content stringlengths 0 625k | subset stringclasses 1
value | meta dict |
|---|---|---|
---
abstract: |
We construct a two dimensional unoriented open/closed topological field theory from a finite graded group $\pi:\hat{G}\twoheadrightarrow \{1,-1\}$, a $\pi$-twisted $2$-cocycle $\hat{\theta}$ on $B \hat{G}$ and a character $\lambda: \hat{G}\rightarrow U(1)$. The underlying oriented theory is a twisted ... | arxiv_math | {
"id": "2310.03566",
"title": "Frobenius--Schur indicators for twisted Real representation theory and\n two dimensional unoriented topological field theory",
"authors": "Levi Gagnon-Ririe, Matthew B. Young",
"categories": "math.RT math.QA",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We present a comprehensive theory on the well-posedness of a one-dimensional nonlinear backward stochastic differential equation (1D BSDE for short), where the generator $g$ has a one-sided linear/super-linear growth in the first unknown variable $y$ and an at most quadratic growth in the second unkno... | arxiv_math | {
"id": "2309.06233",
"title": "A user's guide to 1D nonlinear backward stochastic differential\n equations with applications and open problems",
"authors": "Shengjun Fan, Ying Hu, Shanjian Tang",
"categories": "math.PR",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
bibliography:
- On_Ruh_In.bib
---
# Introduction
Harmonic numbers, with a history dating back to antiquity, hold significant importance in various aspects of number theory. On the other hand, the polylogarithm function find practical applications in quantum systems, such as estimating the density of particles and... | arxiv_math | {
"id": "2309.11459",
"title": "New closed forms for a dilogarithmic integral, related integrals, and\n series",
"authors": "Abdulhafeez A. Abdulsalam",
"categories": "math.CA",
"license": "http://creativecommons.org/licenses/by-nc-nd/4.0/"
} |
---
abstract: |
Let $\mathbb{F}_q$ be the field with $q$ elements and of characteristic $p$. For $a\in\mathbb{F}_p$ consider the set $$S_a(n)=\{f\in\mathbb{F}_q[x]\mid\deg(f)=n,~f\text{ irreducible, monic and} \operatorname{Tr}(f)=a\}.$$ In a recent paper, Robert Granger proved for $q=2$ and $n\ge 2$ $$|S_1(n)|-|S_0(... | arxiv_math | {
"id": "2310.01872",
"title": "On the Iterative Behaviour of the Number of Irreducible Polynomials with\n Certain Properties over Finite Fields",
"authors": "Max Schulz",
"categories": "math.NT math.CO",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We prove a four-term exact sequence of surface orbifold pure braid groups for all genus $\geq 1$, $2$-dimensional orientable orbifolds with cone points. This corrects our earlier result in [@Rou21].
address: |
School of Mathematics\
Tata Institute\
Homi Bhabha Road\
Mumbai 400005, India
author... | arxiv_math | {
"id": "2309.12155",
"title": "A four-term exact sequence of surface orbifold pure braid groups",
"authors": "S K Roushon",
"categories": "math.GT math.GR",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We show that a Killing field on a compact pseudo.7pt\--.4ptKähler ddbar manifold is necessarily (real) holomorphic. Our argument works without the ddbar assumption in real dimension four. The claim about holomorphicity of Killing fields on compact pseudo.7pt\--.4ptKähler manifolds appears in a 2012 pa... | arxiv_math | {
"id": "2309.09820",
"title": "Killing fields on compact pseudo-K\\\"ahler manifolds",
"authors": "Andrzej Derdzinski and Ivo Terek",
"categories": "math.DG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Let $(M^n,g_0)$ be a smooth compact Riemannian manifold of dimension $n\geq 3$ with non-empty boundary $\partial M$. Let $\Gamma\subset\mathbb{R}^n$ be a symmetric convex cone and $f$ a symmetric defining function for $\Gamma$ satisfying standard assumptions. Under an algebraic condition on $\Gamma$, ... | arxiv_math | {
"id": "2310.01346",
"title": "The $\\sigma_k$-Loewner-Nirenberg problem on Riemannian manifolds for\n $k<\\frac{n}{2}$",
"authors": "Jonah A. J. Duncan and Luc Nguyen",
"categories": "math.AP math.DG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
It is provided a local characterization of quasi-crystal graphs, by presenting a set of local axioms, similar to the ones introduced by Stembridge for crystal graphs of simply-laced root systems. It is also shown that quasi-crystal graphs satisfying these axioms are closed under the tensor product rec... | arxiv_math | {
"id": "2309.14898",
"title": "A local characterization of quasi-crystal graphs",
"authors": "Alan J. Cain, Ant\\'onio Malheiro, F\\'atima Rodrigues, In\\^es Rodrigues",
"categories": "math.CO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this paper, we propose an alternative technique to dynamic programming for solving stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probabilities. We then propose a regularized version of this problem obtained by s... | arxiv_math | {
"id": "2309.01534",
"title": "An entropy penalized approach for stochastic control problems. Complete\n version",
"authors": "Thibaut Bourdais (OC, ENSTA Paris), Nadia Oudjane (EDF R\\&D),\n Francesco Russo (OC, ENSTA Paris)",
"categories": "math.OC math.PR",
"license": "http://arxiv.org/licenses/nonexclu... |
---
author:
- "Geir Bogfjellmo[^1], Charles Curry[^2], Sylvie Vega--Molino[^3]"
bibliography:
- References.bib
title: The Prytz connections
---
# Introduction and historical background
A *planimeter* is a mechanical or electronic device for measuring the area of a region $\Omega$, typically by tracing its outline. Th... | arxiv_math | {
"id": "2309.02174",
"title": "The Prytz connections",
"authors": "Geir Bogfjellmo, Charles Curry, Sylvie Vega-Molino",
"categories": "math.DG",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this paper we study embeddings between de Branges-Rovnyak spaces $H(b)$ and harmonically weighted Dirichlet spaces $\mathcal{D}(\mu)$ in terms of the boundary spectrum of $b$ and the support of the measure $\mu$, by using elementary reproducing kernel estimates. We completely characterize the embed... | arxiv_math | {
"id": "2310.03604",
"title": "Embedding model and de Branges-Rovnyak spaces in Dirichlet spaces",
"authors": "Carlo Bellavita, Eugenio Alberto Dellepiane",
"categories": "math.FA math.CV",
"license": "http://creativecommons.org/licenses/by-nc-nd/4.0/"
} |
---
abstract: |
We prove that a substitution is aperiodic if and only if some of its associated generating functions are transcendental. These generating functions have a recursive structure arising from the substitution which we use to study their roots in the case of the Fibonacci substitution.
address:
- Departmen... | arxiv_math | {
"id": "2309.16100",
"title": "Generating functions of substitutions",
"authors": "Aisling Pouti, Christopher Ramsey, Nicolae Strungaru",
"categories": "math.CO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We develop a theory of generalized solutions of the nonlinear evolution equations for complex-valued functions of a real positive time variable and $p$-adic spatial variable, which can be seen as non-Archimedean counterparts of the fractional porous medium equation.
In this case, we face the proble... | arxiv_math | {
"id": "2310.03323",
"title": "Existence and uniqueness for $p$-adic counterpart of the porous medium\n equation",
"authors": "Alexandra Antoniouk, Anatoly Kochubei, Oleksii Nikitchenko",
"categories": "math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We use high-low frequency methods developed in the context of decoupling to prove sharp (up to $C_\varepsilon R^\varepsilon$) square function estimates for the moment curve $(t,t^2,\ldots,t^n)$ in $\mathbb R^n$. Our inductive scheme incorporates sharp square function estimates for auxiliary conical se... | arxiv_math | {
"id": "2309.13759",
"title": "A sharp square function estimate for the moment curve in $\\mathbb{R}^n$",
"authors": "Larry Guth and Dominique Maldague",
"categories": "math.CA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
This article is intended towards the study of the bidual of generalized group algebra $L^1(G,\mathcal{A})$ equipped with two Arens product, where $G$ is any locally compact group and $\mathcal{A}$ is a Banach algebra. We show that the left topological center of $(L^1(G)\hat\otimes\mathcal{A})^{**}$ is... | arxiv_math | {
"id": "2309.09525",
"title": "Geometry of Banach algebra $\\mA$ and the bidual of $L^1(G,\\mA)$",
"authors": "Lav Kumar Singh",
"categories": "math.FA",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this paper, combining Nash-Moser iteration and Sallof-Coste type Sobolev ineualities, we establish fundamental and concise $C^0$ and $C^1$ estimates for solutions to a class of nonlinear elliptic equations of the form $$\Delta u(x)+a(x)u(x)\ln u(x)+b(x)u(x)=0,$$ which possesses abundant geometric b... | arxiv_math | {
"id": "2309.13686",
"title": "Boundedness and gradient estimates for solutions to $\\Delta u +\n a(x)u\\log u + b(x)u = 0$ on Riemannian manifolds",
"authors": "Jie Wang and Youde Wang",
"categories": "math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this paper, we prove the strong unique continuation property for the following fourth order degenerate elliptic equation $$\begin{aligned}
\Delta^2_{X}u=Vu,\end{aligned}$$ where $\Delta_{X}=\Delta_{x}+|x|^{2\alpha}\Delta_{y}$ ($0<\alpha\leq1$), with $x\in\mathbb{R}^{m}, y\in\mathbb{R}^{n}$, denot... | arxiv_math | {
"id": "2309.09172",
"title": "Strong unique continuation property for fourth order Baouendi-Grushin\n type subelliptic operators with strongly singular potential",
"authors": "Hairong Liu, Xiaoping Yang",
"categories": "math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
By the means of lower and upper fuzzy approximations we define quasiorders. Their properties are used to prove our main results. First, we characterize those pairs of fuzzy sets which form fuzzy rough sets w.r.t. a t-similarity relation $\theta$ on $U$, for certain t-norms and implicators. Then we est... | arxiv_math | {
"id": "2309.04280",
"title": "On the lattice of fuzzy rough sets",
"authors": "D\\'avid G\\'eg\\'eny, S\\'andor Radeleczki",
"categories": "math.GM",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
address:
- ", , "
- ", , "
author:
- Anwar Ahmad
- Muhammad Ali
- Salman A. Malik
title: "Unraveling Forward and Backward Source Problems for a Nonlocal Integrodifferential Equation: A Journey through Operational Calculus for Dzherbashian-Nersesian Operator"
---
# Introduction and Problems Statement {#intro.mokin}... | arxiv_math | {
"id": "2309.14386",
"title": "Unraveling Forward and Backward Source Problems for a Nonlocal\n Integrodifferential Equation: A Journey through Operational Calculus for\n Dzherbashian-Nersesian Operator",
"authors": "Anwar Ahmad, Muhammad Ali, Salman A. Malik",
"categories": "math.AP",
"license": "http://c... |
---
abstract: |
We consider invertible linear maps with additive spherical bounded noise. We show that minimal attractors of such random dynamical systems are unique, strictly convex and have a continuously differentiable boundary. Moreover, we present an auxiliary finite-dimensional deterministic *boundary map* for ... | arxiv_math | {
"id": "2310.03437",
"title": "Attractors of Linear Maps with Bounded Noise",
"authors": "Jeroen S.W. Lamb, Martin Rasmussen, Wei Hao Tey",
"categories": "math.DS",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this paper, the Laplacian characteristic polynomial of uniform hypergraphs with cut vertices or pendant edges and the Laplacian matching polynomial of uniform hypergraphs are characterized. The multiplicity of the zero Laplacian eigenvalue of uniform hypertrees is given, which proves the conjecture... | arxiv_math | {
"id": "2310.00360",
"title": "The multiplicity of the zero Laplacian eigenvalue of uniform hypertrees",
"authors": "Ge Lin, Changjiang Bu",
"categories": "math.CO",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
# Realizing the symplectic group as a Galois group over the function field $\mathop{\mathrm{\mathbb{F}}}_q(t)$ {#realizing-the-symplectic-group-as-a-galois-group-over-the-function-field-mathopmathrmmathbbf_qt .unnumbered}
Rod Gow and Gary McGuire\
\
School of Mathematics and Statistics\
University College Dublin\
Ire... | arxiv_math | {
"id": "2309.00880",
"title": "Realizing the symplectic group as a Galois group over the function field\n $\\mathbb{F}_q(t)$",
"authors": "Rod Gow and Gary McGuire",
"categories": "math.NT",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
This article answers the question of V.M. Buchstaber about the growth function of a particular $n$-valued group. This question is closely related to discrete integrable systems. In this paper, we will find a formula for the growth function in the case when $n$ is prime. In addition, we will prove a po... | arxiv_math | {
"id": "2309.14251",
"title": "Growth function for an $n$-valued dynamics",
"authors": "M. Chirkov",
"categories": "math.DS nlin.SI",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We consider the $L^{2}$-boundedness of the solution itself of the Cauchy problem for wave equations with time-dependent wave speeds. We treat it in the one-dimensional Euclidean space ${\bf R}$. To study these, we adopt a simple multiplier method by using a special property equiped with the one dimens... | arxiv_math | {
"id": "2309.05986",
"title": "Some attempts on $L^{2}$ boundedness for 1-D wave equations with time\n variable coeffecients",
"authors": "Ryo Ikehata",
"categories": "math.AP",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We show that the local Burkholder functional ${\mathcal B}_K$ is quasiconvex. In the limit of $p$ going to $2$ we find a class of non-polyconvex functionals which are quasiconvex on the set of matrices with positive determinant.
In order to prove the validity of lower semicontinuity arguments in th... | arxiv_math | {
"id": "2309.03495",
"title": "The local Burkholder functional, quasiconvexity and Geometric Function\n Theory",
"authors": "Kari Astala, Daniel Faraco, Andr\\'e Guerra, Aleksis Koski, Jan\n Kristensen",
"categories": "math.AP math.CV",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to constructing a filtration for cluster analysis via persistent homol... | arxiv_math | {
"id": "2310.00350",
"title": "Cluster-Persistence for Weighted Graphs",
"authors": "Omer Bobrowski and Primoz Skraba",
"categories": "math.AT",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
It is known that, for the algebra of functions on a Kleinian singularity, the parameter space of deformations and the parameter space of quantizations coincide. We prove that, for a Kleinian singularity of type $\mathbf{A}$ or $\mathbf{D}$, isomorphisms between the quantizations are essentially the sa... | arxiv_math | {
"id": "2309.17350",
"title": "Automorphism groups of deformations and quantizations of Kleinian\n singularities",
"authors": "Simone Castellan",
"categories": "math.RA math.AG math.RT",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We provide explicit faithful re-embeddings for all hyperelliptic curves of genus at most three and an algorithmic way to construct them. Both in the faithful tropicalization algorithm and the proofs of correctness, we showcase [Oscar]{.smallcaps}-methods for commutative algebra, polyhedral and tropica... | arxiv_math | {
"id": "2310.02947",
"title": "Faithful tropicalization of hyperelliptic curves",
"authors": "Hannah Markwig, Lukas Ristau, Victoria Schleis",
"categories": "math.AG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We study semilinear elliptic equations with the fractional Laplacian in $\mathbb{R}$. The equations with single power nonlinearities have been observed by Weinstein(1987), Frank--Lenzmann(2013) and so on. We focus on the equations with double power nonlinearities and consider the existence of ground s... | arxiv_math | {
"id": "2309.01304",
"title": "On solitary wave solutions to dispersive equations with double power\n nonlinearities",
"authors": "Kaito Kokubu",
"categories": "math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Let $G, H$ be two non-empty graphs and $k$ be a positive integer. The Gallai-Ramsey number $\operatorname{gr}_k(G:H)$ is defined as the minimum positive integer $N$ such that for all $n\geq N$, every $k$-edge-coloring of $K_n$ contains either a rainbow subgraph $G$ or a monochromatic subgraph $H$. The... | arxiv_math | {
"id": "2309.08370",
"title": "Gallai-Ramsey multiplicity for rainbow small trees",
"authors": "Xueliang Li, Yuan Si",
"categories": "math.CO",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex relaxations of sparse StQPs arising from a mixed-binary quadr... | arxiv_math | {
"id": "2310.04340",
"title": "On Tractable Convex Relaxations of Standard Quadratic Optimization\n Problems under Sparsity Constraints",
"authors": "Immanuel Bomze and Bo Peng and Yuzhou Qiu and E. Alper\n Y{\\i}ld{\\i}r{\\i}m",
"categories": "math.OC",
"license": "http://creativecommons.org/licenses/by/4... |
---
abstract: |
In this paper, we study the absolute continuity of radial projections of missing digits measures. We show that for large enough missing digits measures $\lambda$ on $\mathbb{R}^n,n\geq 2,$ for all $x\in\mathbb{R}^n\setminus \mathrm{supp}(\lambda),$ $\Pi_x(\lambda)$ is absolutely continuous with a dens... | arxiv_math | {
"id": "2309.01298",
"title": "On the absolute continuity of radial and linear projections of missing\n digits measures",
"authors": "Han Yu",
"categories": "math.MG math.NT",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
Praeger-Xu graphs are connected, symmetric, 4-regular graphs that are unusual both in that their automorphism groups are large, and in that vertex stabilizer subgroups are also large. Determining number and distinguishing number are parameters that measure the symmetry of a graph by investigating addi... | arxiv_math | {
"id": "2309.11474",
"title": "Symmetry Parameters of Praeger-Xu Graphs",
"authors": "Sally Cockburn and Max Klivans",
"categories": "math.CO",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
This paper studies the effect of perturbations on the gradient flow of a general constrained nonlinear programming problem, where the perturbation may arise from inaccurate gradient estimation in the setting of data-driven optimization. Under suitable conditions on the objective function, the perturbe... | arxiv_math | {
"id": "2310.02930",
"title": "Small-Disturbance Input-to-State Stability of Perturbed Gradient Flows:\n Applications to LQR Problem",
"authors": "Leilei Cui, Zhong-Ping Jiang, Eduardo D. Sontag",
"categories": "math.OC cs.SY eess.SY",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
author:
- |
Ce Xu${}^{a,}$[^1] and Jianqiang Zhao${}^{b,}$[^2]\
a. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, P.R. China\
b. Department of Mathematics, The Bishop's School, La Jolla, CA 92037, USA
title: "**On Some Unramified Families of Motivic Euler Sums**"
---
It is well k... | arxiv_math | {
"id": "2309.06925",
"title": "On Some Unramified Families of Motivic Euler Sums",
"authors": "Ce Xu and Jianqiang Zhao",
"categories": "math.NT math.AG",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
With rectangular doubling weight, a generalized Hardy-Littlewood-Sobolev inequality for rectangular fractional integral operators is verified. The result is a nice application of $M$-linear embedding theorem for dyadic rectangles.
address: Research and Support Center on Higher Education for the Heari... | arxiv_math | {
"id": "2309.15410",
"title": "The rectangular fractional integral operators",
"authors": "Hitoshi Tanaka",
"categories": "math.CA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Renewable energy sources (RES) has become common in modern power systems, helping to address decarbonization and energy security goals. Despite being attractive, RES such as solar and have low inertia and high uncertainty, thus compromising power grid stability and increasing the risk of energy blacko... | arxiv_math | {
"id": "2310.02509",
"title": "Importance Sampling Approach for Dynamic Stochastic Optimal Power Flow\n Control",
"authors": "Aleksander Lukashevich, Aleksander Bulkin, Roland Grinis, Ilya Makarov\n and Yury Maximov",
"categories": "math.OC stat.CO",
"license": "http://arxiv.org/licenses/nonexclusive-distr... |
---
abstract: |
We construct finite time blowup solutions to the parabolic-elliptic Keller-Segel system $$\partial_t u = \Delta u - \nabla \cdot (u \nabla \mathcal{K}_u), \quad -\Delta \mathcal{K}_u = u \quad \textup{in}\;\; \mathbb{R}^d,\; d = 3,4,$$ and derive the final blowup profile $$u(r,T) \sim c_d \frac{|\log ... | arxiv_math | {
"id": "2309.13932",
"title": "Construction of type I-Log blowup for the Keller-Segel system in\n dimensions $3$ and $4$",
"authors": "V. T. Nguyen, N. Nouaili, H. Zaag",
"categories": "math.AP",
"license": "http://creativecommons.org/publicdomain/zero/1.0/"
} |
---
abstract: |
Let $K$ be an algebraically closed field of characteristic zero, $P_n=K[x_1,\ldots ,x_n]$ the polynomial ring, and $W_n(K)$ the Lie algebra of all $K$-derivations on $P_n$. One of the most important subalgebras of $W_n(K)$ is the triangular subalgebra $u_n(K) = P_0\partial_1+\cdots+P_{n-1}\partial_n$,... | arxiv_math | {
"id": "2310.05243",
"title": "On maximality of some solvable and locally nilpotent subalgebras of the\n Lie algebra $W_n(K)$",
"authors": "D. Efimov, M. Sydorov, K. Sysak",
"categories": "math.RA",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We consider two decision problems in infinite groups. The first problem is Subgroup Intersection: given two finitely generated subgroups $\langle \mathcal{G} \rangle, \langle \mathcal{H} \rangle$ of a group $G$, decide whether the intersection $\langle \mathcal{G} \rangle \cap \langle \mathcal{H} \ran... | arxiv_math | {
"id": "2309.08811",
"title": "Subgroup and Coset Intersection in abelian-by-cyclic groups",
"authors": "Ruiwen Dong",
"categories": "math.GR cs.DM",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this paper, we give the Jacobi polynomials for first-order generalized Reed--Muller codes. We show as a corollary the nonexistence of combinatorial $3$-designs in these codes.
address: School of Fundamental Science and Engineering, Waseda University, Tokyo 169--8555, Japan
author:
- Ryosuke Yamaguc... | arxiv_math | {
"id": "2309.01119",
"title": "Jacobi polynomials for first-order generalized Reed--Muller codes",
"authors": "Ryosuke Yamaguchi",
"categories": "math.CO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
author:
- "Diego Chamorro[^1]"
- "Gastón Vergara-Hermosilla[^2]"
title: "**Lebesgue spaces with variable exponent: some applications to the Navier-Stokes equations**"
---
\
**Keywords: Lebesgue spaces of variable exponent; Navier-Stokes equations; mild solutions.**\
**Mathematics Subject Classification: 35Q30; 76D... | arxiv_math | {
"id": "2309.10420",
"title": "Lebesgue spaces with variable exponent: some applications to the\n Navier-Stokes equations",
"authors": "Diego Chamorro (LaMME), Gast\\'on Vergara-Hermosilla (LaMME)",
"categories": "math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
The author has shown that the category of analytic contravariant functors on $\mathbf{gr}$, the category of finitely-generated free groups, is equivalent to the category of left modules over the PROP associated to the Lie operad, working over $\mathbb{Q}$. This exploited properties of the polynomial f... | arxiv_math | {
"id": "2309.07605",
"title": "On the Passi and the Mal'cev functors",
"authors": "Geoffrey Powell",
"categories": "math.AT",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
author:
-
title: Discrepancy estimates related to the fractional parts of $b^n/n$.
---
# Introduction {#sec1}
Let $b\in\mathbb{N}, b\ge2$. In 2013, Cilleruelo et al. [@CKLRS] proved that $$\label{Seq}
\left\{\frac{b^n\pmod{n}}{n}:n\in\mathbb{N}\right\}$$ is dense in $[0,1]$. (See also [@D2] for a number of i... | arxiv_math | {
"id": "2309.14748",
"title": "Discrepancy estimates related to the fractional parts of $b^n/n$",
"authors": "Martin Lind",
"categories": "math.NT",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this paper we define a continuous version of multiple zeta functions with double variables. They can be analytically continued to meromorphic functions on $\mathbb{C}^r$ with only simple poles at some special hyperplanes. The evaluations of these functions at positive integers (continuous multiple ... | arxiv_math | {
"id": "2309.15765",
"title": "A continuous version of multiple zeta values with double variables",
"authors": "Jia Li",
"categories": "math.NT",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We consider the class numbers of imaginary quadratic extensions $F(\sqrt{-p})$, for certain primes $p$, of totally real quadratic fields $F$ which have class number one. Using seminal work of Shintani, we obtain two elementary class number formulas for many such fields. The first expresses the class n... | arxiv_math | {
"id": "2309.04066",
"title": "Class Number Formulas for Certain Biquadratic Fields",
"authors": "Elizabeth Athaide, Emma Cardwell, Christina Thompson",
"categories": "math.NT",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
**LOCALLY NILPOTENT POLYNOMIALS OVER $\mathbb{Z}$** **Sayak Sengupta**\
Department of Mathematics and Statistics, Binghamton University - SUNY, Binghamton, New York, USA\
`sengupta@math.binghamton.edu`\
**Abstract**
For a polynomial $u=u(x)$ in $\mathbb{Z}[x]$ and $r\in\mathbb{Z}$, we consider the orbit of $u$ at $r$... | arxiv_math | {
"id": "2309.10303",
"title": "Locally nilpotent polynomials over $\\mathbb{Z}$",
"authors": "Sayak Sengupta",
"categories": "math.NT math.DS",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We show that for certain sequences escaping to infinity in the $\operatorname{SL}_3\mathbb{R}$ Hitchin component, growth rates of trace functions are described by natural Finsler metrics. More specifically, as the Labourie-Loftin cubic differential gets big, logarithms of trace functions are approxima... | arxiv_math | {
"id": "2309.10290",
"title": "Limits of Convex Projective Surfaces and Finsler Metrics",
"authors": "Charles Reid",
"categories": "math.DG math.DS",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We find Fano threefolds $X$ admitting Kähler-Ricci solitons (KRS) with non-trivial moduli, which are ${\mathbb T}$-varieties of complexity two. More precisely, we show that the weighted K-stability of $(X,\xi_0)$ (where $\xi_0$ is the soliton candidate) is equivalent to certain GIT-stability. In parti... | arxiv_math | {
"id": "2309.14212",
"title": "K\\\"ahler-Ricci solitons on Fano threefolds with non-trivial moduli",
"authors": "Minghao Miao and Linsheng Wang",
"categories": "math.AG math.DG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Wave propagation problems are typically formulated as partial differential equations (PDEs) on unbounded domains to be solved. The classical approach to solving such problems involves truncating them to problems on bounded domains by designing the artificial boundary conditions or perfectly matched la... | arxiv_math | {
"id": "2309.02446",
"title": "Data Generation-based Operator Learning for Solving Partial Differential\n Equations on Unbounded Domains",
"authors": "Jihong Wang, Xin Wang, Jing Li, Bin Liu",
"categories": "math.NA cs.NA math-ph math.MP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Let $S$ and $T$ be smooth projective varieties over an algebraically closed field. Suppose that $S$ is a surface admitting a decomposition of the diagonal. We show that, away from the characteristic of $k$, if an algebraic correspondence $T \to S$ acts trivially on the unramified cohomology, then it a... | arxiv_math | {
"id": "2309.00430",
"title": "Torsion birational motives of surfaces and unramified cohomology",
"authors": "Kanetomo Sato, Takao Yamazaki",
"categories": "math.AG math.KT math.NT",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Describing the equality conditions of the *Alexandrov--Fenchel inequality* .03cmhas been a major open problem for decades. We prove that in the case of convex polytopes, this description is not in the polynomial hierarchy unless the polynomial hierarchy collapses to a finite level. This is the first h... | arxiv_math | {
"id": "2309.05764",
"title": "Equality cases of the Alexandrov--Fenchel inequality are not in the\n polynomial hierarchy",
"authors": "Swee Hong Chan and Igor Pak",
"categories": "math.CO cs.CC cs.CG cs.DM math.MG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
# Main Theorem {#sec:main-thm}
In this section, we prove our main theorem ([\[main th\]](#main th){reference-type="ref" reference="main th"}), characterizing closed symmetric monoidal structures on the category of graphs.
For the remainder of the paper, we impose the following assumption:
[\[assumption4\]]{#assumpti... | arxiv_math | {
"id": "2310.00493",
"title": "Closed symmetric monoidal structures on the category of graphs",
"authors": "Chris Kapulkin and Nathan Kershaw",
"categories": "math.CT math.CO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We prove that the smallest elements of Shi parts and cone type parts exist and form Garside shadows. The latter resolves a conjecture of Parkinson and the second author as well as a conjecture of Hohlweg, Nadeau and Williams.
address:
- Department of Mathematics and Statistics, McGill University, Bur... | arxiv_math | {
"id": "2310.06267",
"title": "A Pair of Garside Shadows",
"authors": "Piotr Przytycki and Yeeka Yau",
"categories": "math.GR math.CO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this work we study the notions of structural and universal completeness both from the algebraic and logical point of view. In particular, we provide new algebraic characterizations of quasivarieties that are actively and passively universally complete, and passively structurally complete. We apply ... | arxiv_math | {
"id": "2309.14151",
"title": "Structural and universal completeness in algebra and logic",
"authors": "Paolo Aglian\\`o and Sara Ugolini",
"categories": "math.LO",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We introduce anisotropic Hölder spaces useful for the study of the regularity theory for non local kinetic operators $\mathscr{L}$ whose prototypal example is $$\mathscr{L}u (t,x,v) = \int_{{\mathbb {R}}^d} \frac{C_{d,s}}{|v - v'|^{d+2s}} (u(t,x,v') - u(t,x,v)) \mathrm{d}v' +
\langle v , \na... | arxiv_math | {
"id": "2309.16350",
"title": "Intrinsic H\\\"older spaces for fractional kinetic operators",
"authors": "Maria Manfredini, Stefano Pagliarani, Sergio Polidoro",
"categories": "math.AP",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this paper, we present controlled finite continuous frames in a finite dimensional Hilbert space and we study some properties of them. Parseval controlled integral frames are presented and we characterize operators that construct controlled integral finite frames.
address:
- $^{1}$Department of Mat... | arxiv_math | {
"id": "2310.05992",
"title": "Controlled finite continuous frames",
"authors": "Hafida Massit, Mohamed Rossafi and Choonkil Park",
"categories": "math.FA",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this paper we study some subgroups and their decompositions in semi-direct product of the twisted virtual braid group $TVB_n$. In particular, the twisted virtual pure braid group $TVP_n$ is the kernel of an epimorphism of $TVB_n$ onto the symmetric group $S_n$. We find the set of generators and def... | arxiv_math | {
"id": "2310.04154",
"title": "Twisted Virtual Braid Group",
"authors": "Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Komal Negi, and Madeti\n Prabhakar",
"categories": "math.GR",
"license": "http://creativecommons.org/licenses/by-sa/4.0/"
} |
---
abstract: |
This short note provides explicit solutions to the linearized Boussinesq equations around the stably stratified Couette flow posed on ${\mathbb T}\times{\mathbb R}$. We consider the long-time behavior of such solutions and prove inviscid damping of the perturbed density and velocity field for any posi... | arxiv_math | {
"id": "2309.08419",
"title": "Explicit solutions and linear inviscid damping in the Euler-Boussinesq\n equation near a stratified Couette flow in the periodic strip",
"authors": "Michele Coti Zelati and Marc Nualart",
"categories": "math.AP physics.flu-dyn",
"license": "http://creativecommons.org/licenses/... |
---
author:
-
-
-
bibliography:
- multimatroid-tens.bib
title: Tensor products of multimatroids and a Brylawski-type formula for the transition polynomial
---
# Introduction
Let $G$ and $H$ be graphs, $G$ loopless and bridgeless, and $H$ with a distinguished edge $e$ that is neither a loop nor a bridge. The tensor... | arxiv_math | {
"id": "2309.00493",
"title": "Tensor products of multimatroids and a Brylawski-type formula for the\n transition polynomial",
"authors": "Iain Moffatt, Steven Noble and Maya Thompson",
"categories": "math.CO",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We establish robust exponential convergence for $r p$--Finite Element Methods (FEMs) applied to fourth order singularly perturbed boundary value problems, in a *balanced norm* which is stronger than the usual energy norm associated with the problem. As a corollary, we get robust exponential convergenc... | arxiv_math | {
"id": "2309.10387",
"title": "Balanced norm estimates for $rp$-Finite Element Methods applied to\n singularly perturbed fourth order boundary value problems",
"authors": "Torsten Lin{\\ss} and Christos Xenophontos",
"categories": "math.NA cs.NA",
"license": "http://creativecommons.org/licenses/by-nc-nd/4.0... |
---
abstract: |
We derive stochastic compressible Euler Equation from a Hamiltonian microscopic dynamics. We consider systems of interacting particles with Hölder noise and potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical measures as... | arxiv_math | {
"id": "2309.15947",
"title": "From Hamiltonian Systems to Compressible Euler Equation driven by\n additive Holder noise",
"authors": "Jesus Correa, Juan Londo\\~no, Christian Olivera",
"categories": "math.AP math.PR",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this paper, we study precise deviations including precise large deviations and moderate deviations for discrete Hawkes processes for large time asymptotics by using mod-$\phi$ convergence theory.
address:
- School of Mathematics, SHUFE
- School of Mathematics, SHUFE
author:
- Ying-Li Wang
- Ping He... | arxiv_math | {
"id": "2309.03627",
"title": "Precise Deviations for a discrete Hawkes process",
"authors": "Ying-Li Wang and Ping He",
"categories": "math.PR",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
**Abstract:** We study implications and consequences of well-posed solutions of Cauchy problems of a Novikov equation describing pseudospherical surfaces. We show that if the co-frame of dual one-forms satisfies certain conditions for a given periodic initial datum, then there exists exactly two famil... | arxiv_math | {
"id": "2309.06291",
"title": "Existence and uniqueness of periodic pseudospherical surfaces emanating\n from Cauchy problems",
"authors": "Nilay Duruk Mutlubas and Igor Leite Freire",
"categories": "math.DG math-ph math.AP math.MP",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In a recent paper, we stated conjectural presentations for the equivariant quantum K ring of partial flag varieties, motivated by physics considerations. In this companion paper, we analyze these presentations mathematically. We prove that if the conjectured relations hold, then they must form a compl... | arxiv_math | {
"id": "2310.03826",
"title": "Quantum K Whitney relations for partial flag varieties",
"authors": "Wei Gu, Leonardo C. Mihalcea, Eric Sharpe, Weihong Xu, Hao Zhang, and\n Hao Zou",
"categories": "math.AG hep-th math.CO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Problem 21 of Brauer's list of problems from 1963 asks whether for any positive integer $k$ there are finitely many isomorphism classes of groups that occur as the defect group of a block with $k$ irreducible characters. We solve this problem for principal blocks. Another long-standing open problem (f... | arxiv_math | {
"id": "2310.00134",
"title": "Brauer's problem 21 for principal blocks",
"authors": "Alexander Moret\\'o, Noelia Rizo, and A. A. Schaeffer Fry",
"categories": "math.GR math.RT",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
arxiv_math | {
"id": "2310.05272",
"title": "Liquid functional calculus",
"authors": "Kendric Schefers",
"categories": "math.AG math-ph math.MP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} | |
---
author:
- Oliver Hinder
bibliography:
- master.bib
title: Worst-case analysis of restarted primal-dual hybrid gradient on totally unimodular linear programs
---
# Introduction
Consider the following linear program:
[\[primal-LP\]]{#primal-LP label="primal-LP"}
\_x \^m_2 c\^x\
Ax = b\
x
and its dual:
\_y \^m_1... | arxiv_math | {
"id": "2309.03988",
"title": "Worst-case analysis of restarted primal-dual hybrid gradient on totally\n unimodular linear programs",
"authors": "Oliver Hinder",
"categories": "math.OC",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We consider a superposition operator of the form $$\int_{[0, 1]} (-\Delta)^s u\, d\mu(s),$$ for a signed measure $\mu$ on the interval of fractional exponents $[0,1]$, joined to a nonlinearity whose term of homogeneity equal to one is "jumping", i.e. it may present different coefficients in front of t... | arxiv_math | {
"id": "2309.13895",
"title": "An existence theory for superposition operators of mixed order subject\n to jumping nonlinearities",
"authors": "Serena Dipierro, Kanishka Perera, Caterina Sportelli and Enrico\n Valdinoci",
"categories": "math.AP",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We study pattern avoidance for permutations of $[n]$ with a fixed leading term and find exact formulas for the number of permutations avoiding single and pairs of patterns of length three. Our counting argument is then adapted to enumerating permutations avoiding both 3412 and 3421 by leading terms. I... | arxiv_math | {
"id": "2309.15964",
"title": "Enumerating pattern-avoiding permutations by leading terms",
"authors": "\\\"Omer E\\u{g}ecio\\u{g}lu, Collier Gaiser, Mei Yin",
"categories": "math.CO",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
author:
- Elías Mochán
bibliography:
- Bibliografia.bib
title: Polytopality of 2-orbit maniplexes
---
# Introduction {#s:Intro}
Abstract polytopes are posets with some properties that generalize those of the face lattice of convex and skeletal polytopes. Since their introduction by Schulte in [@EgonPHD], the main... | arxiv_math | {
"id": "2309.15791",
"title": "Politopality of 2-orbit maniplexes",
"authors": "El\\'ias Moch\\'an",
"categories": "math.CO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We will develop some elements in stochastic analysis in the Wasserstein space $\mathbb{P}_2(M)$ over a compact Riemannian manifold $M$, such as intrinsic Itô formulae, stochastic regular curves and parallel translations along them. We will establish the existence of parallel translations along regular... | arxiv_math | {
"id": "2309.08702",
"title": "Stochastic differential equations and stochastic parallel translations\n in the Wasserstein space",
"authors": "Hao Ding, Shizan Fang, Xiang-dong Li",
"categories": "math.PR",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this work, we consider the generalized Benjamin-Bona-Mahony equation $$\partial_t u+\partial_x u+\partial_x( |u|^pu)-\partial_t \partial_x^{2}u=0,
\quad(t,x) \in \mathbb{R} \times \mathbb{R},$$ with $p>4$. This equation has the traveling wave solutions $\phi_{c}(x-ct),$ for any frequency $c>1.$... | arxiv_math | {
"id": "2309.00791",
"title": "Instability of the solitary waves for the Generalized\n Benjamin-Bona-Mahony Equation",
"authors": "Rui Jia and Yifei Wu",
"categories": "math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Under investigation in this paper is the dynamics and probability of heads in the toss of a coin with symmetric inhomogeneous density. Such coins are assumed to have diagonal inertia matrix. The rotational motion of the coin is determined by the initial angular momentum and initial position of the coi... | arxiv_math | {
"id": "2310.02662",
"title": "Dynamics and Probability in the Toss of a Coin with Symmetric\n Inhomogeneous Density",
"authors": "Shilun Li",
"categories": "math.PR math.DS",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
Finite dimensional (FD) models, i.e., deterministic functions of time/space and finite sets of random variables, are constructed for target vector-valued random processes/fields. They are required to have two properties. First, standard Monte Carlo algorithms can be used to generate their samples, ref... | arxiv_math | {
"id": "2310.03183",
"title": "Extremes of vector-valued processes by finite dimensional models",
"authors": "Hui Xu and Mircea D. Grigoriu",
"categories": "math.PR",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
This paper studies a class of strongly monotone games involving non-cooperative agents that optimize their own time-varying cost functions. We assume that the agents can observe other agents' historical actions and choose actions that best respond to other agents' previous actions; we call this a best... | arxiv_math | {
"id": "2309.00307",
"title": "Convergence Analysis of the Best Response Algorithm for Time-Varying\n Games",
"authors": "Zifan Wang, Yi Shen, Michael M. Zavlanos, Karl H. Johansson",
"categories": "math.OC cs.GT cs.MA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We show that the endomorphisms of a compact connected group that extend to endomorphisms of every compact overgroup are precisely the trivial one and the inner automorphisms; this is an analogue, for compact connected groups, of results due to Schupp and Pettet on discrete groups (plain or finite). A ... | arxiv_math | {
"id": "2309.12791",
"title": "Extensible endomorphisms of compact groups",
"authors": "Alexandru Chirvasitu",
"categories": "math.GR math.CT math.RT",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We answer an open problem posed by Mossel--Oleszkiewicz--Sen regarding relations between $p$-log-Sobolev inequalities for $p\in(0,1]$. We show that for any interval $I\subset(0,1]$, there exist $q,p\in I$, $q<p$, and a measure $\mu$ for which the $q$-log-Sobolev inequality holds, while the $p$-log-Sob... | arxiv_math | {
"id": "2309.01263",
"title": "$P$-log-Sobolev inequalities on $\\mathbb{N}$",
"authors": "Bart{\\l}omiej Polaczyk",
"categories": "math.PR",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
Using a description of the cohomology of local systems on the moduli space of abelian surfaces with a full level two structure, together with a computation of Euler characteristics we find the isotypical decomposition, under the symmetric group on 6 letters, of spaces of vector-valued Siegel modular f... | arxiv_math | {
"id": "2309.04388",
"title": "Dimension formulas for spaces of vector-valued Siegel modular forms of\n degree two and level two",
"authors": "Jonas Bergstr\\\"om and Fabien Cl\\'ery",
"categories": "math.NT math.AG",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In highly diffusion regimes when the mean free path $\varepsilon$ tends to zero, the radiative transfer equation has an asymptotic behavior which is governed by a diffusion equation and the corresponding boundary condition. Generally, a numerical scheme for solving this problem has the truncation erro... | arxiv_math | {
"id": "2309.09394",
"title": "Numerical analysis of a spherical harmonic discontinuous Galerkin method\n for scaled radiative transfer equations with isotropic scattering",
"authors": "Qiwei Sheng, Cory Hauck, Yulong Xing",
"categories": "math.NA cs.NA",
"license": "http://arxiv.org/licenses/nonexclusive-d... |
---
abstract: |
We consider probability measures arising from the Cauchy summation identity for the LLT (Lascoux--Leclerc--Thibon) symmetric polynomials of rank $n \geqslant 1$. We study the asymptotic behaviour of these measures as one of the two sets of polynomials in the Cauchy identity stays fixed, while the othe... | arxiv_math | {
"id": "2309.05970",
"title": "Coloured corner processes from asymptotics of LLT polynomials",
"authors": "Amol Aggarwal, Alexei Borodin, Michael Wheeler",
"categories": "math.PR math-ph math.CO math.MP",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
A version of Radon-Nikodym theorem for the Choquet integral w.r.t. monotone measures is proved. Without any presumptive condition, we obtain a necessary and sufficient condition for the ordered pair $(\mu, \nu)$ of finite monotone measures to have the so-called Radon-Nikodym property related to a nonn... | arxiv_math | {
"id": "2309.11868",
"title": "A Radon-Nikodym theorem for monotone measures",
"authors": "Yao Ouyang and Jun Li",
"categories": "math.FA",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We provide a criterion for certain algebraic objects over Jacobson schemes to be forms of each other based on their behaviour at closed fibres. This criterion permits to answer a question that I. Burban had asked the authors.
Reductive group scheme, torsor, Lie algebras.\
14L30, 17B67, 11E72, 14E... | arxiv_math | {
"id": "2309.08212",
"title": "Fiberwise criteria for Twisted Forms of Algebraic Structures",
"authors": "Philippe Gille (ICJ, AGL), Arturo Pianzola (CAECE)",
"categories": "math.AG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We prove that two closed subsets of complex space $\mathbb{C}^n$ with corresponding complex homothetic sections (projections) are complex homothetic. The proof uses a new Helly-type theorem for cosets of closed subgroups of $\mathbb{S}^1$.
address: UNAM, Mexico
author:
- Jorge Luis Arocha
- Javier Bra... | arxiv_math | {
"id": "2310.06206",
"title": "Complex homothetic sections and projections through a Helly type Theorem\n for cosets of $\\S^1$",
"authors": "Jorge Luis Arocha, Javier Bracho and Luis Montejano",
"categories": "math.MG",
"license": "http://creativecommons.org/publicdomain/zero/1.0/"
} |
---
abstract: |
We discuss Cartan-Schouten metrics (Riemannian or pseudo-Riemannian metrics that are parallel with respect to the Cartan-Schouten canonical connection) on perfect Lie groups and in particular, on cotangent bundles of simple Lie groups. Applications are foreseen in Information Geometry. Throughout this... | arxiv_math | {
"id": "2310.02114",
"title": "On dual quaternions, dual split quaternions and Cartan-Schouten metrics\n on perfect Lie groups",
"authors": "Andre Diatta, Bakary Manga and Fatimata Sy",
"categories": "math.DG cs.IT math-ph math.IT math.MG math.MP",
"license": "http://creativecommons.org/licenses/by-nc-nd/4.... |
---
abstract: |
We produce the first regular unimodular triangulation of an arbitrary matroid base polytope. We then extend our triangulation to integral generalized permutahedra. Prior to this work it was unknown whether each matroid base polytope admitted a unimodular cover.
author:
- Spencer Backman
- Gaku Liu
bib... | arxiv_math | {
"id": "2309.10229",
"title": "A Regular Unimodular Triangulation of the Matroid Base Polytope",
"authors": "Spencer Backman, Gaku Liu",
"categories": "math.CO math.MG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We investigate elliptic irregular obstacle problems with $p$-growth involving measure data. Emphasis is on the strongly singular case $1 < p \le 2-1/n$, and we obtain several new comparison estimates to prove gradient potential estimates in an intrinsic form. Our approach can be also applied to derive... | arxiv_math | {
"id": "2309.09835",
"title": "Singular elliptic measure data problems with irregular obstacles",
"authors": "Sun-Sig Byun, Kyeong Song, Yeonghun Youn",
"categories": "math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We study the singular series associated to a cubic form with integer coefficients. If the number of variables is at least $10$, we prove the absolute convergence (and hence positivity) under the assumption of Davenport's Geometric Condition, improving on a result of Heath-Brown. For the case of $9$ va... | arxiv_math | {
"id": "2310.02036",
"title": "The singular series of a cubic form in many variables and a new proof of\n Davenport's Shrinking Lemma",
"authors": "Christian Bernert",
"categories": "math.NT",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
Classifying the nonflat hypersurfaces in Euclidean space $f\colon M^n\to\mathbb{R}^{n+1}$ that locally admit smooth infinitesimal deformations that preserve the Gauss map infinitesimally was a problem only considered by Schouten [@Sc] in 1928. He found two conditions that are necessary and sufficient,... | arxiv_math | {
"id": "2309.16086",
"title": "The infinitesimal deformations of hypersurfaces that preserve the Gauss\n map",
"authors": "Marcos Dajczer and Miguel Ibieta Jimenez",
"categories": "math.DG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
The performance of sparse matrix computation highly depends on the matching of the matrix format with the underlying structure of the data being computed on. Different sparse matrix formats are suitable for different structures of data. Therefore, the first challenge is identifying the matrix structur... | arxiv_math | {
"id": "2309.02442",
"title": "Observe Locally, Classify Globally: Using GNNs to Identify Sparse Matrix\n Structure",
"authors": "Khaled Abdelaal and Richard Veras",
"categories": "math.NA cs.AI cs.LG cs.NA cs.PF",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We generalize a Furstenberg-type result of Orponen-Shmerkin to higher dimensions, leading to an $\varepsilon$-improvement in Kaufman's projection theorem for hyperplanes and an unconditional discretized radial projection theorem in the spirit of Orponen-Shmerkin-Wang. Our proof relies on a new inciden... | arxiv_math | {
"id": "2309.04097",
"title": "Discretized Radial Projections in $\\mathbb{R}^d$",
"authors": "Kevin Ren",
"categories": "math.CA math.CO math.MG",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We show how to construct, for a Lagrangian of arbitrary order, a Lepage equivalent satisfying the closure property: that the Lepage equivalent vanishes precisely when the Lagrangian is null. The construction uses a homotopy operator for the horizontal differential of the variational bicomplex. A choic... | arxiv_math | {
"id": "2309.01594",
"title": "Lepage equivalents and the Variational Bicomplex",
"authors": "D. J. Saunders",
"categories": "math.DG",
"license": "http://creativecommons.org/licenses/by-nc-sa/4.0/"
} |
---
abstract: |
Consider the Schrödinger--Bopp--Podolsky system $$\tag{$\mathrm{SBP}_\epsilon$}\label{SBP_epsilon}
\begin{cases}
-\epsilon^2\Delta u+\parens{V+K\phi}u=u\abs{u}^{p-1};\\
\Delta^2\phi-\Delta\phi=4\pi K u^2
\end{cases}
~\text{in}~\mathbb{R}^3$$ for sufficiently small $\epsilon>0$, where... | arxiv_math | {
"id": "2309.01841",
"title": "Concentrated solutions to the Schr\\\"odinger--Bopp--Podolsky system with\n a positive potential",
"authors": "Gustavo de Paula Ramos",
"categories": "math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Over the last two decades, the field of geometric curve evolutions has attracted significant attention from scientific computing. One of the most popular numerical methods for solving geometric flows is the so-called BGN scheme, which was proposed by Barrett, Garcke, and Nürnberg (J. Comput. Phys., 22... | arxiv_math | {
"id": "2309.12875",
"title": "A second-order in time, BGN-based parametric finite element method for\n geometric flows of curves",
"authors": "Wei Jiang, Chunmei Su and Ganghui Zhang",
"categories": "math.NA cs.NA",
"license": "http://creativecommons.org/publicdomain/zero/1.0/"
} |
---
abstract: |
We prove some polynomial identities from which we deduce congruences modulo $p^2$ for the Fermat quotient $\frac{2^p-2}{p}$ for any odd prime $p$ (Proposition 1 and Theorem 1). These congruences are simpler than the one obtained by Jothilingam in 1985 ([@Jothilingam]) which involves listing quadratic ... | arxiv_math | {
"id": "2309.09491",
"title": "Polynomial identities and Fermat quotients",
"authors": "Takao Komatsu and B. Sury",
"categories": "math.NT",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We study the asymptotic behavior and the scattering from infinity problem for the massive Maxwell-Klein-Gordon system in the Lorenz gauge, which were previously only studied for the massless system. For a general class of initial data, in particular of nonzero charge, we derive the precise asymptotic ... | arxiv_math | {
"id": "2309.15834",
"title": "Asymptotics and Scattering for massive Maxwell-Klein-Gordon equations",
"authors": "Xuantao Chen",
"categories": "math.AP math-ph math.MP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Given a configuration of pebbles on the vertices of a graph $G$, a pebbling move removes two pebbles from a vertex and puts one pebble on an adjacent vertex. The pebbling number of a graph $G$ is the smallest number of pebbles required such that, given an arbitrary initial configuration of pebbles, on... | arxiv_math | {
"id": "2310.00580",
"title": "Lollipop and Cubic Weight Functions for Graph Pebbling",
"authors": "Marshall Yang, Carl Yerger, Runtian Zhou",
"categories": "math.CO",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
Anisotropic diffusion processes with a diffusion tensor are important in image analysis, physics, and engineering. However, their numerical approximation has a strong impact on dissipative artefacts and deviations from rotation invariance. In this work, we study a large family of finite difference dis... | arxiv_math | {
"id": "2309.05575",
"title": "Anisotropic Diffusion Stencils: From Simple Derivations over Stability\n Estimates to ResNet Implementations",
"authors": "Karl Schrader, Joachim Weickert, Michael Krause",
"categories": "math.NA cs.LG cs.NA eess.IV",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/... |
---
abstract: |
We present the development and analysis of a reinforcement learning (RL) algorithm designed to solve continuous-space mean field game (MFG) and mean field control (MFC) problems in a unified manner. The proposed approach pairs the actor-critic (AC) paradigm with a representation of the mean field dist... | arxiv_math | {
"id": "2309.10953",
"title": "Deep Reinforcement Learning for Infinite Horizon Mean Field Problems in\n Continuous Spaces",
"authors": "Andrea Angiuli, Jean-Pierre Fouque, Ruimeng Hu, Alan Raydan",
"categories": "math.OC cs.LG",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We consider non-local energy forms of fractional Laplace type on quasicircles and prove that they can be approximated by similar energy forms on polygonal curves. The approximation is in terms of generalized Mosco convergence along a sequence of varying Hilbert spaces. The domains of the energy forms ... | arxiv_math | {
"id": "2310.04549",
"title": "Non-local boundary energy forms for quasidiscs: Codimension gap and\n approximation",
"authors": "Simone Creo, Michael Hinz, Maria Rosaria Lancia",
"categories": "math.FA math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
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