satisfy the HL equations coupled with an anisotropic fluid with heat flow. It is found that the scalars $K$ and $K_{ij}K^{ij}$ are singular only at the center for the de Sitter Schwarzschild solution, but singular at both the center and $ r = (3M/|\Lambda|)^{1/3}$ for the anti-de Sitter Schwarzschild solution. The singularity at $ r = (3M/|\Lambda|)^{1/3}$ is absent in GR. In addition, all the generalized LMP solutions have two scalar curvature singularities, located at either $r = 0$ and $r=r_{s} > 0$, or $r=r_{1}$ and $r= r_{2}$ with $r_{2} > r_{1} > 0$, or $r=r_{s} > 0$ and $r = \infty$, depending on the choice of the free parameter $\lambda$.
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1001.0156
The optimization of entanglement evolution for two-mode Gaussian pure states under one-side Gaussian map is studied. Even there isn't complete information about the one-side Gaussian noisy channel, one can still maximize the entanglement distribution by testing the channel with only two specific states.
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1001.0157
We show that every central simple algebra A over a field k is Brauer equivalent to a quotient of a finite dimensional Hopf algebra over the same field (that is- A is Hopf Schur). If the characteristic of the field is zero, or if the algebra has a Galois splitting field of degree prime to the characteristic of k, we can take this Hopf algebra to be semisimple. We also show that if F is any finite extension of k, then F is a quotient of a finite dimensional Hopf algebra over k. We use it in order to show why the algebric closeness assumption is necessary in a weak form of Kaplansky's tenth conjecture, due to Stefan
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1001.0158
The recent extensions of domain theory have proved particularly efficient to study lattice-valued maxitive measures, when the target lattice is continuous. Maxitive measures are defined analogously to classical measures with the supremum operation in place of the addition. Building further on the links between domain theory and idempotent analysis highlighted by Lawson (2004), we investigate the concept of domain-valued linear forms on an idempotent (semi)module. In addition to proving representation theorems for continuous linear forms, we address two applications: the idempotent Radon--Nikodym theorem and the idempotent Riesz representation theorem. To unify similar results from different mathematical areas, our analysis is carried out in the general Z framework of domain theory.
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1001.0159
Vesicles are becoming a quite popular model for the study of red blood cells (RBCs). This is a free boundary problem which is rather difficult to handle theoretically. Quantitative computational approaches constitute also a challenge. In addition, with numerical studies, it is not easy to scan within a reasonable time the whole parameter space. Therefore, having quantitative analytical results is an essential advance that provides deeper understanding of observed features and can be used to accompany and possibly guide further numerical development. In this paper shape evolution equations for a vesicle in a shear flow are derived analytically with precision being cubic (which is quadratic in previous theories) with regard to the deformation of the vesicle relative to a spherical shape. The phase diagram distinguishing regions of parameters where different types of motion (tank-treading, tumbling and vacillating-breathing) are manifested is presented. This theory reveals unsuspected features: including higher order terms and harmonics (even if they are not directly excited by the shear flow) is necessary, whatever the shape is close to a sphere. Not only does this theory cure a quite large quantitative discrepancy between previous theories and recent experiments and numerical studies, but also it reveals a new phenomenon: the VB mode band in parameter space, which is believed to saturate after a moderate shear rate, exhibits a striking widening beyond a critical shear rate. The widening results from excitation of fourth order harmonic. The obtained phase diagram is in a remarkably good agreement with recent three dimensional numerical simulations based on the boundary integral formulation. Comparison of our results with experiments is systematically made.
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1001.0161
After introducing the basic ingredients of Loop Quantum Cosmology, I will briefly discuss some of its phenomenological aspects. Those can give some useful insight about the full Loop Quantum Gravity theory and provide an answer to some long-standing questions in early universe cosmology.
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1001.0162
Given integers a_0 \le a_1 \le ... \le a_{t+c-2} and b_1 \le ... \le b_t, we denote by W(b;a) \subset Hilb^p(\PP^{n}) the locus of good determinantal schemes X \subset \PP^{n} of codimension c defined by the maximal minors of a t x (t+c-1) homogeneous matrix with entries homogeneous polynomials of degree a_j-b_i. The goal of this short note is to extend and complete the results given by the authors in [10] and determine under weakened numerical assumptions the dimension of W(b;a), as well as whether the closure of W(b;a) is a generically smooth irreducible component of the Hilbert scheme Hilb^p(\PP^{n}).
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1001.0163
This work presents short-time Monte Carlo simulations for the two dimensional Majority-vote model starting from ordered and disordered states. It has been found that there are two pseudo-critical points, each one within the error-bar range of previous reported values performed using fourth order cumulant crossing method. The results show that the short-time dynamic for this model has a dependence on the initial conditions. Based on this dependence a method is proposed for the evaluation of the pseudo critical points and the extraction of the dynamical critical exponent $z$ and the static critical exponent $\beta/\nu$ for this model.
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1001.0164
We analyze the properties of the soliton solutions of a class of models describing one-dimensional BEC with spin F. We describe the minimal sets of scattering data which determine uniquely both the corresponding potential of the Lax operator and its scattering matrix. Next we give several reductions of these MNLS, derive their N-soliton solutions and analyze the soliton interactions. Finally we prove an important theorem proving that if the initial conditions satisfy the reduction then one gets a solution of the reduced MNLS.
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1001.0165
Progenitor scenarios for short gamma-ray bursts (short GRBs) include coalescenses of two neutron stars or a neutron star and black hole, which would necessarily be accompanied by the emission of strong gravitational waves. We present a search for these known gravitational-wave signatures in temporal and directional coincidence with 22 GRBs that had sufficient gravitational-wave data available in multiple instruments during LIGO's fifth science run, S5, and Virgo's first science run, VSR1. We find no statistically significant gravitational-wave candidates within a [-5, +1) s window around the trigger time of any GRB. Using the Wilcoxon-Mann-Whitney U test, we find no evidence for an excess of weak gravitational-wave signals in our sample of GRBs. We exclude neutron star-black hole progenitors to a median 90% CL exclusion distance of 6.7 Mpc.
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1001.0166
We consider a class of multicomponent nonlinear Schrodinger equations (MNLS) related to the symmetric BD.I-type symmetric spaces. As important particular case of these MNLS we obtain the Kulish-Sklyanin model. Some new reductions and their effects on the soliton solutions are obtained by proper modifying the Zakahrov-Shabat dressing method.
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1001.0167
A write-once memory (wom) is a storage medium formed by a number of ``write-once'' bit positions (wits), where each wit initially is in a `0' state and can be changed to a `1' state irreversibly. Examples of write-once memories include SLC flash memories and optical disks. This paper presents a low complexity coding scheme for rewriting such write-once memories, which is applicable to general problem configurations. The proposed scheme is called the \emph{position modulation code}, as it uses the positions of the zero symbols to encode some information. The proposed technique can achieve code rates higher than state-of-the-art practical solutions for some configurations. For instance, there is a position modulation code that can write 56 bits 10 times on 278 wits, achieving rate 2.01. In addition, the position modulation code is shown to achieve a rate at least half of the optimal rate.
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1001.0168
We analyze a class of multicomponent nonlinear Schrodinger equations (MNLS) related to the symmetric BD.I-type symmetric spaces and their reductions. We briefly outline the direct and the inverse scattering method for the relevant Lax operators and the soliton solutions. We use the Zakharov-Shabat dressing method to obtain the two-soliton solution and analyze the soliton interactions of the MNLS equations and some of their reductions.
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1001.0169
Jolissaint and Stalder introduced definitions of mixing and weak mixing for von Neumann subalgebras of finite von Neumann algebras. In this note, we study various algebraic and analytical properties of subalgebras with these mixing properties. We prove some basic results about mixing inclusions of von Neumann algebras and establish a connection between mixing properties and normalizers of von Neumann subalgebras. The special case of mixing subalgebras arising from inclusions of countable discrete groups finds applications to ergodic theory, in particular, a new generalization of a classical theorem of Halmos on the automorphisms of a compact abelian group. For a finite von Neumann algebra $M$ and von Neumann subalgebras $A$, $B$ of $M$, we introduce a notion of weak mixing of $B\subseteq M$ relative to $A$. We show that weak mixing of $B\subset M$ relative to $A$ is equivalent to the following property: if $x\in M$ and there exist a finite number of elements $x_1,...,x_n\in M$ such that $Ax\subset \sum_{i=1}^nx_iB$, then $x\in B$. We conclude the paper with an assortment of further examples of mixing subalgebras arising from the amalgamated free product and crossed product constructions.
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1001.0171
The structural and electronic properties of oxidized graphene are investigated on the basis of the genetic algorithm and density functional theory calculations. We find two new low energy semiconducting phases of the fully oxidized graphene (C1O). In one phase, there is parallel epoxy pair chains running along the zigzag direction. In contrast, the ground state phase with a slightly lower energy and a much larger band gap contains epoxy groups in three different ways: normal epoxy, unzipped epoxy, and epoxy pair. For partially oxidized graphene, a phase separation between bare graphene and fully oxidized graphene is predicted.
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1001.0172
A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally rigid framework has a positive semi-definite stress matrix of maximal rank. Connelly showed that the existence of such a positive semi-definite stress matrix is sufficient for universal rigidity, so this provides a characterization of universal rigidity for generic frameworks. We also extend our argument to give a new result on the genericity of strict complementarity in semidefinite programming.
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1001.0173
We present a multifrequency radio investigation of the Crab-like pulsar wind nebula (PWN) G54.1+0.3 using the Very Large Array. The high resolution of the observations reveals that G54.1+0.3 has a complex radio structure which includes filamentary and loop-like structures that are magnetized, a diffuse extent similar to the associated diffuse X-ray emission. But the radio and X-ray structures in the central region differ strikingly, indicating that they trace very different forms of particle injection from the pulsar and/or particle acceleration in the nebula. No spectral index gradient is detected in the radio emission across the PWN, whereas the X-ray emission softens outward in the nebula. The extensive radio polarization allows us to image in detail the intrinsic magnetic field, which is well-ordered and reveals that a number of loop-like filaments are strongly magnetized. In addition, we determine that there are both radial and toroidal components to the magnetic field structure of the pulsar wind nebula. Strong mid-IR emission detected in Spitzer Space Telescope data is closely correlated with the radio emission arising from the southern edge of G54.1+0.3. In particular, the distributions of radio and X-ray emission compared with the mid-IR emission suggest that the PWN may be interacting with this interstellar cloud. This may be the first PWN where we are directly detecting its interplay with an interstellar cloud that has survived the impact of the supernova explosion associated with the pulsar's progenitor.
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1001.0174
We study framed links in irreducible 3-manifolds that are $Z$-homology 3-spheres or atoroidal $Q$-homology 3-spheres. We calculate the dual of the Kauffman skein module over the ring of two variable power series with complex coefficients. For links in $S^3$ we give a new construction of the classical Kauffman polynomial.
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1001.0175
Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with multivariate Gaussian priors. Its key properties are: 1) it has simple, generic code applicable to many models, 2) it has no free parameters, 3) it works well for a variety of Gaussian process based models. These properties make our method ideal for use while model building, removing the need to spend time deriving and tuning updates for more complex algorithms.
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1001.0176
For a nilpotent Lie algebra $L$ of dimension $n$ and dim$(L^2)=m$, we find the upper bound dim$(M(L))\leq {1/2}(n+m-2)(n-m-1)+1$, where $M(L)$ denotes the Schur multiplier of $L$. In case $m=1$ the equality holds if and only if $L\cong H(1)\oplus A$, where $A$ is an abelian Lie algebra of dimension $n-3$ and H(1) is the Heisenberg algebra of dimension 3.
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1001.0177
Given a relatively minimal fibration $f: S \to \Bbb P^1$ on a rational surface $S$ with general fiber $C$ of genus $g$, we investigate under what conditions the inequality $6(g-1)\le K_f^2$ occurs, where $K_f$ is the canonical relative sheaf of $f$. We give sufficient conditions for having such inequality, depending on the genus and gonality of $C$ and the number of certain exceptional curves on $S$. We illustrate how these results can be used for constructing fibrations with the desired property. For fibrations of genus $11\le g\le 49$ we prove the inequality: $$ 6(g-1) +4 -4\sqrt g \le K_f^2.$$
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1001.0178
We prove the existence of a family of initial data for Einstein equations which represent small deformations of the extreme Kerr black hole initial data. The data in this family have the same asymptotic geometry as extreme Kerr. In particular, the deformations preserve the angular momentum and the area of the cylindrical end.
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1001.0179
We prove that an arbitrary Poisson structure omega^{ij}(u) and an arbitrary closed 3-form T_{ijk}(u) generate the local Poisson structure A^{ij}(u,u_x) = M^i_s(u,u_x)omega^{sj}(u), where M^i_s(u,u_x)(delta^s_j + omega^{sp}(u)T_{pjk}(u)u^k_x) = delta^i_j, on the corresponding loop space. We obtain also a special graded epsilon-deformation of an arbitrary Poisson structure omega^{ij}(u) by means of an arbitrary closed 3-form T_{ijk}(u).
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1001.0181
According to the widely accepted statistical interpretation of black hole entropy the mean separation between energy levels of black hole should be exponentially small. But this sharply disagrees with the value obtained from the quantization of black hole area. It is shown that the new statistical interpretation of black hole entropy proposed in my paper arXiv:0911.5635 gives the correct value.
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1001.0182
The first principles density functional theory (DFT) is applied to study effects of molecular adsorption on optical losses of silver (111) surface. The ground states of the systems including water, methanol, and ethanol molecules adsorbed on Ag (111) surface were obtained by the total energy minimization method within the local density approximation (LDA). Optical functions were calculated within the Random Phase Approximation (RPA) approach. Contribution of the surface states to optical losses was studied by calculations of the dielectric function of bare Ag (111) surface. Substantial modifications of the real and imaginary parts of the dielectric functions spectra in the near infrared and visible spectral regions, caused by surface states and molecular adsorption, were obtained. The results are discussed in comparison with available experimental data.
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1001.0183
The description of Fermi acceleration developing in the phase-randomized simplified Fermi-Ulam model (SFUM) can be achieved in terms of a random walk taking place in momentum space. Within this framework the evolution of the probability density function of particle velocities is determined by the Fokker-Planck equation (FPE). However, the standard treatment in the literature leads to a result, which even though is in agreement with the numerical results, it is inconsistent with the transport coefficients used for the construction of the FPE. In this work we present a consistent scheme for the description of Fermi acceleration, resolving this contradiction.
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1001.0184
In this paper we explore loops of non-autonomous Hamiltonian diffeomorphisms with degenerate fixed maxima. We show that such loops can not have totally degenerate fixed global maxima. This has applications for the Hofer geometry of the group of Hamiltonians for certain symplectic 4 manifolds and also gives criteria for certain 4 manifolds to be uniruled.
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1001.0185
Physicists gathered in august at Dresden for a conference about "Quantum Criticality and Novel Phases". As one part of the meeting, nine panelists hosted an open and free-wheeling discussion on the topic of the meeting. This article outlines the discussions that took place during at this panel-meeting on the afternoon of August 3rd, 2009.
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1001.0186
Toeplitz's Square Peg Problem asks whether every continuous simple closed curve in the plane contains the four vertices of a square. It has been proved for various classes of sufficiently smooth curves, some of which are dense, none of which are open. In this paper we prove it for several open classes of curves, one of which is also dense. This can be interpreted in saying that the Square Peg Problem is solved for generic curves. The latter class contains all previously known classes for which the Square Peg Problem has been proved in the affirmative. [footnote] We also prove results about rectangles inscribed in immersed curves. Finally, we show that the problem of finding a regular octahedron on metric 2-spheres has a "topological counter-example", that is, a certain test map with boundary condition exists.
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1001.0187
A hybrid model of the Deutsch-Jozsa algorithm is presented, inspired by the proposals of hybrid computation by S. Lloyd and P. van Loock et. al. The model is based on two observations made about both the discrete and continuous algorithms already available. First, the Fourier transform is a single-step operation in a continuous-variable (CV) setting. Additionally, any implementation of the oracle is nontrivial in both schemes. The steps of the computation are very similar to those in the CV algorithm, with the main difference being the way in which the qunats, or quantum units of analogic information, and the qubits interact in the oracle. Using both discrete and continuous states of light, linear devices, and photo-detection, an optical implementation of the oracle is proposed. For simplicity, infinitely squeezed states are used in the continuous register, whereas the optical qubit is encoded in the dual-rail logic of the KLM protocol. The initial assumption of ideal states as qunats will be dropped to study the effects of finite squeezing in the quality of the computation.
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1001.0188
In this article we study post-model selection estimators that apply ordinary least squares (OLS) to the model selected by first-step penalized estimators, typically Lasso. It is well known that Lasso can estimate the nonparametric regression function at nearly the oracle rate, and is thus hard to improve upon. We show that the OLS post-Lasso estimator performs at least as well as Lasso in terms of the rate of convergence, and has the advantage of a smaller bias. Remarkably, this performance occurs even if the Lasso-based model selection "fails" in the sense of missing some components of the "true" regression model. By the "true" model, we mean the best s-dimensional approximation to the nonparametric regression function chosen by the oracle. Furthermore, OLS post-Lasso estimator can perform strictly better than Lasso, in the sense of a strictly faster rate of convergence, if the Lasso-based model selection correctly includes all components of the "true" model as a subset and also achieves sufficient sparsity. In the extreme case, when Lasso perfectly selects the "true" model, the OLS post-Lasso estimator becomes the oracle estimator. An important ingredient in our analysis is a new sparsity bound on the dimension of the model selected by Lasso, which guarantees that this dimension is at most of the same order as the dimension of the "true" model. Our rate results are nonasymptotic and hold in both parametric and nonparametric models. Moreover, our analysis is not limited to the Lasso estimator acting as a selector in the first step, but also applies to any other estimator, for example, various forms of thresholded Lasso, with good rates and good sparsity properties. Our analysis covers both traditional thresholding and a new practical, data-driven thresholding scheme that induces additional sparsity subject to maintaining a certain goodness of fit. The latter scheme has theoretical guarantees similar to those of Lasso or OLS post-Lasso, but it dominates those procedures as well as traditional thresholding in a wide variety of experiments.
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1001.0189
Torsional oscillator experiments show evidence of mass decoupling in solid 4He. This decoupling is amplitude dependent, suggesting a critical velocity for supersolidity. We observe similar behavior in the elastic shear modulus. By measuring the shear modulus over a wide frequency range, we can distinguish between an amplitude dependence which depends on velocity and one which depends on some other parameter like displacement. In contrast to the torsional oscillator behavior, the modulus depends on the magnitude of stress, not velocity. We interpret our results in terms of the motion of dislocations which are weakly pinned by 3He impurities but which break away when large stresses are applied.
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1001.0191
For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple restricted Lie algebras of types W(m;1) and S(m;1) (m>=2), in terms of numerical and group-theoretical invariants. Our main tool is automorphism group schemes, which we determine for the simple restricted Lie algebras of types S(m;1) and H(m;1). The ground field is assumed to be algebraically closed of characteristic p>3.
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1001.0192
Time-resolved low resolution Hubble Space Telescope ultraviolet spectra together with ground-based optical photometry and spectra are used to constrain the temperatures and pulsation properties of six cataclysmic variables containing pulsating white dwarfs. Combining our temperature determinations for the five pulsating white dwarfs that are several years past outburst with past results on six other systems shows that the instability strip for accreting pulsating white dwarfs ranges from 10,500-15,000K, a wider range than evident for ZZ Ceti pulsators. Analysis of the UV/optical pulsation properties reveals some puzzling aspects. While half the systems show high pulsation amplitudes in the UV compared to their optical counterparts, others show UV/optical amplitude ratios that are less than one or no pulsations at either wavelength region.
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1001.0193
A triple of positive integers (d,h,m) is admissible if for any m given masses in R^d there exist h hyperplanes that cut each of these masses into 2^h equal pieces. We present an elementary reduction which combined with results by Ramos (1996) yields all the admissible triples that were known up to now (with one exception) as well as new ones.
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1001.0194
We formulate and prove (in {\sf ZFC}) a strong coloring theorem which holds at successors of singular cardinals, and use it to answer several questions concerning Shelah's principle $Pr_1(\mu^+,\mu^+,\mu^+,\cf(\mu))$ for singular $\mu$.
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1001.0195
In this paper, we study refinements of some inequalities related to Young inequality for scalar and for operator. As our main results, we show refined Young inequalities for two positive operators. This results refine the ordering relations among the arithmetic mean, the geometric mean and the harmonic mean. Finally, we give supplements for refined Young inequalities for two positive real numbers. And then we also give operator inequalities based on the supplemental inequalities.
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1001.0196
We describe our work in implementing a wide-area distributed file system for the NSF TeraGrid. The system, called XUFS, allows private distributed name spaces to be created for transparent access to personal files across over 9000 computer nodes. XUFS builds on many principles from prior distributed file systems research, but extends key design goals to support the workflow of computational science researchers. Specifically, XUFS supports file access from the desktop to the wide-area network seamlessly, survives transient disconnected operations robustly, and demonstrates comparable or better throughput than some current high performance file systems on the wide-area network.
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1001.0197
SOFIA is an airborne, gyroscopically stabilized 2.5m infrared telescope, mounted to a spherical bearing. Unlike its predecessors, SOFIA will work in absolute coordinates, despite its continually changing position and attitude. In order to manage this, SOFIA must relate equatorial and telescope coordinates using a combination of avionics data and star identification, manage field rotation and track sky images. We describe the algorithms and systems required to acquire and maintain the equatorial reference frame, relate it to tracking imagers and the science instrument, set up the oscillating secondary mirror, and aggregate pointings into relocatable nods and dithers.
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1001.0198
There are several fundamental differences between four-dimensional and higher-dimensional gravitational waves, namely in the so called braneworld set-up. One of them is their asymptotic behavior within the Cauchy problem. This study is connected with the so called Hadamard problem, which aims at the question of Huygens principle validity. We investigate the effect of braneworld scenarios on the character of propagation of gravitational waves on FRW background.
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1001.0199
SOFIA is a 2.5 meter airborne infrared telescope, mounted in a Boeing 747SP aircraft. Due to the large size of the telescope, only a few degrees of azimuth are available at the telescope bearing. This means the heading of the aircraft is fundamentally associated with the telescope's observation targets, and the ground track necessary to enable a given mission is highly complex and dependent on the coordinates, duration, and order of observations to be performed. We have designed and implemented a Flight Management Infrastructure (FMI) product in order to plan and execute such missions in the presence of a large number of external constraints (e.g. restricted airspace, international boundaries, elevation limits of the telescope, aircraft performance, winds at altitude, and ambient temperatures). We present an overview of the FMI, including the process, constraints and basic algorithms used to plan and execute SOFIA missions.
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1001.0201
We motivate and then prove a generalized pythagorean theorem for parallelepipeds in Euclidean space.
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1001.0202
We discuss contact invariant structures on the space of solutions of a third-order ordinary differential equation. Associated to any third-order differential equation modulo contact transformations, Chern introduced a degenerate conformal Lorentzian metric on the space of 2-jets of functions of one variable. When the Wuenschmann invariant vanishes, the degenerate metric descends to a proper conformal Lorentzian metric on the space of solutions. In the general case, when the Wuenschmann invariant is not zero, we define the notion of a causal geometry, and show that the space of solutions supports one. The Wuenschmann invariant is then related to the projective curvature of the indicatrix curve cut out by the causal geometry in the projective tangent space. When the Wuenschmann vanishes, the causal structure is then precisely the sheaf of null geodesics of the Chern conformal structure. We then introduce a Lagrangian and associated Hamiltonian from which the degenerate conformal Lorentzian metric are constructed. Finally, necessary and sufficient conditions are given for a rank three degenerate conformal Lorentzian metric in four dimensions to correspond to a third-order differential equation.
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1001.0203
Suppose $X$ is a right process which is associated with a non-symmetric Dirichlet form $(\mathcal{E},D(\mathcal{E}))$ on $L^{2}(E;m)$. For $u\in D(\mathcal{E})$, we have Fukushima's decomposition: $\tilde{u}(X_{t})-\tilde{u}(X_{0})=M^{u}_{t}+N^{u}_{t}$. In this paper, we investigate the strong continuity of the generalized Feynman-Kac semigroup defined by $P^{u}_{t}f(x)=E_{x}[e^{N^{u}_{t}}f(X_{t})]$. Let $Q^{u}(f,g)=\mathcal{E}(f,g)+\mathcal{E}(u,fg)$ for $f,g\in D(\mathcal{E})_{b}$. Denote by $J_1$ the dissymmetric part of the jumping measure $J$ of $(\mathcal{E},D(\mathcal{E}))$. Under the assumption that $J_1$ is finite, we show that $(Q^{u},D(\mathcal{E})_{b})$ is lower semi-bounded if and only if there exists a constant $\alpha_0\ge 0$ such that $\|P^{u}_{t}\|_2\leq e^{\alpha_0 t}$ for every $t>0$. If one of these conditions holds, then $(P^{u}_{t})_{t\geq0}$ is strongly continuous on $L^{2}(E;m)$. If $X$ is equipped with a differential structure, then this result also holds without assuming that $J_1$ is finite.
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1001.0204
We established a sample of millimeter-wave and gamma-ray bright active galactic nuclei matching the WMAP catalog with the EGRET catalog, highest energy photons and the Fermi bright source list. We have monitored over 80 of these objects in the near infrared, obtaining over 2000 JHKs data points directly comparable with Fermi data. We present examples of correlated near infrared and gamma-ray activity of known blazars and recently identified sources.
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1001.0205
In order to investigate the metallic state in high-mobility Si-MOS structures, we have further developed and precised the dipole trap model which was originally proposed by B.L. Altshuler and D.L. Maslov [Phys. Rev. Lett.\ 82, 145 (1999)]. Our additional numerical treatment enables us to drop several approximations and to introduce a limited spatial depth of the trap states inside the oxide as well as to include a distribution of trap energies. It turns out that a pronounced metallic state can be caused by such trap states at appropriate energies whose behavior is in good agreement with experimental observations.
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1001.0206
We formulate and investigate a general stochastic control problem under a progressive enlargement of filtration. The global information is enlarged from a reference filtration and the knowledge of multiple random times together with associated marks when they occur. By working under a density hypothesis on the conditional joint distribution of the random times and marks, we prove a decomposition of the original stochastic control problem under the global filtration into classical stochastic control problems under the reference filtration, which are determined in a finite backward induction. Our method revisits and extends in particular stochastic control of diffusion processes with finite number of jumps. This study is motivated by optimization problems arising in default risk management, and we provide applications of our decomposition result for the indifference pricing of defaultable claims, and the optimal investment under bilateral counterparty risk. The solutions are expressed in terms of BSDEs involving only Brownian filtration, and remarkably without jump terms coming from the default times and marks in the global filtration.
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1001.0207
We consider a generalization of the Frobenius Problem where the object of interest is the greatest integer which has exactly $j$ representations by a collection of positive relatively prime integers. We prove an analogue of a theorem of Brauer and Shockley and show how it can be used for computation.
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1001.0208
We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is capable of simulating a very wide class of tile systems, including itself. Specifically, we give a tile set that simulates the assembly of any tile assembly system in a class of systems that we call \emph{locally consistent}: each tile binds with exactly the strength needed to stay attached, and that there are no glue mismatches between tiles in any produced assembly. Our construction is reminiscent of the studies of \emph{intrinsic universality} of cellular automata by Ollinger and others, in the sense that our simulation of a tile system $T$ by a tile system $U$ represents each tile in an assembly produced by $T$ by a $c \times c$ block of tiles in $U$, where $c$ is a constant depending on $T$ but not on the size of the assembly $T$ produces (which may in fact be infinite). Also, our construction improves on earlier simulations of tile assembly systems by other tile assembly systems (in particular, those of Soloveichik and Winfree, and of Demaine et al.) in that we simulate the actual process of self-assembly, not just the end result, as in Soloveichik and Winfree's construction, and we do not discriminate against infinite structures. Both previous results simulate only temperature 1 systems, whereas our construction simulates tile assembly systems operating at temperature 2.
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1001.0209
We derive a uniform exponential decay of the total energy for the nonlinear Klein-Gordon equation with a damping around spatial infinity in the whole space or in the exterior of a star shaped obstacle.
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1001.0211
A purely state-dependent cost function can be modified by introducing a control-dependent term rewarding submaximal control utilization. A moderation incentive is identically zero on the boundary of the admissible control region and non-negative on the interior; it is bounded above by the infimum of the state-dependent cost function, so that the instantaneous total cost is always non-negative. The conservation law determined by the Maximum Principle, in combination with the condition that the moderation incentive equal zero on the boundary of the admissible control region, plays a crucial role in the analysis; in some situations, the initial and final values of the auxiliary variable are uniquely determined by the condition that the conserved quantity equal zero along a solution of the arbitrary duration synthesis problem. Use of an alternate system of evolution equations, parametrized by the auxiliary variable, for one-degree of freedom controlled acceleration systems, can significantly simplify numerical searches for solutions of the arbitrary duration synthesis problem. A one-parameter family of 'elliptical' moderation incentives is introduced; the behavior of the well-known quadratic control cost and its incentive analog is compared to that of the elliptical incentives in two simple controlled acceleration examples. The elliptical incentives yield smooth solutions with controls remaining in the interior of the admissible region, while the quadratic incentive allows piecewise smooth solutions with controls moving on and off the boundary of the admissible region; in these examples, the arbitrary duration synthesis problem for the traditional quadratic control cost has no solution; the total cost is a monotonically decreasing function of the duration.
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1001.0212
We describe the quasi-isometric classification of fundamental groups of irreducible non-geometric 3-manifolds which do not have "too many" arithmetic hyperbolic geometric components, thus completing the quasi-isometric classification of 3--manifold groups in all but a few exceptional cases.
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1001.0213
For testing gravity and detecting gravitational waves in space, deep-space laser ranging using drag-free spacecraft is a common method. Deep space provides a large arena and a long integration time. Laser technology provides measurement sensitivity, while drag-free technology ensures that gravitational phenomenon to be measured with least spurious noises. In this talk, we give an overview of motivations and methods of various space missions/proposals testing relativistic gravity and detecting gravitational waves, and refer to various references.
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1001.0214
We have discussed the Tsallis entropy in finite $N$-unit nonextensive systems, by using the multivariate $q$-Gaussian probability distribution functions (PDFs) derived by the maximum entropy methods with the normal average and the $q$-average ($q$: the entropic index). The Tsallis entropy obtained by the $q$-average has an exponential $N$ dependence: $S_q^{(N)}/N \simeq \:e^{(1-q)N \:S_1^{(1)}} $ for large $N$ ($\gg \frac{1}{(1-q)} >0$). In contrast, the Tsallis entropy obtained by the normal average is given by $S_q^{(N)}/N \simeq [1/(q-1)N]$ for large $N$ ($\gg \frac{1}{(q-1)} > 0)$. $N$ dependences of the Tsallis entropy obtained by the $q$- and normal averages are generally quite different, although the both results are in fairly good agreement for $\vert q-1 \vert \ll 1.0$. The validity of the factorization approximation to PDFs which has been commonly adopted in the literature, has been examined. We have calculated correlations defined by $C_m= \langle (\delta x_i \:\delta x_j)^m \rangle -\langle (\delta x_i)^m \rangle\: \langle (\delta x_j)^m \rangle$ for $i \neq j$ where $\delta x_i=x_i -\langle x_i \rangle$, and the bracket $\langle \cdot \rangle$ stands for the normal and $q$-averages. The first-order correlation ($m=1$) expresses the intrinsic correlation and higher-order correlations with $m \geq 2$ include nonextensivity-induced correlation, whose physical origin is elucidated in the superstatistics.
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1001.0215
The standard model of particle physics assumes that neutrinos are massless, although adding non-zeros is required by the experimentally established phenomenon of neutrino oscillations requires neutrinos to have non-zero mass. Sterile neutrinos (or right-handed neutrinos) are a good warm dark matter candidate. We find that the excess of the intensity in the 8.7 keV line (at the energy of the FeXXVI Ly$\gamma$ line) in the spectrum of the Galactic center observed by the Suzaku X-ray mission cannot be explained by standard ionization and recombination processes. We suggest that the origin of this excess is via decays of sterile neutrinos with a mass of 17.4 keV and estimate the value of the mixing angle. The estimated value of the mixing angle $\sin^2(2\theta)=(4.1 \pm 2.2)\times10^{-12}$ lies in the allowed region of the mixing angle of dark matter sterile neutrino with a mass of 17-18 keV.
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1001.0216
The Kepler Mission relies on precise differential photometry to detect the 80 parts per million (ppm) signal from an Earth-Sun equivalent transit. Such precision requires superb instrument stability on time scales up to ~2 days and systematic error removal to better than 20 ppm. To this end, the spacecraft and photometer underwent 67 days of commissioning, which included several data sets taken to characterize the photometer performance. Because Kepler has no shutter, we took a series of dark images prior to the dust cover ejection, from which we measured the bias levels, dark current, and read noise. These basic detector properties are essentially unchanged from ground-based tests, indicating that the photometer is working as expected. Several image artifacts have proven more complex than when observed during ground testing, as a result of their interactions with starlight and the greater thermal stability in flight, which causes the temperature-dependent artifact variations to be on the timescales of transits. Because of Kepler's unprecedented sensitivity and stability, we have also seen several unexpected systematics that affect photometric precision. We are using the first 43 days of science data to characterize these effects and to develop detection and mitigation methods that will be implemented in the calibration pipeline. Based on early testing, we expect to attain Kepler's planned photometric precision over 80%-90% of the field of view.
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1001.0217
It is proved that the simplex is a strict local minimum for the volume product, P(K)=min(vol(K) vol(K^z)), K^z is the polar body of K with respect to z, the minimum is taken over z in the interior of K, in the Banach-Mazur space of n-dimensional (classes of ) convex bodies. Linear local stability in the neighborhood of the simplex is proved as well. The proof consists of an extension to the non-symmetric setting of methods that were recently introduced by Nazarov, Petrov, Ryabogin and Zvavitch, as well as proving results of independent interest, concerning stability of square order of volumes of polars of non-symmetric convex bodies.
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1001.0218
To stress the effect of the pairing position deviating from the Fermi level, we must investigate the pairs in the wave vector space, and then we use the dynamic equation to study some correlation functions. This article shows that the Fermi pocket is related to the effect of free electron states on the ARPES experiment. This also leads us to understand why the Fermi arc appears in Bi2212 while the Fermi pocket appears in Bi2201 with the valence bandwidth and the work function known for them.
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1001.0219
A BV algebra is a formal framework within which the BV quantization algorithm is implemented. In addition to the gauge symmetry, encoded in the BV master equation, the master action often exhibits further global symmetries, which may be in turn gauged. We show how to carry this out in a BV algebraic set up. Depending on the nature of the global symmetry, the gauging involves coupling to a pure ghost system with a varying amount of ghostly supersymmetry. Coupling to an N=0 ghost system yields an ordinary gauge theory whose observables are appropriately classified by the invariant BV cohomology. Coupling to an N=1 ghost system leads to a topological gauge field theory whose observables are classified by the equivariant BV cohomology. Coupling to higher $N$ ghost systems yields topological gauge field theories with higher topological symmetry. In the latter case, however, problems of a completely new kind emerge, which call for a revision of the standard BV algebraic framework.
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1001.0221
We present leading-order (LO) cross sections for the production of three top quarks ($tt\tb$,$t\tb\tb$) at the Large Hadron Collider (LHC). We find a total LO cross section for triple-top production in the Standard Model of $\sigma \approx 2 $ fb at $\sqrt{s}=14$ TeV and we give examples of two new physics models which have a significant enhancement to this channel. In the Minimal Supersymmetric Standard Model (MSSM), there are regions of parameter space where the decays of gluino pairs into final states including three tops has a cross section $\sigma \approx 41$ fb. In a leptophobic $Z'$ model featuring right-handed couplings of the $u$-quark to the top, we find $\sigma \approx 28$ fb. With efficient identification and reconstruction of the top quarks, the triple-top signal could potentially provide evidence for new physics at the LHC.
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1001.0222
Casimir energy is calculated for the 5D electromagnetism and 5D scalar theory in the {\it warped} geometry. It is compared with the flat case. A new regularization, called {\it sphere lattice regularization}, is taken. In the integration over the 5D space, we introduce two boundary curves (IR-surface and UV-surface) based on the {\it minimal area principle}. It is a {\it direct} realization of the geometrical approach to the {\it renormalization group}. The regularized configuration is {\it closed-string like}. We do {\it not} take the KK-expansion approach. Instead, the position/momentum propagator is exploited, combined with the {\it heat-kernel method}. All expressions are closed-form (not KK-expanded form). The {\it generalized} P/M propagators are introduced. We numerically evaluate $\La$(4D UV-cutoff), $\om$(5D bulk curvature, warp parameter) and $T$(extra space IR parameter) dependence of the Casimir energy. We present two {\it new ideas} in order to define the 5D QFT: 1) the summation (integral) region over the 5D space is {\it restricted} by two minimal surfaces (IR-surface, UV-surface) ; or 2) we introduce a {\it weight function} and require the dominant contribution, in the summation, is given by the {\it minimal surface}. Based on these, 5D Casimir energy is {\it finitely} obtained after the {\it proper renormalization procedure.} The {\it warp parameter} $\om$ suffers from the {\it renormalization effect}. The IR parameter $T$ does not. We examine the meaning of the weight function and finally reach a {\it new definition} of the Casimir energy where {\it the 4D momenta(or coordinates) are quantized} with the extra coordinate as the Euclidean time (inverse temperature). We examine the cosmological constant problem and present an answer at the end. Dirac's large number naturally appears.
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