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5.0

Jun 28, 2018
06/18

by
Daniel Allcock; Itamar Gal; Alice Mark

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We develop the notational system developed by Conway and Sloane for working with quadratic forms over the 2-adic integers, and prove its validity. Their system is far better for actual calculations than earlier methods, and has been used for many years, but it seems that no proof has been published before now.

Topics: Number Theory, Mathematics

Source: http://arxiv.org/abs/1511.04614

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2.0

Jun 30, 2018
06/18

by
Lior Bary-Soroker; Moshe Jarden; Danny Neftin

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We describe the Sylow subgroups of Gal(Q) for an odd prime p, by observing and studying their decomposition as a semidirect product of Z_p acting on F, where F is a free pro-p group, and Z_p are the p-adic integers. We determine the finite Z_p-quotients of F and more generally show that every split embedding problem of Z_p-groups for F is solvable. Moreover, we analyze the Z_p-action on generators of F.

Topics: Mathematics, Number Theory, Group Theory

Source: http://arxiv.org/abs/1403.3266

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3.0

Jun 29, 2018
06/18

by
Franziska Wutz

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We show the existence of a hypersurface that contains a given closed subscheme of a projective space over a finite field and intersects a smooth quasi-projective scheme smoothly, under some condition on the dimension. This generalizes a Bertini theorem by Poonen and is the finite field analogue of a Bertini theorem by Altman and Kleiman. Furthermore, we add the possibility of modifying finitely many local conditions of the hypersurface. We show that the condition on the dimension is fulfilled...

Topics: Number Theory, Mathematics

Source: http://arxiv.org/abs/1611.09092

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2.0

Jun 30, 2018
06/18

by
Yang Cao; Yongqi Liang; Fei Xu

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We prove that any open subset $U$ of a semi-simple simply connected quasi-split linear algebraic group $G$ with ${codim} (G\setminus U, G)\geq 2$ over a number field satisfies strong approximation by establishing a fibration of $G$ over a toric variety. We also extend this result to strong approximation with Brauer-Manin obstruction for groupic varieties of which all invertible functions are constant. As a by-product of the fibration method, we provide an example which satisfies strong...

Topics: Algebraic Geometry, Number Theory, Mathematics

Source: http://arxiv.org/abs/1701.07259

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2.0

Jun 30, 2018
06/18

by
Katarzyna Paluch

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In the maximum asymmetric traveling salesman problem (Max ATSP) we are given a complete directed graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum weight. In this paper we give a fast combinatorial $\frac 34$-approximation algorithm for Max ATSP. It is based on a novel use of {\it half-edges}, matchings and a new method of edge coloring. (A {\it half-edge} of edge $(u,v)$ is informally speaking "either a head or a tail of...

Topics: Discrete Mathematics, Data Structures and Algorithms, Computing Research Repository

Source: http://arxiv.org/abs/1401.3670

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4.0

Jun 28, 2018
06/18

by
Alex Bartel; Hendrik W. Lenstra

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We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are infinite. This work is motivated by the Cohen-Lenstra heuristics on class groups. The number theoretic implications will be addressed in a separate paper.

Topics: Number Theory, Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1510.02758

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Jun 30, 2018
06/18

by
Dzmitry Badziahin

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The $p$-adic Littlewood conjecture (PLC) states that $\liminf_{q\to\infty} q\cdot |q|_p \cdot ||qx|| = 0$ for every prime $p$ and every real $x$. Let $w_{CF}(x)$ be an infinite word composed of the continued fraction expansion of $x$ and let $\mathrm{T}$ be the standard left shift map. Assuming that $x$ is a counterexample to PLC we get several restrictions on limit elements of the sequence $\{\mathrm{T}^n w_{CF}(x)\}_{n\in\mathbb{N}}$. As a consequence we show that for any such limit element...

Topics: Mathematics, Number Theory

Source: http://arxiv.org/abs/1406.3594

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2.0

Jun 30, 2018
06/18

by
Habib Ammari; Matias Ruiz; Sanghyeon Yu; Hai Zhang

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This paper is concerned with the inverse problem of reconstructing a small object from far field measurements. The inverse problem is severally ill-posed because of the diffraction limit and low signal to noise ratio. We propose a novel methodology to solve this type of inverse problems based on an idea from plasmonic sensing. By using the field interaction with a known plasmonic particle, the fine detail information of the small object can be encoded into the shift of the resonant frequencies...

Topics: Spectral Theory, Mathematical Physics, Analysis of PDEs, Mathematics

Source: http://arxiv.org/abs/1704.04870

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3.0

Jun 28, 2018
06/18

by
Emmanuel Jeandel

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We prove that every polycyclic group of nonlinear growth admits a strongly aperiodic SFT and has an undecidable domino problem. This answers a question of [4] and generalizes the result of [2].

Topics: Mathematics, Discrete Mathematics, Computing Research Repository, Group Theory

Source: http://arxiv.org/abs/1510.02360

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4.0

Jun 29, 2018
06/18

by
Matthew Aldridge; Oliver Johnson; Jonathan Scarlett

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We consider nonadaptive group testing where each item is placed in a constant number of tests. The tests are chosen uniformly at random with replacement, so the testing matrix has (almost) constant column weights. We show that performance is improved compared to Bernoulli designs, where each item is placed in each test independently with a fixed probability. In particular, we show that the rate of the practical COMP detection algorithm is increased by 31% in all sparsity regimes. In dense...

Topics: Statistics Theory, Statistics, Information Theory, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1602.03471

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5.0

Jun 30, 2018
06/18

by
Beatrice Pelloni; David A. Smith

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The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the {\em unified transform} introduced by Fokas in the 90's. On the other hand, it is known that many initial-boundary value problems can be solved via a classical transform pair, constructed via the spectral analysis of the associated spatial operator. For...

Topics: Mathematics, Spectral Theory, Analysis of PDEs

Source: http://arxiv.org/abs/1408.3657

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3.0

Jun 30, 2018
06/18

by
Souvik Chandra; Dhagash Mehta; Aranya Chakrabortty

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The solution space of any set of power flow equations may contain different number of real-valued solutions. The boundaries that separate these regions are referred to as power flow solution space boundaries. Knowledge of these boundaries is important as they provide a measure for voltage stability. Traditionally, continuation based methods have been employed to compute these boundaries on the basis of initial guesses for the solution. However, with rapid growth of renewable energy sources...

Topics: Systems and Control, Algebraic Geometry, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1704.04792

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Jun 28, 2018
06/18

by
Colin D. Reid; Phillip R. Wesolek

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In finite group theory, chief factors play an important and well-understood role in the structure theory. We here develop a theory of chief factors for Polish groups. In the development of this theory, we prove a version of the Schreier refinement theorem. We also prove a trichotomy for the structure of topologically characteristically simple Polish groups. The development of the theory of chief factors requires two independently interesting lines of study. First we consider injective,...

Topics: Group Theory, Mathematics, Logic

Source: http://arxiv.org/abs/1509.00719

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3.0

Jun 30, 2018
06/18

by
Nicolas Privault

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We derive integral representations in terms of the Macdonald functions for the square modulus $s\mapsto | \Gamma ( a + i s ) |^2$ of the Gamma function and its Fourier transform when $a 0$. This representation is based on a renormalization argument using modified Bessel functions of the second kind, and it applies to the representation of the solutions of the Fokker-Planck equation.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1410.5043

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3.0

Jun 30, 2018
06/18

by
Sara van de Geer

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We examine the rate of convergence of the Lasso estimator of lower dimensional components of the high-dimensional parameter. Under bounds on the $\ell_1$-norm on the worst possible sub-direction these rates are of order $\sqrt {|J| \log p / n }$ where $p$ is the total number of parameters, $J \subset \{ 1, \ldots, p \}$ represents a subset of the parameters and $n$ is the number of observations. We also derive rates in sup-norm in terms of the rate of convergence in $\ell_1$-norm. The...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1403.7023

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7.0

Jun 27, 2018
06/18

by
Michael Hintermüller; Tobias Keil; Donat Wegner

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This paper is concerned with the distributed optimal control of a time-discrete Cahn--Hilliard/Navier--Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a family of coupled systems in each time instance of a variational inequality of fourth order and the Navier--Stokes equation. By proposing a suitable time-discretization, energy estimates are proved and the existence of solutions to the primal system and of optimal...

Topics: Optimization and Control, Analysis of PDEs, Mathematics

Source: http://arxiv.org/abs/1506.03591

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2.0

Jun 29, 2018
06/18

by
Maximilian Hanusch

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The intention of this thesis is to provide general tools and concepts that allow to perform a mathematically substantiated symmetry reduction in (quantum) gauge field theories. Here, the main focus is on the framework of loop quantum gravity (LQG), where we concentrate on the reduction of the quantum configuration space, and the construction of a normalized Radon measures on the reduced one. More precisely, we introduce a new way to symmetry reduce the LQG-configuration space directly on the...

Topics: Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1601.05531

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4.0

Jun 30, 2018
06/18

by
Silas L. Fong; Vincent Y. F. Tan

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This paper establishes that the strong converse holds for some classes of discrete memoryless multimessage multicast networks (DM-MMNs) whose corresponding cut-set bounds are tight, i.e., coincide with the set of achievable rate tuples. The strong converse for these classes of DM-MMNs implies that all sequences of codes with rate tuples belonging to the exterior of the cut-set bound have average error probabilities that necessarily tend to one (and are not simply bounded away from zero)....

Topics: Mathematics, Computing Research Repository, Information Theory

Source: http://arxiv.org/abs/1407.2417

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5.0

Jun 30, 2018
06/18

by
Christos A. Athanasiadis

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The chromatic quasisymmetric function of a graph was introduced by Shareshian and Wachs as a refinement of Stanley's chromatic symmetric function. An explicit combinatorial formula, conjectured by Shareshian and Wachs, expressing the chromatic quasisymmetric function of the incomparability graph of a natural unit interval order in terms of power sum symmetric functions, is proven. The proof uses a formula of Roichman for the irreducible characters of the symmetric group.

Topics: Mathematics, Combinatorics

Source: http://arxiv.org/abs/1409.2595

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6.0

Jun 29, 2018
06/18

by
Asghar Rahimi; Bayaz Daraby; Zahra Darvishi

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Extending the concept of frame to continuous frame, in this manuscript we will show that under certain conditions on the measure of $\Omega$ and the dimension of $\h$ we can construct continuous frames. Also, some examples are given.

Topics: Functional Analysis, Mathematics

Source: http://arxiv.org/abs/1606.08981

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5.0

Jun 29, 2018
06/18

by
Giorgio Fabbri; Francesco Russo

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The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking values in a Banach space H, is the sum of a local martingale and a suitable orthogonal process. The concept of weak Dirichlet process fits the notion of convolution type processes, a class including mild solutions for stochastic evolution equations on infinite...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1606.03828

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2.0

Jun 30, 2018
06/18

by
Tobias Gruber; Sebastian Cammerer; Jakob Hoydis; Stephan ten Brink

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We revisit the idea of using deep neural networks for one-shot decoding of random and structured codes, such as polar codes. Although it is possible to achieve maximum a posteriori (MAP) bit error rate (BER) performance for both code families and for short codeword lengths, we observe that (i) structured codes are easier to learn and (ii) the neural network is able to generalize to codewords that it has never seen during training for structured, but not for random codes. These results provide...

Topics: Information Theory, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1701.07738

3
3.0

Jun 30, 2018
06/18

by
Iskander A. Taimanov

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We describe the action of the (Mobius) inversion on the data of the Weierstrass representation of surfaces in the three-space and show that the Moutard transformation of two-dimensional Dirac operators has a geometrical meaning: it maps the potential $U$ of a surface $S$ into the potential of its inversion.

Topics: Mathematics, Nonlinear Sciences, Exactly Solvable and Integrable Systems, Differential Geometry

Source: http://arxiv.org/abs/1408.4464

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3.0

Jun 29, 2018
06/18

by
J. M. Landsberg; Mateusz Michałek

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Let M_n denote the matrix multiplication tensor for nxn matrices. We use the border substitution method combined with Koszul flattenings to prove the border rank lower bound of 2n^2-log(n)-1 for M_n.

Topics: Algebraic Geometry, Computational Complexity, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1608.07486

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Topics: Radio Program, NPR programs, Harvard Law School alumni, Harvard University alumni, Federal...

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5.0

Jun 27, 2018
06/18

by
Jana Majerová

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The correlation integral and determinism are quantitative characteristics of a dynamical system based on the recurrence of orbits. For strongly non-chaotic interval maps, the determinism equals 1 for every small enough threshold. This means that trajectories of such systems are perfectly predictable in the infinite horizon. In this paper we study the correlation integral and determinism for the family of $2^\infty$ non-chaotic maps, first considered by Delahaye in 1980. The determinism in a...

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1506.02246

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3.0

Jun 30, 2018
06/18

by
Tetsu Mizumachi; Nikolay Tzvetkov

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In this article, we will prove $L^2(\mathbb{R})$-stability of $1$-solitons for the KdV equation by using exponential stability property of the semigroup generated by the linearized operator. The proof follows the lines of recent stability argument of Mizumachi [Asymptotic stability of lattice solitons in the energy space, Comm. Math. Phys., (2009)] and Mizumachi, Pego and Quintero [Asymptotic stability of solitary waves in the Benney-Luke model of water waves, Differential Integral Equations,...

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1403.5321

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2.0

Jun 29, 2018
06/18

by
Lucia Alessandrini

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A product of K\"ahler manifolds also carries a K\"ahler metric. In this short note we would like to study the product of generalized $p-$K\"ahler manifolds, compact or not. The results we get extend the known results (balanced, SKT, sG manifolds), and are optimal in the compact case. Hence we can give new non-trivial examples of generalized $p-$K\"ahler manifolds.

Topics: Symplectic Geometry, Differential Geometry, Mathematics

Source: http://arxiv.org/abs/1607.06238

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5.0

Jun 30, 2018
06/18

by
Raphaël Leone; Thierry Gourieux

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This paper provides a modern presentation of Noether's theory in the realm of classical dynamics, with application to the problem of a particle submitted to both a potential and a linear dissipation. After a review of the close relationships between Noether symmetries and first integrals, we investigate the variational point symmetries of the Lagrangian introduced by Bateman, Caldirola and Kanai. This analysis leads to the determination of all the time-independent potentials allowing such...

Topics: Mathematics, Mathematical Physics

Source: http://arxiv.org/abs/1412.7523

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2.0

Jun 28, 2018
06/18

by
Michael Megrelishvili; Luie Polev; Menachem Shlossberg

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A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. We provide a sufficient and necessary condition for the minimality of the semidirect product $G\leftthreetimes P,$ where $G$ is a compact topological group and $P$ is a topological subgroup of $Aut(G)$. We prove that $G\leftthreetimes P$ is minimal for every closed subgroup $P$ of $Aut(G)$. In case $G$ is abelian, the same is true for every subgroup $P \subseteq Aut(G)$. We show, in contrast, that...

Topics: Group Theory, General Topology, Mathematics

Source: http://arxiv.org/abs/1511.07021

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4.0

Jun 29, 2018
06/18

by
Chanfei Wang; Tiejun Lv; Hui Gao; Shaoshi Yang

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Soft noncoherent detection, which relies on calculating the \textit{a posteriori} probabilities (APPs) of the bits transmitted with no channel estimation, is imperative for achieving excellent detection performance in high-dimensional wireless communications. In this paper, a high-performance belief propagation (BP)-based soft multiple-symbol differential detection (MSDD) framework, dubbed BP-MSDD, is proposed with its illustrative application in differential space-time block-code (DSTBC)-aided...

Topics: Information Theory, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1608.01296

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7.0

Jun 27, 2018
06/18

by
James O. Berger; Jose M. Bernardo; Dongchu Sun

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Rejoinder to Overall Objective Priors by James O. Berger, Jose M. Bernardo, Dongchu Sun [arXiv:1504.02689]

Topics: Statistics, Mathematics, Statistics Theory

Source: http://arxiv.org/abs/1504.07081

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2.0

Jun 29, 2018
06/18

by
Paweł Gładki; Murray Marshall

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Two fields are Witt equivalent if their Witt rings of symmetric bilinear forms are isomorphic. Witt equivalent fields can be understood to be fields having the same quadratic form theory. The behavior of finite fields, local fields, global fields, as well as function fields of curves defined over archimedean local fields under Witt equivalence is well-understood. Numbers of classes of Witt equivalent fields with finite numbers of square classes are also known in some cases. Witt equivalence of...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1601.08085

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2.0

Jun 30, 2018
06/18

by
Elena Celledoni; Robert I. McLachlan; David I. McLaren; Brynjulf Owren; G. R. W. Quispel

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Applying Kahan's discretization to the reduced Nahm equations, we obtain two classes of integrable mappings.

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1702.00280

2
2.0

Jun 29, 2018
06/18

by
Iosif Pinelis

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It is well known that under general regularity conditions the distribution of the maximum likelihood estimator (MLE) is asymptotically normal. Very recently, bounds of the optimal order $O(1/\sqrt n)$ on the closeness of the distribution of the MLE to normality in the so-called bounded Wasserstein distance were obtained, where $n$ is the sample size. However, the corresponding bounds on the Kolmogorov distance were only of the order $O(1/n^{1/4})$. In this note, bounds of the optimal order...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1601.02177

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3.0

Jun 29, 2018
06/18

by
Keenan Kidwell

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We prove analogues of the major algebraic results of Greenberg-Vatsal for Selmer groups of $p$-ordinary newforms over $\mathbf{Z}_p$-extensions which may be neither cyclotomic nor anticyclotomic, under a number of technical hypotheses, including a cotorsion assumption on the Selmer groups. The main complication which arises in our work is the possible presence of finite primes which can split completely in the $\mathbf{Z}_p$-extension being considered, resulting in the local cohomology groups...

Topics: Number Theory, Mathematics

Source: http://arxiv.org/abs/1611.02727

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3.0

Jun 29, 2018
06/18

by
Mahdi Haghifam; Behrooz Makki; Masoumeh Nasiri-Kenari; Tommy Svensson

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This paper investigates the outage probability and the throughput of relay networks with wireless information and energy transfer where the relays harvest energy from the transmitted radio-frequency signal of the source. Considering different power consumption models, we derive the outage probability for both adaptive and non-adaptive power allocations at the relay. With a total energy consumption constraint at the source, we provide closed-form expressions for the optimal time sharing and...

Topics: Information Theory, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1607.07087

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5.0

Jun 27, 2018
06/18

by
Tao Luo; Zhouping Xin; Huihui Zeng

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This paper proves the nonlinear asymptotic stability of the Lane-Emden solutions for spherically symmetric motions of viscous gaseous stars if the adiabatic constant $\gamma$ lies in the stability range $(4/3, 2)$. It is shown that for small perturbations of a Lane-Emden solution with same mass, there exists a unique global (in time) strong solution to the vacuum free boundary problem of the compressible Navier-Stokes-Poisson system with spherical symmetry for viscous stars, and the solution...

Topics: Analysis of PDEs, Mathematics

Source: http://arxiv.org/abs/1506.03906

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2.0

Jun 30, 2018
06/18

by
Kenro Furutani; Irina Markina; Alexander Vasil'ev

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The aim of our paper is to construct pseudo $H$-type algebras from the covering free nilpotent two-step Lie algebra as the quotient algebra by an ideal. We propose an explicit algorithm of construction of such an ideal by making use of a non-degenerate scalar product. Moreover, as a bypass result, we recover the existence of a rational structure on pseudo $H$-type algebras, which implies the existence of lattices on the corresponding pseudo $H$-type Lie groups. Our approach substantially uses...

Topics: Mathematics, Representation Theory, Differential Geometry

Source: http://arxiv.org/abs/1410.3767

Topics: Radio Program, Mass media, Council of European National Top Level Domain Registries members, Social...

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3.0

Jun 30, 2018
06/18

by
Christopher M. Drupieski

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In this paper we compute extension groups in the category of strict polynomial superfunctors and thereby exhibit certain "universal extension classes" for the general linear supergroup. Some of these classes restrict to the universal extension classes for the general linear group exhibited by Friedlander and Suslin, while others arise from purely super phenomena. We then use these extension classes to show that the cohomology ring of a finite supergroup scheme---equivalently of a...

Topics: Mathematics, Representation Theory, K-Theory and Homology

Source: http://arxiv.org/abs/1408.5764

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9.0

Jun 28, 2018
06/18

by
Nikolaos I. Miridakis; Dimitrios D. Vergados; Angelos Michalas

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The performance of an underlay cognitive (secondary) dual-hop relaying system with multiple antennas and hardware impairments at each transceiver is investigated. In particular, the outage probability of the end-to-end (e2e) communication is derived in closed-form, when either transmit antenna selection with maximum ratio combining (TAS/MRC), or TAS with selection combining (TAS/SC) are established in each hop. Simplified asymptotic outage expressions are also obtained, which manifest the...

Topics: Information Theory, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1509.00166

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4.0

Jun 28, 2018
06/18

by
Kent Tsz Kan Cheung; Shaoshi Yang; Lajos Hanzo

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The energy spectral efficiency maximization (ESEM) problem of a multi-user, multi-relay, multi-cell system is considered, where all the network nodes are equipped with multi-antenna transceivers. To deal with the potentially excessive interference originating from a plethora of geographically distributed transmission sources, a pair of transmission protocols based on interference alignment (IA) are conceived. The first, termed the full-IA, avoids all intra-cell interference (ICI) and other-cell...

Topics: Information Theory, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1510.01385

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5.0

Jun 30, 2018
06/18

by
Ken Shirakawa; Hiroshi Watanabe; Noriaki Yamazaki

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Two main existence theorems are proved for two nonstandard systems of parabolic initial-boundary value problems. The systems are based on the "$ \phi $-$ \eta $-$ \theta $ model" proposed by Kobayashi [RIMS Kokyuroku, 1210 (2001), 68-77] as a phase-field model of planar grain boundary motion under isothermal solidification. Although each of the systems has specific characteristics and mathematical difficulties, the proofs of the main theorems are based on the time discretization...

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1408.4204

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Jun 26, 2018
06/18

by
Vladimir Nikiforov

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In 1993 Hong asked what are the best bounds on the $k$'th largest eigenvalue $\lambda_{k}(G)$ of a graph $G$ of order $n$. This challenging question has never been tackled for any $22,$ and even tighter bounds are obtained for the $k$'th largest singular value $\lambda_{k}^{\ast}(G).$ Some of these bounds are based on Taylor's strongly regular graphs, and other on a method of Kharaghani for constructing Hadamard matrices. The same kind of constructions are applied to other open problems, like...

Topics: Mathematics, Combinatorics

Source: http://arxiv.org/abs/1502.00359

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2.0

Jun 29, 2018
06/18

by
Anderson L. A. de Araujo

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We present a result of existence of infinitely many solutions for the Dirichlet problem involving the p-Laplacian in annular domains, when $p\leq N$, contouring the failure of compactness of $W^{1,p}(\Omega)$ in $C^0(\bar{\Omega})$ applying a variable change.

Topics: Classical Analysis and ODEs, Analysis of PDEs, Mathematics

Source: http://arxiv.org/abs/1607.02468

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Jun 30, 2018
06/18

by
Gonzalo Contreras

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We present a theorem by Contreras, Iturriaga and Siconolfi in which we give a setting to generalize the homogenization of the Hamilton-Jacobi equation from tori to other manifolds.

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1412.8126

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Jun 29, 2018
06/18

by
Aydın Aytuna

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We investigate tameness in the Fr\'echet spaces O(M) of analytic functions on Stein manifolds M equipped with the compact open topology. Actually we will look into tameness in the more general class of nuclear Fr\'echet spaces with the properties weak DN and Omega, and then specialize to analytic function spaces. We show that for a Stein manifold M, tameness of O(M) is equivalent to the hyperconvexity of M.

Topics: Complex Variables, Mathematics

Source: http://arxiv.org/abs/1603.01835

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Jun 29, 2018
06/18

by
Raphaël Danchin; Xin Zhang

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In our recent work dedicated to the Boussinesq equations [Danchin and Zhang 2016], we established the persistence of solutions with piecewise constant temperature along interfaces with H\"older regularity. We here address the same problem for the inhomogeneous Navier-Stokes equations satisfied by a viscous incompressibleand inhomogeneous fluid. We establish that, indeed, in the slightly inhomogeneous case, patches of densities with $\mathcal{C}^{1, \varepsilon}$ regularity propagate for...

Topics: Analysis of PDEs, Mathematics

Source: http://arxiv.org/abs/1612.00282

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Jun 28, 2018
06/18

by
Peter G. Casazza; Daniel Freeman; Richard G. Lynch

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We extend the concept of weaving Hilbert space frames to the Banach space setting. Similar to frames in a Hilbert space, we show that for any two approximate Schauder frames for a Banach space, every weaving is an approximate Schauder frame if and only if there is a uniform constant $C\geq 1$ such that every weaving is a $C$-approximate Schauder frame. We also study weaving Schauder bases, where it is necessary to introduce two notions of weaving. On one hand, we can ask if two Schauder bases...

Topics: Functional Analysis, Mathematics

Source: http://arxiv.org/abs/1511.06093