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Finite groups with gcd(χ(1), χc (1)) a prime gcd(χ(1), χc (1))为质数的有限群

IF 1.7 4区数学 Q1 MATHEMATICS

Open Mathematics

Pub Date : 2024-08-22 DOI: 10.1515/math-2024-0037

Li Gao, Zhongbi Wang, Guiyun Chen

The aim of this article is to study how the greatest common divisor of the degree and codegree of an irreducible character of a finite group influences its structure. We study a finite group <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>G</m:mi> </m:math> G with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="normal">gcd</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>χ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> <m:msup> <m:mrow> <m:mi>χ</m:mi> </m:mrow> <m:mrow> <m:mi>c</m:mi> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {rm{gcd }}left(chi left(1),{chi }^{c}left(1)) a prime for almost all irreducible characters <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>χ</m:mi> </m:math> chi of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>G</m:mi> </m:math> G , and obtain the following two conclusions: (1) There does not exist any finite group <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>G</m:mi> </m:math> G such that <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="normal">gcd</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>χ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> <m:msup> <m:mrow> <m:mi>χ</m:mi> </m:mrow> <m:mrow> <m:mi>c</m:mi> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mo>)</m:mo> </m:mrow> <

本文的目的是研究有限群不可还原特征的度数和代号的最大公因子如何影响其结构。我们研究一个有限群 G，其 gcd ( χ ( 1 ) , χ c ( 1 ) ) {rm{gcd }}left(chi left(1),{chi}^{c}left(1))是 G G 的几乎所有不可还原字符 χ chi 的素数，并得到以下两个结论：（1）不存在任何有限群 G G，使得 gcd ( χ ( 1 ) , χ c ( 1 ) ) {chi left(1),{chi}^{c}left(1))是素数，对于每个 χ ∈ Irr ( G ) ♯ chi in {rm{Irr}}{left(G)}^{sharp }，其中 Irr ( G ) ♯ chi 在{rm{Irr}}{left(G)}^{sharp }中。 (2) 让 G G 是一个有限群，如果 gcd ( χ ( 1 ) , χ c ( 1 ) ) (1),{chi }^{c}left(1)) 是素数，对于每个 χ ∈ Irr ( G ) Lin ( G ) chi leftin {rm{Irr}}left(G)backslash {rm{Lin}}left(G) 、则 G G 是可解的，其中 Lin ( G ) {rm{Lin}}left(G) 是 G G 的所有线性不可还原字符的集合。

引用次数: 0

Small values and functional laws of the iterated logarithm for operator fractional Brownian motion 算子分数布朗运动的迭代对数的小值和函数规律

IF 1.7 4区数学 Q1 MATHEMATICS

Open Mathematics

Pub Date : 2024-08-22 DOI: 10.1515/math-2024-0045

Wensheng Wang, Jingshuang Dong

The multivariate Gaussian random fields with matrix-based scaling laws are widely used for inference in statistics and many applied areas. In such contexts, interests are often Hölder regularities of spatial surfaces in any given direction. This article analyzes the almost sure sample function behavior for operator fractional Brownian motion, including multivariate fractional Brownian motion. We obtain the estimations of small ball probability and the strongly locally nondeterministic for operator fractional Brownian motion in any given direction. By applying these estimates, we obtain Chung type laws of the iterated logarithm for operator fractional Brownian motion. Our results show that the precise Hölder regularities of these spatial surfaces are completely determined by the real parts of the eigenvalues of self-similarity exponent and the covariance matrix at time point 1.

具有基于矩阵的缩放规律的多元高斯随机场被广泛用于统计学和许多应用领域的推理。在这种情况下，人们感兴趣的往往是任意给定方向上空间曲面的荷尔德规则性。本文分析了算子分数布朗运动（包括多元分数布朗运动）的几乎确定的样本函数行为。我们得到了任意给定方向上算子分数布朗运动的小球概率和强局部非确定性的估计值。通过应用这些估计值，我们得到了算子分数布朗运动迭代对数的 Chung 型定律。我们的结果表明，这些空间曲面的精确霍尔德规则性完全由时间点 1 的自相似性指数和协方差矩阵特征值的实部决定。

引用次数: 0

The limit theorems on extreme order statistics and partial sums of i.i.d. random variables 极序统计和 i.i.d. 随机变量部分和的极限定理

IF 1.7 4区数学 Q1 MATHEMATICS

Open Mathematics

Pub Date : 2024-08-17 DOI: 10.1515/math-2024-0047

Gaoyu Li, Chengxiu Ling, Zhongquan Tan

This article proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.

本文证明了极序统计与独立且同分布随机变量部分和的联合版本的几个弱极限定理。这些结果还扩展到几乎确定的极限版本。

引用次数: 0

Convergence rate of the truncated Euler-Maruyama method for highly nonlinear neutral stochastic differential equations with time-dependent delay 有时间延迟的高度非线性中性随机微分方程的截断欧拉-丸山方法收敛率

IF 1.7 4区数学 Q1 MATHEMATICS

Open Mathematics

Pub Date : 2024-08-14 DOI: 10.1515/math-2024-0038

Aleksandra M. Petrović

This article can be considered as a continuation of Petrović and Milošević [The truncated Euler-Maruyama method for highly nonlinear neutral stochastic differential equations with time-dependent delay, Filomat 35 (2021), no. 7, 2457–2484], where the authors established the

L q

{L}^{q}

-convergence of the truncated Euler-Maruyama (EM) method for neutral stochastic differential equations with time-dependent delay under the Khasminskii-type condition. However, the convergence rate of the method has not been studied there, which is the main goal of this article. Also, there are some restrictions on the truncated coefficients of the considered equations, and these restrictions sometimes might force the step size to be so small that the application of the truncated EM method would be limited. Therefore, the convergence rate without these restrictions will be considered in this article. Moreover, one of the sufficient conditions for obtaining the main result of this article, which is related to Lipschitz constants for the neutral term and delay function, is weakened. In that way, some of the results of the cited article are generalized. The main result of this article is proved by employing two conditions related to the increments to the coefficients and the neutral term of the equations under consideration, among other conditions. The main theoretical result is illustrated by an example.

本文可视为 Petrović 和 Milošević [The truncated Euler-Maruyama method for highly nonlinear neutral stochastic differential equations with time-dependent delay, Filomat 35 (2021), no. 7, 2457-2484] 的延续。 -型条件下，具有时延的中性随机微分方程的截断欧拉-Maruyama（EM）方法的收敛性。然而，该方法的收敛速率尚未得到研究，而这正是本文的主要目标。此外，对所考虑方程的截断系数也有一些限制，这些限制有时可能会迫使步长太小，从而限制截断电磁法的应用。因此，本文将考虑没有这些限制的收敛速率。此外，本文主要结果的一个充分条件（与中性项和延迟函数的 Lipschitz 常量有关）被弱化了。这样，引用文章中的一些结果就得到了推广。本文的主要结果是通过采用与所考虑方程的系数增量和中性项有关的两个条件以及其他条件证明的。主要理论结果通过一个例子来说明。

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引用次数: 0

On the energy decay of a coupled nonlinear suspension bridge problem with nonlinear feedback 论具有非线性反馈的耦合非线性悬索桥问题的能量衰减

IF 1.7 4区数学 Q1 MATHEMATICS

Open Mathematics

Pub Date : 2024-08-14 DOI: 10.1515/math-2024-0042

Mohammad M. Al-Gharabli

In this article, we study a mathematical model for a one-dimensional suspension bridge problem with nonlinear damping. The model takes into consideration the vibration of the bridge deck in the vertical plane and main cable from which the bridge deck is suspended by the suspenders. We use the multiplier method to establish explicit and generalized decay results, without imposing restrictive growth assumption near the origin on the damping terms. Our results substantially improve, extend, and generalize some earlier related results in the literature.

本文研究了具有非线性阻尼的一维悬索桥问题的数学模型。该模型考虑了桥面在垂直面上的振动和主缆的振动，悬索将桥面悬挂在主缆上。我们使用乘法器方法建立了显式和广义的衰减结果，而不对阻尼项施加原点附近的限制性增长假设。我们的结果大大改进、扩展和概括了早期文献中的一些相关结果。

引用次数: 0

Variational approach to Kirchhoff-type second-order impulsive differential systems 基尔霍夫型二阶脉冲微分系统的变量方法

IF 1.7 4区数学 Q1 MATHEMATICS

Open Mathematics

Pub Date : 2024-08-13 DOI: 10.1515/math-2024-0025

Wangjin Yao, Huiping Zhang

In this study, we consider a Kirchhoff-type second-order impulsive differential system with the Dirichlet boundary condition and obtain the existence and multiplicity of solutions to the impulsive problem via variational methods.

在本研究中，我们考虑了一个具有 Dirichlet 边界条件的 Kirchhoff 型二阶脉冲微分系统，并通过变分法获得了脉冲问题解的存在性和多重性。

引用次数: 0

Singularities of spherical surface in R4 R4 中球面的奇异点

IF 1.7 4区数学 Q1 MATHEMATICS

Open Mathematics

Pub Date : 2024-08-10 DOI: 10.1515/math-2024-0033

Haiming Liu, Yuefeng Hua, Wanzhen Li

In this article, we mainly study the geometric properties of spherical surface of a curve on a hypersurface

Sigma

in four-dimensional Euclidean space. We define a family of tangent height functions of a curve on

Sigma

as the main tool for research and combine the relevant knowledge of singularity theory. It is shown that there are three types of singularities of spherical surface, that is, in the local sense, the spherical surface is respectively diffeomorphic to the cuspidal edge, the swallowtail, and the cuspidal beaks. In addition, we give two examples of the spherical surface.

本文主要研究四维欧几里得空间中超曲面 Σ Sigma 上曲线球面的几何性质。我们定义了 Σ Sigma 上曲线的切高函数族作为主要研究工具，并结合奇点理论的相关知识。研究表明，球面存在三种奇异性，即在局部意义上，球面分别衍射为尖顶边、燕尾和尖顶喙。此外，我们还举了两个球面的例子。

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引用次数: 0

Pullback attractors for fractional lattice systems with delays in weighted space 加权空间中带有延迟的分数网格系统的回拉吸引子

IF 1.7 4区数学 Q1 MATHEMATICS

Open Mathematics

Pub Date : 2024-08-08 DOI: 10.1515/math-2024-0026

Xintao Li, Shengwen Wang

This article deals with the asymptotic behavior of fractional lattice systems with time-varying delays in weighted space. First, we establish some sufficient conditions for the existence and uniqueness of solutions. Subsequently, we demonstrate the existence of pullback attractors for the considered fractional lattice systems.

本文讨论加权空间中具有时变延迟的分数网格系统的渐近行为。首先，我们建立了一些解的存在性和唯一性的充分条件。随后，我们证明了所考虑的分数网格系统存在回拉吸引子。

引用次数: 0

A comprehensive review of the recent numerical methods for solving FPDEs 最新 FPDE 数值求解方法综述

IF 1.7 4区数学 Q1 MATHEMATICS

Open Mathematics

Pub Date : 2024-08-07 DOI: 10.1515/math-2024-0036

Fahad Alsidrani, Adem Kılıçman, Norazak Senu

Fractional partial differential equations (FPDEs) have gained significant attention in various scientific and engineering fields due to their ability to describe complex phenomena with memory and long-range interactions. Solving FPDEs analytically can be challenging, leading to a growing need for efficient numerical methods. This review article presents the recent analytical and numerical methods for solving FPDEs, where the fractional derivatives are assumed in Riemann-Liouville’s sense, Caputo’s sense, Atangana-Baleanu’s sense, and others. The primary objective of this study is to provide an overview of numerical techniques commonly used for FPDEs, focusing on appropriate choices of fractional derivatives and initial conditions. This article also briefly illustrates some FPDEs with exact solutions. It highlights various approaches utilized for solving these equations analytically and numerically, considering different fractional derivative concepts. The presented methods aim to expand the scope of analytical and numerical solutions available for time-FPDEs and improve the accuracy and efficiency of the techniques employed.

由于分数偏微分方程（FPDE）能够描述具有记忆和长程相互作用的复杂现象，因此在各个科学和工程领域都受到了极大的关注。用分析方法求解 FPDE 具有挑战性，因此对高效数值方法的需求与日俱增。这篇综述文章介绍了最近用于求解 FPDE 的分析和数值方法，其中假定的分数导数有 Riemann-Liouville 意义上的分数导数、Caputo 意义上的分数导数、Atangana-Baleanu 意义上的分数导数等。本研究的主要目的是概述 FPDE 常用的数值技术，重点是分数导数和初始条件的适当选择。本文还简要说明了一些具有精确解的 FPDE。文章重点介绍了在分析和数值求解这些方程时使用的各种方法，并考虑了不同的分数导数概念。所介绍的方法旨在扩大时间-有限差分方程的分析和数值求解范围，并提高所采用技术的精度和效率。

引用次数: 0

A singular perturbation result for a class of periodic-parabolic BVPs 一类周期性抛物线 BVP 的奇异扰动结果

IF 1.7 4区数学 Q1 MATHEMATICS

Open Mathematics

Pub Date : 2024-08-06 DOI: 10.1515/math-2024-0020

Santiago Cano-Casanova, Sergio Fernández-Rincón, Julián López-Gómez

In this article, we obtain a very sharp version of some singular perturbation results going back to Dancer and Hess [Behaviour of a semilinear periodic-parabolic problem when a parameter is small, Lecture Notes in Mathematics, Vol. 1450, Springer-Verlag, Berlin, 1990, pp. 12–19] and Daners and López-Gómez [The singular perturbation problem for the periodic-parabolic logistic equation with indefinite weight functions, J. Dynam. Differential Equations 6 (1994), 659–670] valid for a general class of semilinear periodic-parabolic problems of logistic type under general boundary conditions of mixed type. The results of Dancer and Hess [Behaviour of a semilinear periodic-parabolic problem when a parameter is small, Lecture Notes in Mathematics, Vol. 1450, Springer-Verlag, Berlin, 1990, pp. 12–19] and [The singular perturbation problem for the periodic-parabolic logistic equation with indefinite weight functions, J. Dynam. Differential Equations 6 (1994), 659–670] were found, respectively, for Neumann and Dirichlet boundary conditions with

L = − Δ

{mathfrak{L}}=-Delta

. In this article,

{mathfrak{L}}

stands for a general second-order elliptic operator.

在本文中，我们得到了一些奇异扰动结果的非常尖锐的版本，这些结果可追溯到 Dancer 和 Hess [Behaviour of a semilinear periodic-parabolic problem when a parameter is small, Lecture Notes in Mathematics, Vol. 1450, Springer-Verlag, Berlin, 1990, pp.Differential Equations 6 (1994), 659-670] 对混合型一般边界条件下的一般类 logistic 半线性周期-抛物问题有效。Dancer 和 Hess [Behaviour of a semilinear periodic-parabolic problem when a parameter is small, Lecture Notes in Mathematics, Vol. 1450, Springer-Verlag, Berlin, 1990, pp.Differential Equations 6 (1994), 659-670] 分别发现了 L = - Δ {mathfrak{L}}=-Delta 的 Neumann 和 Dirichlet 边界条件。本文中，L {mathfrak{L}} 代表一般二阶椭圆算子。

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