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61

Jun 30, 2018
06/18

by
A. O. Smirnov; E. G. Semenova; V. Zinger; N. Zinger

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A periodic two-phase algebro-geometric solution of the focusing nonlinear Schr\"odinger equation is constructed in terms of elliptic Jacobi theta-functions. A dependence of this solution on the parameters of a spectral curve is investigated. An existence of a real smooth finite-gap solution of NLS equation with complex initial phase is proven. Degenerations of the constructed solution to one-phase traveling wave solution and solutions in the form of the plane waves are carried.

Topics: Mathematics, Nonlinear Sciences, Exactly Solvable and Integrable Systems, Mathematical Physics,...

Source: http://arxiv.org/abs/1407.7974

7
7.0

Jun 30, 2018
06/18

by
Adriana Gonzalez; Laurent Jacques

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The 2-D phase unwrapping problem aims at retrieving a "phase" image from its modulo $2\pi$ observations. Many applications, such as interferometry or synthetic aperture radar imaging, are concerned by this problem since they proceed by recording complex or modulated data from which a "wrapped" phase is extracted. Although 1-D phase unwrapping is trivial, a challenge remains in higher dimensions to overcome two common problems: noise and discontinuities in the true phase...

Topics: Mathematics, Optimization and Control

Source: http://arxiv.org/abs/1407.8040

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7.0

Jun 30, 2018
06/18

by
Alexandru Dimca; Stefan Papadima; Alexandru Suciu

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We relate the geometry of the resonance varieties associated to a commutative differential graded algebra model of a space to the finiteness properties of the completions of its Alexander-type invariants. We also describe in simple algebraic terms the non-translated components of the degree-one characteristic varieties for a class of non-proper complex manifolds.

Topics: Mathematics, Algebraic Topology, Algebraic Geometry

Source: http://arxiv.org/abs/1407.8027

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4.0

Jun 30, 2018
06/18

by
Andreas Buhr; Christian Engwer; Mario Ohlberger; Stephan Rave

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The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement for the application of RB schemes is the availability of an a posteriori error estimator to reliably estimate the error introduced by the reduction process. However, straightforward implementations of standard residual based estimators show poor numerical stability, rendering them unusable if high accuracy is...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1407.8005

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4.0

Jun 30, 2018
06/18

by
Anna M. Barry; F. Hajir; P. G. Kevrekidis

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In this work, we construct suitable generating functions for vortices of alternating signs in the realm of Bose-Einstein condensates. In addition to the vortex-vortex interaction included in earlier fluid dynamics constructions of such functions, the vortices here precess around the center of the trap. This results in the generating functions of the vortices of positive charge and of negative charge satisfying a modified, so-called, Tkachenko differential equation. From that equation, we...

Topics: Nonlinear Sciences, Quantum Gases, Mathematics, Pattern Formation and Solitons, Mathematical...

Source: http://arxiv.org/abs/1407.7965

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5.0

Jun 30, 2018
06/18

by
Assaf Ben-Yishai; Ofer Shayevitz

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Consider a pair of terminals connected by two independent additive white Gaussian noise channels, and limited by individual power constraints. The first terminal would like to reliably send information to the second terminal, within a given error probability. We construct an explicit interactive scheme consisting of only (non-linear) scalar operations, by endowing the Schalkwijk-Kailath noiseless feedback scheme with modulo arithmetic. Our scheme achieves a communication rate close to the...

Topics: Mathematics, Computing Research Repository, Information Theory

Source: http://arxiv.org/abs/1407.8022

6
6.0

Jun 30, 2018
06/18

by
Awais Khawar; Ahmed Abdelhadi; T. Charles Clancy

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Multiple-input multiple-output (MIMO) radar is a relatively new concept in the field of radar signal processing. Many novel MIMO radar waveforms have been developed by considering various performance metrics and constraints. In this paper, we show that finite alphabet constant-envelope (FACE) quadrature-pulse shift keying (QPSK) waveforms can be designed to realize a given covariance matrix by transforming a constrained nonlinear optimization problem into an unconstrained nonlinear optimization...

Topics: Networking and Internet Architecture, Mathematics, Computing Research Repository, Information Theory

Source: http://arxiv.org/abs/1407.8510

6
6.0

Jun 30, 2018
06/18

by
Benjamin Dodson; Andrew Lawrie

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In this paper we study the focusing cubic wave equation in 1+5 dimensions with radial initial data as well as the one-equivariant wave maps equation in 1+3 dimensions with the model target manifolds $\mathbb{S}^3$ and $\mathbb{H}^3$. In both cases the scaling for the equation leaves the $\dot{H}^{\frac{3}{2}} \times \dot{H}^{\frac{1}{2}}$-norm of the solution invariant, which means that the equation is super-critical with respect to the conserved energy. Here we prove a conditional scattering...

Topics: Mathematics, Analysis of PDEs, Mathematical Physics

Source: http://arxiv.org/abs/1407.8199

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3.0

Jun 30, 2018
06/18

by
Boris A. Malomed; Dmitry E. Pelinovsky

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We justify the Thomas--Fermi approximation for the elliptic problem with the repulsive nonlinear confinement used in the recent physical literature. The method is based on the resolvent estimates and the fixed-point iterations.

Topics: Nonlinear Sciences, Mathematics, Analysis of PDEs, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1407.8043

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4.0

Jun 30, 2018
06/18

by
Caihua Chen; Shiqian Ma; Junfeng Yang

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In this paper, we first propose a general inertial proximal point method for the mixed variational inequality (VI) problem. Based on our knowledge, without stronger assumptions, convergence rate result is not known in the literature for inertial type proximal point methods. Under certain conditions, we are able to establish the global convergence and a $o(1/k)$ convergence rate result (under certain measure) of the proposed general inertial proximal point method. We then show that the...

Topics: Mathematics, Optimization and Control

Source: http://arxiv.org/abs/1407.8238

4
4.0

Jun 30, 2018
06/18

by
Chia-Yu Hsieh; YunKyong Hyon; Hijin Lee; Tai-Chia Lin; Chun Liu

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In order to describe the dynamics of crowded ions (charged particles), we use an energetic variation approach to derive a modified Poisson-Nernst-Planck (PNP) system which includes an extra dissipation due to the effective velocity differences between ion species. Such a system is more complicated than the original PNP system but with the same equilibrium states. Using Schauder's fixed-point theorem, we develop a local existence theorem of classical solutions for the modified PNP system....

Topics: Mathematics, Analysis of PDEs, Mathematical Physics

Source: http://arxiv.org/abs/1407.8245

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6.0

Jun 30, 2018
06/18

by
Chuanhai Liu; Ryan Martin

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The development of statistical methods for valid and efficient probabilistic inference without prior distributions has a long history. Fisher's fiducial inference is perhaps the most famous of these attempts. We argue that, despite its seemingly prior-free formulation, fiducial and its various extensions are not prior-free and, therefore, do not meet the requirements for prior-free probabilistic inference. In contrast, the inferential model (IM) framework is genuinely prior-free and is shown to...

Topics: Mathematics, Statistics Theory, Statistics, Methodology

Source: http://arxiv.org/abs/1407.8225

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4.0

Jun 30, 2018
06/18

by
Chunhua Wang; Changlin Xiang

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Let $1 p^{2}+p,a(0)>0$ and $\Omega$ satisfies some geometry conditions if $0\in\partial\Omega$, say, all the principle curvatures of $\partial\Omega$ at $0$ are negative, then the above problem has infinitely many solutions.

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1407.7982

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9.0

Jun 30, 2018
06/18

by
Cédric M. Campos; J. M. Sanz-Serna

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We study a method, Extra Chance Generalized Hybrid Monte Carlo, to avoid rejections in the Hybrid Monte Carlo method and related algorithms. In the spirit of delayed rejection, whenever a rejection would occur, extra work is done to find a fresh proposal that, hopefully, may be accepted. We present experiments that clearly indicate that the additional work per sample carried out in the extra chance approach clearly pays in terms of the quality of the samples generated.

Topics: Probability, Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1407.8107

4
4.0

Jun 30, 2018
06/18

by
David Dumas; Michael Wolf

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We construct and study a natural homeomorphism between the moduli space of polynomial cubic differentials of degree d on the complex plane and the space of projective equivalence classes of oriented convex polygons with d+3 vertices. This map arises from the construction of a complete hyperbolic affine sphere with prescribed Pick differential, and can be seen as an analogue of the Labourie-Loftin parameterization of convex RP^2 structures on a compact surface by the bundle of holomorphic cubic...

Topics: Mathematics, Differential Geometry

Source: http://arxiv.org/abs/1407.8149

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3.0

Jun 30, 2018
06/18

by
David Sutter; Tobias Sutter; Peyman Mohajerin Esfahani; Renato Renner

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We propose an iterative method for approximating the capacity of classical-quantum channels with a discrete input alphabet and a finite dimensional output, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. To provide an $\varepsilon$-close estimate to the capacity, the presented algorithm requires $O(\tfrac{(N \vee M) M^3 \log(N)^{1/2}}{\varepsilon})$, where $N$ denotes the input...

Topics: Quantum Physics, Mathematics, Computing Research Repository, Information Theory

Source: http://arxiv.org/abs/1407.8202

4
4.0

Jun 30, 2018
06/18

by
Diogo A. Gomes; Hiroyoshi Mitake

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In this paper, we investigate the existence and uniqueness of solutions to a stationary mean field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian with possibly singular congestion effects. Thanks to a new class of a-priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions.

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1407.8267

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65

Jun 30, 2018
06/18

by
E. Costa; R. Diógenes; E. Ribeiro

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In a remarkable article published in 1982, M. Gromov introduced the concept of minimal volume, namely, the minimal volume of a manifold $M^n$ is defined to be the greatest lower bound of the total volumes of $M^n$ with respect to complete Riemannian metrics whose sectional curvature is bounded above in absolute value by 1. While the minimal curvature, introduced by G. Yun in 1996, is the smallest pinching of the sectional curvature among metrics of volume 1. The goal of this article is to...

Topics: Mathematics, Differential Geometry, Geometric Topology

Source: http://arxiv.org/abs/1407.8137

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69

Jun 30, 2018
06/18

by
Emma Carberry; Martin Ulrich Schmidt

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Constant mean curvature (CMC) tori in Euclidean 3-space are described by an algebraic curve, called the spectral curve, together with a line bundle on this curve and a point on $ S ^ 1 $, called the Sym point. For a given spectral curve the possible choices of line bundle and Sym point are easily described. The space of spectral curves of tori is totally disconnected. Hence to characterise the "moduli space" of CMC tori one should, for each genus $g$, determine the closure...

Topics: Mathematics, Differential Geometry

Source: http://arxiv.org/abs/1407.7986

3
3.0

Jun 30, 2018
06/18

by
Farhad A. Goodarzi; Daewon Lee; Taeyoung Lee

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We derived a coordinate-free form of equations of motion for a complete model of a quadrotor UAV with a payload which is connected via a flexible cable according to Lagrangian mechanics on a manifold. The flexible cable is modeled as a system of serially-connected links and has been considered in the full dynamic model. A geometric nonlinear control system is presented to exponentially stabilize the position of the quadrotor while aligning the links to the vertical direction below the...

Topics: Mathematics, Optimization and Control

Source: http://arxiv.org/abs/1407.8164

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5.0

Jun 30, 2018
06/18

by
Fernando Cordero; Lavinia Perez-Ostafe

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We study the arbitrage opportunities in the presence of transaction costs in a sequence of binary markets approximating the fractional Black-Scholes model. This approximating sequence was constructed by Sottinen and named fractional binary markets. Since, in the frictionless case, these markets admit arbitrage, we aim to determine the size of the transaction costs needed to eliminate the arbitrage from these models. To gain more insight, we first consider only 1-step trading strategies and we...

Topics: Probability, Mathematics, Quantitative Finance, Pricing of Securities

Source: http://arxiv.org/abs/1407.8068

5
5.0

Jun 30, 2018
06/18

by
Franziska Jahnke; Jochen Koenigsmann

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Admitting a non-trivial $p$-henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, $p$-henselianity is an elementary property in the language of rings. We are interested in the question when a field admits a non-trivial 0-definable $p$-henselian valuation (in the language of rings). We give a classification of elementary classes of fields in which the canonical $p$-henselian valuation is uniformly 0-definable. We then apply...

Topics: Mathematics, Logic, Commutative Algebra

Source: http://arxiv.org/abs/1407.8156

3
3.0

Jun 30, 2018
06/18

by
Frederic Legoll; William Minvielle

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We consider a variance reduction approach for the stochastic homogenization of divergence form linear elliptic problems. Although the exact homogenized coefficients are deterministic, their practical approximations are random. We introduce a control variate technique to reduce the variance of the computed approximations of the homogenized coefficients. Our approach is based on a surrogate model inspired by a defect-type theory, where a perfect periodic material is perturbed by rare defects....

Topics: Mathematics, Numerical Analysis, Probability

Source: http://arxiv.org/abs/1407.8029

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5.0

Jun 30, 2018
06/18

by
Friedrich Knop; Bernhard Krötz; Eitan Sayag; Henrik Schlichtkrull

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We apply the local structure theorem and the polar decomposition to a real spherical space Z=G/H and control the volume growth on Z. We define the Harish-Chandra Schwartz space on Z. We give a geometric criterion to ensure $L^p$-integrability of matrix coefficients on Z.

Topics: Mathematics, Representation Theory

Source: http://arxiv.org/abs/1407.8006

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8.0

Jun 30, 2018
06/18

by
Gabriel Calsamiglia; Paulo Sad

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We consider the problem of extending germs of plane holomorphic foliations to foliations of compact surfaces. We show that the germs that become regular after a single blow up and admit meromorphic first integrals can be extended, after local changes of coordinates, to foliations of compact surfaces. We also show that the simplest elements in this class can be defined by polynomial equations. On the other hand we prove that, in the absence of meromorphic first integrals there are uncountably...

Topics: Complex Variables, Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1407.8111

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6.0

Jun 30, 2018
06/18

by
Gang Liao; Wenxiang Sun; Shirou Wang

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We prove that entropy map is upper semi-continuous for C1 nonuniformly hyperbolic systems with domination, while it is not true for C1+alpha nonuniformly hyperbolic systems in general. This goes a little against a common intuition that conclusions are parallel between C1+domination systems and C1+alpha systems.

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1407.8102

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3.0

Jun 30, 2018
06/18

by
Genggeng Huang; Congming Li

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In this paper, we apply the moving plane method to the following high order degenerate elliptic equation,\begin{equation*} (-A)^p u=u^\alpha\text{ in } \mathbb R^{n+1}_+,n\geq 1, \end{equation*}where the operator $A=y\partial_y^2+a\partial_y+\Delta_x,a\geq 1$. We get a Liouville theorem for subcritical case and classify the solutions for the critical case.

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1407.7978

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4.0

Jun 30, 2018
06/18

by
Georgios Psaradakis; Daniel Spector

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We consider a multidimensional version of an inequality due to Leray as a substitute for Hardy's inequality in the case $p=n\geq2.$ In this paper we provide an optimal Sobolev-type improvement of this substitute, analogous to the corresponding improvements obtained for $p=2n\geq1$ in G. Psaradakis, An optimal Hardy-Morrey inequality, Calc. Var. Partial Differential Equations 45 (3-4) (2012) 421--441.

Topics: Functional Analysis, Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1407.7983

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4.0

Jun 30, 2018
06/18

by
Hoai-Minh Nguyen

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This paper is devoted to the study of cloaking via anomalous localized resonance (CALR) in the two and three dimensional quasistatic regimes. CALR associated with negative index materials was discovered by Milton and Nicorovicci in [21] and attracted a lot attention in the scientific community. Two key figures of this phenomenon are the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others, and the connection between the localized resonance and the blow...

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1407.7977

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3.0

Jun 30, 2018
06/18

by
I. A. Karimjanov; A. Kh. Khudoyberdiyev; B. A. Omirov

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In this paper the description of solvable Lie algebras with triangular nilradicals is extended to Leibniz algebras. It is proven that the matrices of the left and right operators on elements of Leibniz algebra have upper triangular forms. We establish that solvable Leibniz algebra of a maximal possible dimension with a given triangular nilradical is a Lie algebra. Furthermore, solvable Leibniz algebras with triangular nilradicals of low dimensions are classified.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1407.7956

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7.0

Jun 30, 2018
06/18

by
Javad Noorbakhsh; David Schwab; Allyson Sgro; Thomas Gregor; Pankaj Mehta

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Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales -- from biochemical networks within individual cells to spatially structured cellular populations. Here, we present a family of multiscale models for the emergence of spiral waves...

Topics: Nonlinear Sciences, Quantitative Biology, Mathematics, Pattern Formation and Solitons, Cell...

Source: http://arxiv.org/abs/1407.8210

9
9.0

Jun 30, 2018
06/18

by
Jennifer Hom

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Ozsvath-Stipsicz-Szabo recently defined a one-parameter family, upsilon of K at t, of concordance invariants associated to the knot Floer complex. We compare their invariant to the {-1, 0, 1}-valued concordance invariant epsilon, which is also associated to the knot Floer complex. In particular, we give an example of a knot K with upsilon uniformly equal to zero but epsilon non-zero.

Topics: Mathematics, Geometric Topology

Source: http://arxiv.org/abs/1407.8200

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4.0

Jun 30, 2018
06/18

by
Ji Oon Lee; Kevin Schnelli

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We consider $N\times N$ random matrices of the form $H = W + V$ where $W$ is a real symmetric Wigner matrix and $V$ a random or deterministic, real, diagonal matrix whose entries are independent of $W$. We assume subexponential decay for the matrix entries of $W$ and we choose $V$ so that the eigenvalues of $W$ and $V$ are typically of the same order. For a large class of diagonal matrices $V$ we show that the rescaled distribution of the extremal eigenvalues is given by the Tracy-Widom...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1407.8015

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4.0

Jun 30, 2018
06/18

by
John D. Jakeman; Michael S. Eldred; Khachik Sargsyan

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In this paper we present a basis selection method that can be used with $\ell_1$-minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). The adaptive construction produces anisotropic basis sets that have more terms in important dimensions and limits the number of unimportant terms that increase mutual coherence and thus degrade the performance of $\ell_1$-minimization. The important features and the accuracy of basis selection are demonstrated with a...

Topics: Mathematics, Numerical Analysis, Computing Research Repository

Source: http://arxiv.org/abs/1407.8093

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4.0

Jun 30, 2018
06/18

by
Jonathan L. Gross; Michal Kotrbčík; Timothy Sun

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We derive a quadratic-time algorithm for the genus distribution of any 3-regular, biconnected series-parallel graph, which we extend to any biconnected series-parallel graph of maximum degree at most 3. Since the biconnected components of every graph of treewidth 2 are series-parallel graphs, this yields, by use of bar-amalgamation, a quadratic-time algorithm for every graph of treewidth at most 2 and maximum degree at most 3.

Topics: Mathematics, Discrete Mathematics, Computing Research Repository, Combinatorics

Source: http://arxiv.org/abs/1407.8031

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6.0

Jun 30, 2018
06/18

by
Kanishka Perera; Marco Squassina; Yang Yang

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In this paper we investivate bifurcation results for a class of problem in a smooth bounded domain involving the fractional p-Laplacian operator and with a nonlinearity that reaches the critical growth with respect to the fractional Sobolev embedding.

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1407.8061

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3.0

Jun 30, 2018
06/18

by
Karel Dekimpe; Jonas Deré

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Every expanding map on a closed manifold is topologically conjugate to an expanding map on an infra-nilmanifold, but not every infra-nilmanifold admits an expanding map. In this article we give a complete algebraic characterization of the infra-nilmanifolds admitting an expanding map. We show that, just as in the case of Anosov diffeomorphisms, the existence of an expanding map depends only on the rational holonomy representation of the infra-nilmanifold. A similar characterization is also...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1407.8106

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4.0

Jun 30, 2018
06/18

by
Kesheng Wu; Xiang Zhang

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For an analytic differential system in $\mathbb R^n$ with a periodic orbit, we will prove that if the system is analytically integrable around the periodic orbit, i.e. it has $n-1$ functionally independent analytic first integrals defined in a neighborhood of the periodic orbit, then the system is analytically equivalent to its Poincar\'e--Dulac type normal form. This result is an extension for analytic integrable differential systems around a singularity to the ones around a periodic orbit.

Topics: Mathematics, Classical Analysis and ODEs, Dynamical Systems

Source: http://arxiv.org/abs/1407.7944

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7.0

Jun 30, 2018
06/18

by
Leandro Cagliero; Fernando Szechtman

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Let ${\mathfrak g}$ be a finite dimensional Lie algebra over a field of characteristic 0, with solvable radical ${\mathfrak r}$ and nilpotent radical ${\mathfrak n}=[{\mathfrak g},{\mathfrak r}]$. Given a finite dimensional ${\mathfrak g}$-module $U$, its nilpotency series $ 0\subset U({\mathfrak n}^1)\subset\cdots\subset U({\mathfrak n}^m)=U$ is defined so that $U({\mathfrak n}^1)$ is the 0-weight space of ${\mathfrak n}$ in $U$, $U({\mathfrak n}^2)/U({\mathfrak n}^1)$ is the 0-weight space of...

Topics: Mathematics, Representation Theory

Source: http://arxiv.org/abs/1407.8125

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7.0

Jun 30, 2018
06/18

by
Leonardo Modesto; Leslaw Rachwal

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We hereby introduce and extensively study a class of non-polynomial higher derivative theories of gravity that realize a ultraviolet (UV) completion of Einstein general relativity. These theories are unitary (ghost free) and at most only one-loop divergences survive. The outcome is a class of theories super-renormalizable in even dimension and finite in odd dimension. Moreover, we explicitly prove in D=4 that there exists an extension of the theory that is completely finite and all the beta...

Topics: High Energy Physics - Theory, Mathematics, Mathematical Physics, General Relativity and Quantum...

Source: http://arxiv.org/abs/1407.8036

7
7.0

Jun 30, 2018
06/18

by
Lukas Einkemmer; Alexander Ostermann

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We consider a splitting approach for the Kadomtsev--Petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure can be efficiently implemented. The error made by this numerical scheme is compared to exponential integrators which have been shown in Klein and Roidot (SIAM J. Sci. Comput., 2011) to perform best for stiff solutions of the Kadomtsev--Petviashvili equation. Since many classic high order splitting methods do not perform well, we propose...

Topics: Physics, Mathematics, Numerical Analysis, Computing Research Repository, Computational Physics

Source: http://arxiv.org/abs/1407.8154

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26

Jun 30, 2018
06/18

by
Manish M. Patnaik

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We define unramified Whittaker functions on the p-adic points of an affine Kac-Moody group, and establish an analogue of the Casselman-Shalika formula for these functions.

Topics: Mathematics, Number Theory, Representation Theory

Source: http://arxiv.org/abs/1407.8072

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4.0

Jun 30, 2018
06/18

by
Maral Mostafazadehfard; Aron Simis

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A form in a polynomial ring over a field is said to be homaloidal if its polar map is a Cremona map, i.e., if the rational map defined by the partial derivatives of the form has an inverse rational map. The object of this work is the search for homaloidal polynomials that are the determinants of sufficiently structured matrices. We focus on generic catatalecticants, with special emphasis on the Hankel matrix. An additional focus is on certain degenerations or specializations thereof. In...

Topics: Mathematics, Commutative Algebra, Algebraic Geometry

Source: http://arxiv.org/abs/1407.8089

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4.0

Jun 30, 2018
06/18

by
Markus Seidel

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In this paper we study the semi-Fredholm property of band-dominated operators $A$ and prove that it already implies the Fredholmness of $A$ in all cases where this is not disqualified by obvious reasons. Moreover, this observation is applied to show that the Fredholmness of a band-dominated operator already follows from the surjectivity of all its limit operators.

Topics: Functional Analysis, Mathematics

Source: http://arxiv.org/abs/1407.8104

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3.0

Jun 30, 2018
06/18

by
Martin Lara

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The periodic terms of Brouwer's gravity solution are reconstructed in a nonsingular set of variables which are derived from the well-known polar-nodal variables. This change does not affect the essence of the solution, which still keeps all the benefits of the action-angle variables approach, and yields two major improvements. Namely, the periodic corrections of Brouwer's solution are now valid for any eccentricity below one and any inclination except the critical inclination, and, besides, are...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1407.8076

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10.0

Jun 30, 2018
06/18

by
Massimiliano Mella

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Two divisors in $\mathbb P^n$ are said to be Cremona equivalent if there is a Cremona modification sending one to the other. In this paper I study irreducible cones in $\mathbb P^n$ and prove that two cones are Cremona equivalent if their general hyperplane sections are birational. In particular I produce examples of cones in $\mathbb P^3$ Cremona equivalent to a plane whose plane section is not Cremona equivalent to a line in $\mathbb P^2$.

Topics: Mathematics, Algebraic Geometry

Source: http://arxiv.org/abs/1407.8075

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3.0

Jun 30, 2018
06/18

by
Max R. Atkin; Stefan Zohren

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We consider the expected violations of Bell inequalities from random pure states. More precisely, we focus on a slightly generalised version of the CGLMP inequality, which concerns Bell experiments of two parties, two measurement options and N outcomes and analyse their expected quantum violations from random pure states for varying N, assuming the conjectured optimal measurement operators. It is seen that for small N the Bell inequality is not violated on average, while for larger N it is....

Topics: Quantum Physics, Mathematics, Mathematical Physics

Source: http://arxiv.org/abs/1407.8233

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5.0

Jun 30, 2018
06/18

by
Meysam Alishahi; Hossein Hajiabolhassan

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For a graph $G$, the tree graph ${\cal T}_{G,t}$ has all tree subgraphs of $G$ with $t$ vertices as vertex set and two tree subgraphs are neighbors if they are edge-disjoint. Also, the $r^{th}$ cut number of $G$ is the minimum number of edges between parts of a partition of vertex set of $G$ into two parts such that each part has size at least $r$. We show that if $t=(1-o(1))n$ and $n$ is large enough, then for any dense graph $G$ with $n$ vertices, the chromatic number of the tree graph ${\cal...

Topics: Mathematics, Combinatorics

Source: http://arxiv.org/abs/1407.8035

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7.0

Jun 30, 2018
06/18

by
Michael Albert; Mathilde Bouvel

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The existence of apparently coincidental equalities (also called Wilf-equivalences) between the enumeration sequences, or generating functions, of various hereditary classes of combinatorial structures has attracted significant interest. We investigate such coincidences among non-crossing matchings and a variety of other Catalan structures including Dyck paths, 231-avoiding permutations and plane forests. In particular we consider principal classes defined by not containing an occurrence of a...

Topics: Mathematics, Combinatorics

Source: http://arxiv.org/abs/1407.8261

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9.0

Jun 30, 2018
06/18

by
Michel L. Lapidus; Goran Radunović; Darko Žubrinić

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The theory of 'zeta functions of fractal strings' has been initiated by the first author in the early 1990s, and developed jointly with his collaborators during almost two decades of intensive research in numerous articles and several monographs. In 2009, the same author introduced a new class of zeta functions, called `distance zeta functions', which since then, has enabled us to extend the existing theory of zeta functions of fractal strings and sprays to arbitrary bounded (fractal) sets in...

Topics: Complex Variables, Mathematics, Spectral Theory, Mathematical Physics

Source: http://arxiv.org/abs/1407.8094