Fixed points and graph images for minimal maps on the once punctured torus

A fixed point detection theorem for a family of maps defined on the once punctured torus is proved. As a consequence, we produce an example of a homotopy class [f] of self-maps on the once punctured torus that illustrates the following: (i) there is a map in the homotopy class that has no fixed points, and (ii) if the image of f lies in a 1-complex that embeds as a homotopy equivalence, then f must have a fixed point.     

模范畴与余模范畴之间的等价

本文研究了环上模范畴与余环上余模范畴.运用可裂叉与余可分余环的性质,得到了以上两个范畴等价的一些充分条件,从而推广了文献[6]中的一些结果.

Abstract：

In this article,we consider the categories of modules over rings and categories of comodules over corings.By properties of split forks and coseparable corings,we get some sufficient conditions for the equivalence between above two categories.As a consequence,we generalize some results in[6].     

M(G,x)≤2的图匹配等价的充要条件

对一个图G,设μ(G,x)表示它的匹配多项式,M(G,x)表示μ(G,x)的最大实数根.令Г_1={G|M(G,x)<2}和Г2={G|M(G,x)≤2}.给出了Г_i(i=1,2)中的两个图G和H匹配等价的充要条件.     

几乎完全非线性多项式函数间的EA等价性

简述了几乎完全非线性(APN)多项式函数的研究现状,讨论了两类几乎完全非线性多项式函数间的扩张仿射(EA)等价性,给出了验证EA等价的一般方法.     

基于拓扑优化的声学结构材料分布设计

本文针对结构的声学设计问题进行研究,通过优化两种不同的材料在结构设计域内的拓扑分 布来最小化谐振结构所产生的声场中指定参考面/参考域内的声压。在研究中假定结构为线弹性小变 形结构,材料阻尼为Rayleigh阻尼,声学介质为无粘、可压缩、小扰动流体。对结构响应采用有限 元格式进行计算,对声场采用基于Helmholtz积分的边界元格式进行计算,由于声场在无穷远自由边 界的无反射条件在边界积分中能自动得到满足,该格式特别适合于具有开放边界的声场计算。建立 了结构有限元-声场边界元格式的耦合系统拓扑优化模型,导出了耦合系统敏感度分析的一般格式及 伴随格式。数值算例验证了所提出的结构-声学耦合系统优化方法的有效性和可靠性,并揭示了基于 声学准则的拓扑优化结果的有关特性 关键词边界积分,结构声学耦合系统,拓扑优化,敏感度分析,伴随方法     

Congruence triples on regular semigroups and their generalizations

In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by using the equivalences on S/ℒ, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup.     

奇点模型范畴的Quillen等价

令R是左Gorenstein环.我们构造了奇点反导出模型范畴和奇点余导出模型范畴(见文[Models for singularity categories,Adv Math.,2014,254:187-232])之间的Quillen等价.作为应用,给出了投射,内射模的正合复形的同伦范畴之间的一个具体的等价■.     

Periodic nonautonomous differential equations with noninstantaneous impulsive effects

In this paper, we study a new class of periodic nonautonomous differential equations with periodic noninstantaneous impulsive effects. A concept of noninstantaneous impulsive Cauchy matrix is introduced, and some basic properties are considered. We give the representation of solutions to the homogeneous problem and nonhomogeneous problem by using noninstantaneous impulsive Cauchy matrix, and the variation of constants method, adjoint systems, and periodicity of solutions is verified under standard periodicity conditions. Further, we show the existence and uniqueness of solutions of semilinear problem and establish existence result for periodic solutions via Brouwer fixed point theorem and uniqueness and global asymptotic stability via Banach fixed point theorem.     

函数两种凸性定义等价性的今惑前世之初探

通过研究中点凸函数和一般凸函数这两种凸性定义的早期发展历史和凸性性质来探索两种凸性定义的等价性.结果表明,两种凸性定义不等价;但是,当函数满足连续、可微、半连续和有界这四个条件中的任何一个条件时,两种凸性定义等价.     

一类向量值积分方程的优化问题

提出了一类带有参数的向量值积分的优化问题,将H ardy空间中的一些概念推广到了局部凸空部间,尤其是将H ankel算子、最小模型匹配误差、最优解等概念推广到了局部凸空间.