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Let $f(t_1,\ldots,t_n)$ be a nondegenerate integral quadratic form. We analyze the asymptotic behavior of the function $D_f(X)$, the number of integers of absolute value up to $X$ represented by $f$. When $f$ is isotropic or $n$ is at least…

Number Theory · Mathematics 2023-04-18 Pete L. Clark , Paul Pollack , Jeremy Rouse , Katherine Thompson

This paper is devoted to the proof of uniform H\"older and Lipschitz estimates close to oscillating boundaries, for divergence form elliptic systems with periodically oscillating coefficients. Our main point is that no structure is assumed…

Analysis of PDEs · Mathematics 2015-06-19 Carlos Kenig , Christophe Prange

Over the past several years, numerous authors have explored model theoretically motivated combinatorial conditions that ensure that a graph has an efficient regular decomposition in the sense of Szemer\'edi. In this paper we set out a…

Combinatorics · Mathematics 2025-03-18 C. Terry , J. Wolf

We generalize Roth's theorem on three term arithmetic progressions to translation invariant quadratic forms in at least 17 variables. We use Fourier-analysis, restriction theory, uniformity norms and Roth's density increment method to show…

Number Theory · Mathematics 2013-09-02 Eugen Keil

It has been established on many occasions that the set of quotients of prime numbers is dense in the set of positive real numbers. More recently, it has been proved that the set of quotients of primes in the Gaussian integers is dense in…

Number Theory · Mathematics 2018-07-31 Brian D. Sittinger

We prove complex contraction for zero-free regions of counting weighted set cover problem in which an element can appear in an unbounded number of sets, thus obtaining fully polynomial-time approximation schemes(FPTAS) via Barvinok's…

Data Structures and Algorithms · Computer Science 2022-01-03 Liang Li , Guangzeng Xie

One way to study the combinatorics of finite metric spaces is to study the betweenness relation associated with the metric space. In the hypergraph metrization problem, one has to find and characterize metric betweennesses whose collinear…

Combinatorics · Mathematics 2018-06-07 Péter G. N. Szabó

Correspondence is a ubiquitous problem in computer vision and graph matching has been a natural way to formalize correspondence as an optimization problem. Recently, graph matching solvers have included higher-order terms representing…

Computer Vision and Pattern Recognition · Computer Science 2014-05-27 Mayank Bansal , Kostas Daniilidis

We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces, and hydrodynamic coupling. In the absence of non-conservative forces…

Computational Physics · Physics 2017-12-14 Ruslan L. Davidchack , Thomas E. Ouldridge , Michael V. Tretyakov

Recent progress in gravitational wave observations has positioned Pulsar Timing Arrays as a key tool for detecting the stochastic gravitational wave background in the nanohertz band. It is widely believed that this background is primarily…

High Energy Astrophysical Phenomena · Physics 2026-05-20 Hinano Hisamatsu , Koutarou Kyutoku

Let {\alpha} be a prime Hurwitz integer. H{\alpha}, which is the set of residual class with respect to related modulo function in the rings of Hurwitz integers, is a subset of H, which is the set of all Hurwitz integers. We consider left…

Information Theory · Computer Science 2022-07-27 Ramazan Duran , Murat Guzeltepe

We study double Hurwitz numbers in genus zero counting the number of covers $\CP^1\to\CP^1$ with two branching points with a given branching behavior. By the recent result due to Goulden, Jackson and Vakil, these numbers are piecewise…

Algebraic Geometry · Mathematics 2018-07-18 Sergei Shadrin , Michael Shapiro , Alek Vainshtein

We prove that the Hurwitz action on reflection factorizations of Coxeter elements is transitive up to certain natural constraints in the complex reflection groups G4 and G5. This affirms a more general conjecture by Lewis and Reiner in…

Combinatorics · Mathematics 2018-08-06 Zachery Peterson

Many effective field theories describing gravity cannot arise from an underlying theory based on Riemann geometry or its extensions to include torsion and nonmetricity but may instead emerge from another geometry or may have a nongeometric…

General Relativity and Quantum Cosmology · Physics 2021-08-25 Alan Kostelecky , Zonghao Li

Using the classical recursion relations we compute scattering amplitudes in a spontaneously broken Gauge-Higgs theory into final states involving high multiplicities of massive vector bosons and Higgs bosons. These amplitudes are computed…

High Energy Physics - Phenomenology · Physics 2015-06-23 Valentin V. Khoze

The purpose of this article is to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform (QFT). We study some fundamental properties of this extension such as scaling, translation,…

Classical Analysis and ODEs · Mathematics 2020-11-05 Youssef El Haoui , Said Fahlaoui

Although high-order Maxwell integral equation solvers provide significant advantages in terms of speed and accuracy over corresponding low-order integral methods, their performance significantly degrades in presence of non-smooth…

Numerical Analysis · Mathematics 2025-01-31 Constantine Sideris , Davit Aslanyan , Oscar P. Bruno

This paper deals with the large-scale behaviour of dynamical optimal transport on $\mathbb{Z}^d$-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes…

Analysis of PDEs · Mathematics 2021-10-29 Peter Gladbach , Eva Kopfer , Jan Maas , Lorenzo Portinale

We show that if $h\in \mathbb{Z}[x]$ is a polynomial of degree $k \geq 2$ such that $h(\mathbb{N})$ contains a multiple of $q$ for every $q\in \mathbb{N}$, known as an $\textit{intersective polynomial}$, then any subset of $\{1,2,\dots,N\}$…

Number Theory · Mathematics 2020-06-11 Alex Rice

We study the question under which conditions the zero set of a (cross-) Wigner distribution W (f, g) or a short-time Fourier transform is empty. This is the case when both f and g are generalized Gaussians, but we will construct less…

Classical Analysis and ODEs · Mathematics 2018-11-12 Karlheinz Gröchenig , Philippe Jaming , Eugenia Malinnikova