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Asymptotic distributions of the number of zeros of random polynomials in Hayes equivalence class over a finite field 有限域上 Hayes 等价类中随机多项式零点数的渐近分布
IF 1.2 3区 数学
Finite Fields and Their Applications Pub Date : 2024-11-06 DOI: 10.1016/j.ffa.2024.102524
Zhicheng Gao
{"title":"Asymptotic distributions of the number of zeros of random polynomials in Hayes equivalence class over a finite field","authors":"Zhicheng Gao","doi":"10.1016/j.ffa.2024.102524","DOIUrl":"10.1016/j.ffa.2024.102524","url":null,"abstract":"<div><div>Hayes equivalence is defined on monic polynomials over a finite field <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> in terms of the prescribed leading coefficients and the residue classes modulo a given monic polynomial <em>Q</em>. We study the distribution of the number of zeros in a random polynomial over finite fields in a given Hayes equivalence class. It is well known that the number of distinct zeros of a random polynomial over <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> is asymptotically Poisson with mean 1. We show that this is also true for random polynomials in any given Hayes equivalence class. Asymptotic formulas are also given for the number of such polynomials when the degree of such polynomials is proportional to <em>q</em> and the degree of <em>Q</em> and the number of prescribed leading coefficients are bounded by <span><math><msqrt><mrow><mi>q</mi></mrow></msqrt></math></span>. When <span><math><mi>Q</mi><mo>=</mo><mn>1</mn></math></span>, the problem is equivalent to the study of the distance distribution in Reed-Solomon codes. Our asymptotic formulas extend some earlier results and imply that all words for a large family of Reed-Solomon codes are ordinary, which further supports the well-known <em>Deep-Hole</em> Conjecture.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conflict-free Incidence Coloring of Outer-1-planar Graphs 外-1-平面图的无冲突入射着色
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1033-7
Meng-ke Qi, Xin Zhang
{"title":"Conflict-free Incidence Coloring of Outer-1-planar Graphs","authors":"Meng-ke Qi,&nbsp;Xin Zhang","doi":"10.1007/s10255-024-1033-7","DOIUrl":"10.1007/s10255-024-1033-7","url":null,"abstract":"<div><p>An incidence of a graph <i>G</i> is a vertex-edge pair (<i>v, e</i>) such that <i>v</i> is incidence with <i>e</i>. A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences (<i>u, e</i>) and (<i>v, f</i>) get distinct colors if and only if they conflict each other, i.e., (i) <i>u = v</i>, (ii) <i>uv</i> is <i>e</i> or <i>f</i>, or (iii) there is a vertex <i>w</i> such that <i>uw</i> = <i>e</i> and <i>vw</i> = <i>f</i>. The minimum number of colors used among all conflict-free incidence colorings of a graph is the conflict-free incidence chromatic number. A graph is outer-1-planar if it can be drawn in the plane so that vertices are on the outer-boundary and each edge is crossed at most once. In this paper, we show that the conflict-free incidence chromatic number of an outer-1-planar graph with maximum degree Δ is either 2Δ or 2Δ + 1 unless the graph is a cycle on three vertices, and moreover, all outer-1-planar graphs with conflict-free incidence chromatic number 2Δ or 2Δ + 1 are completely characterized. An efficient algorithm for constructing an optimal conflict-free incidence coloring of a connected outer-1-planar graph is given.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Ananthakrishna Model Under Non-synchronous Perturbation 非同步扰动下的阿南塔克里什纳模型
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1077-8
Yi-wen Tao, Sue Ann Campbell, Jing-li Ren
{"title":"The Ananthakrishna Model Under Non-synchronous Perturbation","authors":"Yi-wen Tao,&nbsp;Sue Ann Campbell,&nbsp;Jing-li Ren","doi":"10.1007/s10255-024-1077-8","DOIUrl":"10.1007/s10255-024-1077-8","url":null,"abstract":"<div><p>The Ananthakrishna model, seeking to explain the Portevin-Le Chatelier effect, is studied with or without non-synchronous perturbations. For the unperturbed model, Bogdanov-Takens bifurcation and zero-Hopf bifurcation are detected. For the perturbed model, rich dynamical behaviors are given by researching the Poincaré map, including solutions of different periods, quasi-periodic solutions, chaotic solutions, and bistability. Moreover, an augmented temperature-dependent perturbation amplitude induces a transition from non-serrated to serrated flow on the stress-time curve. Notably, on the stress-strain curve, the phenomenon of repeated yielding diminishes with an increase in the value of a temperature-dependent parameter, while it persists with an increase in the value of a temperature-independent parameter. Sensitivity analysis sheds light on the factors exerting the most significant influence on dislocation density.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal temporal decay rates of solutions for combustion of compressible fluids 可压缩流体燃烧解决方案的最佳时间衰减率
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-06 DOI: 10.1007/s13324-024-00984-1
Shengbin Fu, Wenting Huang, Weiwei Wang
{"title":"Optimal temporal decay rates of solutions for combustion of compressible fluids","authors":"Shengbin Fu,&nbsp;Wenting Huang,&nbsp;Weiwei Wang","doi":"10.1007/s13324-024-00984-1","DOIUrl":"10.1007/s13324-024-00984-1","url":null,"abstract":"<div><p>This paper investigates the temporal decay rates of solutions to the Cauchy problem of a model, which describes the combustion of the compressible fluid. Suppose that the initial data is a small perturbation near the equilibrium state <span>((rho _infty , 0,theta _infty ,zeta ))</span>, where <span>(rho _infty &gt;0)</span>, <span>(theta _infty &lt;theta _I)</span> (the ignition temperature), and <span>(0&lt; zeta leqslant 1)</span>, we first establish the global-in-time existence of strong solutions via a standard continuity argument. With the additional <span>(L^1)</span>-integrability of the initial perturbation, we then employ the Fourier theory and the cancellation mechanism of low-medium frequent part to derive the optimal temporal decay rates of all-order derivatives of strong solutions. Our work is a natural continuation of previous result in the case of <span>(theta _infty &gt;theta _I)</span> discussed in Wang and Wen (Sci China Math 65:1199–1228 (2022).</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Thickness of Some Complete Bipartite and Tripartite Graphs 一些完整二方图和三方图的厚度
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1128-1
Si-wei Hu, Yi-chao Chen
{"title":"The Thickness of Some Complete Bipartite and Tripartite Graphs","authors":"Si-wei Hu,&nbsp;Yi-chao Chen","doi":"10.1007/s10255-024-1128-1","DOIUrl":"10.1007/s10255-024-1128-1","url":null,"abstract":"<div><p>In this paper, we obtain the thickness for some complete <i>k</i>–partite graphs for <i>k</i> = 2, 3. We first compute the thickness of <i>K</i><sub><i>n,n</i>+8</sub> by giving a planar decomposition of <i>K</i><sub>4<i>k</i>−1,4<i>k</i>+7</sub> for <i>k</i> ≥ 3. Then, two planar decompositions for <i>K</i><sub>1,<i>g,g</i>(<i>g</i>−1)</sub> when <i>g</i> is even and for <span>(K_{1,g,{1over{2}}(g-1)^{2}})</span> when <i>g</i> is odd are obtained. Using a recursive construction, we also obtain the thickness for some complete tripartite graphs. The results here support the long-standing conjecture that the thickness of <i>K</i><sub><i>m,n</i></sub> is <span>(lceil {mnover{2(m+n-2)}}rceil)</span> for any positive integers <i>m, n</i>.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Backward Doubly Stochastic Differential Equations with Stochastic Non-Lipschitz Coefficients 具有随机非 Lipschitz 系数的后向双随机微分方程
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1137-0
Si-yan Xu, Yi-dong Zhang
{"title":"Backward Doubly Stochastic Differential Equations with Stochastic Non-Lipschitz Coefficients","authors":"Si-yan Xu,&nbsp;Yi-dong Zhang","doi":"10.1007/s10255-024-1137-0","DOIUrl":"10.1007/s10255-024-1137-0","url":null,"abstract":"<div><p>In this paper, we prove an existence and uniqueness theorem for backward doubly stochastic differential equations under a new kind of stochastic non-Lipschitz condition which involves stochastic and time-dependent condition. As an application, we use the result to obtain the existence of stochastic viscosity solution for some nonlinear stochastic partial differential equations under stochastic non-Lipschitz conditions.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the well-posedness of boundary value problems for higher order Dirac operators in Rm 论 Rm 中高阶狄拉克算子边界值问题的好求性
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-11-06 DOI: 10.1016/j.jde.2024.10.036
Daniel Alfonso Santiesteban , Ricardo Abreu Blaya , Juan Bory Reyes
{"title":"On the well-posedness of boundary value problems for higher order Dirac operators in Rm","authors":"Daniel Alfonso Santiesteban ,&nbsp;Ricardo Abreu Blaya ,&nbsp;Juan Bory Reyes","doi":"10.1016/j.jde.2024.10.036","DOIUrl":"10.1016/j.jde.2024.10.036","url":null,"abstract":"<div><div>Clifford analysis offers suited framework for a unified treatment of higher-dimensional phenomena. This paper is concerned with boundary value problems for higher order Dirac operators, which are directly related to the Lamé-Navier and iterated Laplace operators. The conditioning of the problems upon the boundaries of the considered domains ensures their well-posedness in the sense of Hadamard.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Corrigendum to “Classifying decomposition and wavelet coorbit spaces using coarse geometry” [J. Funct. Anal. 283(9) (2022) 109637] 利用粗几何学对分解和小波同位空间进行分类》[《函数分析杂志》283(9) (2022) 109637]勘误表
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-11-06 DOI: 10.1016/j.jfa.2024.110714
Hartmut Führ , René Koch
{"title":"Corrigendum to “Classifying decomposition and wavelet coorbit spaces using coarse geometry” [J. Funct. Anal. 283(9) (2022) 109637]","authors":"Hartmut Führ ,&nbsp;René Koch","doi":"10.1016/j.jfa.2024.110714","DOIUrl":"10.1016/j.jfa.2024.110714","url":null,"abstract":"","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ℓ1 -based Bayesian Ideal Point Model for Multidimensional Politics 基于 ℓ1 的多维政治贝叶斯理想点模型
IF 3.7 1区 数学
Journal of the American Statistical Association Pub Date : 2024-11-06 DOI: 10.1080/01621459.2024.2425461
Sooahn Shin, Johan Lim, Jong Hee Park
{"title":"ℓ1 -based Bayesian Ideal Point Model for Multidimensional Politics","authors":"Sooahn Shin, Johan Lim, Jong Hee Park","doi":"10.1080/01621459.2024.2425461","DOIUrl":"https://doi.org/10.1080/01621459.2024.2425461","url":null,"abstract":"Ideal point estimation methods in the social sciences lack a principled approach for identifying multidimensional ideal points. We present a novel method for estimating multidimensional ideal point...","PeriodicalId":17227,"journal":{"name":"Journal of the American Statistical Association","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142589037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lp Solution of Reflected BSDEs with One Continuous Barrier and Quasi-linear Growth Generators 具有一个连续障碍和准线性增长发生器的反射 BSDE 的 Lp 解法
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1133-4
Sheng-jun Fan
{"title":"Lp Solution of Reflected BSDEs with One Continuous Barrier and Quasi-linear Growth Generators","authors":"Sheng-jun Fan","doi":"10.1007/s10255-024-1133-4","DOIUrl":"10.1007/s10255-024-1133-4","url":null,"abstract":"<div><p>This paper is devoted to solving a reflected backward stochastic differential equation (BSDE in short) with one continuous barrier and a quasi-linear growth generator <i>g</i>, which has a linear growth in (<i>y</i>, <i>z</i>), except the upper direction in case of <i>y</i> &lt; 0, and is more general than the usual linear growth generator. By showing the convergence of a penalization scheme we prove existence and comparison theorem of the minimal <i>L</i><sup><i>p</i></sup> (<i>p</i> &gt; 1) solutions for the reflected BSDEs. We also prove that the minimal <i>L</i><sup><i>p</i></sup> solution can be approximated by a sequence of <i>L</i><sup><i>p</i></sup> solutions of certain reflected BSDEs with Lipschitz generators.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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