On the Weyl’s Lemma for Triharmonic Functions

In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.

A Proof of Brouwer’s Fixed Point Theorem Using Sperner’s Lemma

This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.

Identities on q-Harmonic Numbers

With the help of the classical Abel’s lemma on summation by parts and algorithm of q-hypergeometric summations, we deal with the summation, which can be written as multiplication of a q-hypergeometric term and q-harmonic numbers. This enables us to construct and prove identities on q-harmonic numbers. Several examples are also given.

时滞系统稳定性分析和镇定:一种基于Finsler引理的统一观点

从Finsler引理角度,研究时滞系统的时滞相关稳定性分析和镇定问题,发现自由权矩阵方法是该研究框架的一个特例,阐明引入乘子矩阵对分析时变时滞系统稳定性的必要性,讨论乘子矩阵结构对所得结果保守性的影响,提出一些改进的基于线性矩阵不等式的稳定性判据和镇定控制器设计算法,数值算例表明所提出方法的有效性.

黎曼流形上的Toponogov定理在Finsler流形上的推广

在Finsler流形上利用活动标架法,通过沿某一方向提升,获得了弧长第二变分的表达式.还将黎曼流形上的Toponogov定理推广到Finsler流形上.由此可进一步将黎曼几何中与之有关的一些定理进行推广而无须通过繁杂的张量运算.

S-引理及其进展

S-引理是运筹学领域和控制论领域中一个十分重要的定理。本文首先从一个非线性控制系统的全局渐近稳定性分析出发,引出S-过程和S-引理,以及两者之间的联系与区别。接着我们介绍了S-引理的基本内容和最新进展,以及它在复数域和四元数集合上的推广。最后,我们介绍了将齐次型S-引理推广到任意多个对称(或厄米特)矩阵时的一些基本结果。

常旗曲率的单连通完备Finsler流形

研究了常旗曲率（ｋ≤０）的单连通完备Ｆｉｎｓｌｅｒ流形在拟等距映射下的存在唯一性。

New versions of Barbalat's lemma with applications

This note presents a set of new versions of Barbalat＇s lemma combining with positive （negative） definite functions.Based on these results,a set of new formulations of Lyapunov-like lemma are established.A simple example shows the usefulness of our results.

A version of Hill's lemma for Cosserat continuum

On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.

PROJECTIVELY FLAT FINSLER METRICS WITH ALMOST ISOTROPIC S-CURVATURE

This article characterizes projectively fiat Finsler metrics with almost isotropic S-curvature.

The Extension of Robinson's Sequential Lemma and Its Application

A. Robinson＇s sequential lemma is extended to nets in general topological space, and obviously the case of nets in ^＊R is its corollary. As its application, the paper proves a property about topology of uniform convergence.

Wiener's lemma:localization and various approaches

Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including signal processing and communication engineering. Wiener’s lemma states that the localization of matrices and integral operators are preserved un-der inversion. In this introductory note, we re-examine several approaches to Wiener’s lemma for matrices. We also review briefly some recent advances on localization preservation of operations including nonlinear inversion, matrix factorization and optimization.

Approach to a Fifth-Order Boundary Value Problem, via Sperner's Lemma

We consider the five-point boundary value problem for a fifth-order differential equation, where the nonlinearity is superlinear at both the origin and +infinity. Our method of proof combines the Kneser’s theorem with the well-known from combinatorial topology Sperner’s lemma. We also notice that our geometric approach is strongly based on the associated vector field.

Fuzzy Zorn’s lemma with applications

We introduced the fuzzy axioms of choice,fuzzy Zorn’s lemma and fuzzy well-ordering principle,which are the fuzzy versions of the axioms of choice,Zorn’s lemma and well-ordering principle,and discussed the relations among them.As an application of fuzzy Zorn’s lemma,we got the following results:(1)Every proper fuzzy ideal of a ring was contained in a maximal fuzzy ideal.(2)Every nonzero ring contained a fuzzy maximal ideal.(3)Introduced the notion of fuzzy nilpotent elements in a ring R,and proved that the intersection of all fuzzy prime ideals in a commutative ring R is the union of all fuzzy nilpotent elements in R.(4)Proposed the fuzzy version of Tychonoff Theorem and by use of fuzzy Zorn’s lemma,we proved the fuzzy Tychonoff Theorem.

基于Finsler引理的一类连续时间多时滞系统稳定性分析

针对具有多个变时滞的系统,为简化其稳定性判据,首先将动力学方程转化为代数方程,其次运用Finsler引理给出系统稳定的新的判别定理,然后构造Lyapunov-Krasovskii泛函对定理进行严格的数学证明。在此基础上,选择合适的正交补矩阵对稳定性条件作进一步简化。最后通过2个数值算例对结论进行验证。结果表明:给出的定理可简单有效地判别带有多个变时滞系统的稳定性。

常曲率Finsler空间的共形映射

获得两个常曲率Ｆｉｎｓｌｅｒ空间构成共形映射的新条件．

局部射影平坦且具有迷向S-曲率的两类重要的(α,β)-度量

研究了两类重要的分别形如F=α~2/（α-β）和F=α＋εβ＋kβ~2/α的（α,β）-度量,其中α=aij（x）yi yj为黎曼度量,β=bi（x）yi为流形上的1-形式,ε,k≠0为常数.得到了它们为局部射影平坦且具有迷向S-曲率的充要条件.

关于局部对偶平坦且具有迷向S-曲率的Matsumoto度量(英文)

找到了一些方程去刻画局部对偶平坦的Matsumoto度量F=α2/α-β,其中α=aijyiyj,β=biyi.同时对局部对偶平坦且具有迷向S-曲率的Matsumoto度量进行了分类.

共形平坦且具有弱迷向S曲率的(α,β)度量的分类

将黎曼流形上共形平坦结果推广到Finsler流形上。研究(α,β)度量的共形平坦问题,建立(α,β)度量上的特殊坐标系,得到具有弱迷向S曲率且共形平坦的(α,β)度量的性质,给出此时(α,β)度量的分类,即对共形平坦且弱迷向S曲率的(α,β)度量或是黎曼度量或是Minkowski度量。

具有迷向S-曲率的Douglas(α,β)-度量

研究具有迷向S-曲率的Douglas(α,β)-度量F=αφ(β/α),其中α=aij(x)yiyj～(1/2)为黎曼度量,β=bi(x)yi为流形上的1-形式.得到其为具有迷向S-曲率的Douglas度量的充要条件是β关于α是平行的.进一步,完全地分类了局部射影平坦且具有迷向S-曲率的(α,β)-度量.