在满足广义指数型二分性条件下的线性化

本文将Ｈａｒｔｍａｎ线性化定理和Ｐａｌｍｅｒ线性化定理推广到具有广义指数型二分性的系统,证明了等价函数的强一致连续性;作为应用,在例子中给出了一类系 统的稳定性的判别方法．     

不具单调性的均衡系统问题的解的存在性

该文引入并研究了一类不具单调性的均衡系统问题。利用Brouwer不定点定理，在有限维空间下得到了均衡系统问题的解的存在性。在无限维情形，通过引入函数族的(S)_{+-}条件，证明了基于(S)_{+-}条件下的均衡系统问题的解的存在性。     

Morphic-环与SF-环

以正则环为桥梁,研究了morphic-环与SF-环之间的关系.主要工作如下:(i)研究了SF-环成为morphic-环的若干条件;(ii)讨论了在一定条件下SF-环与morphic-环的等价性;(iii)给出了利用morphic-环对半单环在约化条件下的一个刻划.     

随机环境中马氏链的常返性和瞬时性

讨论了随机环境马氏链中具有强π不可约性链的常返性的判定,从而得到了强π不可约链常返性判定的充分必要条件,同时给出了在一定条件下随机环境中的马氏链的瞬时性判定的几个充分条件.     

一类次线性基尔霍夫方程解的存在性（英文）

本文研究一类不确定型的基尔霍夫方程.在线性泛函满足新的次线性增长条件和扰动势能合适的条件下,利用变分法得到该类方程的非平凡解的存在性.     

(ω)性质的判定

利用新定义的谱集,刻画了Hilbert空间上有界线性算子满足(ω_1)性质和(ω)性质的等价条件.另外,利用该谱集,对算子函数的(ω)性质进行了判定.     

整值随机变量序列发生次数与条件概率和的等价性

在没有独立性、平稳性和相依性假设的条件下,利用分析方法讨论了整值随机变量序列取某个数值的次数与随机变量序列取该数值的条件概率和的等价性问题,建立并证明了若干强极限定理.     

(h,ψ)-广义切导数与最优性条件

借助于Ben-Tal广义代数运算定义了广义（h，ψ）-Clarke切锥、广义（h，ψ）-邻接切锥和广义（h，ψ）-伴随切锥，由此定义了广义（h，ψ）-Clarke方向导数、广义（h，ψ）-邻接方向导数、广义（h，ψ）-伴随方向导数及（h，ψ）-广义梯度，由此给出了具有（h，ψ）-凸性的的实值函数最优解的判别条件，文章是Ben-Bal代数在凸分析理论中的应用，所有结果和所用方法可以应用于多目标优化的研究。     

一类带负位势函数的超线性p-Laplace方程基态解的存在性

在没有Ambrosetti-Rabinowitz条件的情况下,运用(C)。序列和变分方法讨论了pLaplace方程基态解的存在性.通过选择合适的:Banach空间,证明了R~N上一类带负位势函数的超线性p-Laplace方程基态解的存在性.     

函数强伪凸性与映射强伪单调性

1　引　　言Schaible在[1]中引入七类单调映射,并证明对其中六类,函数的某种广义凸性都和相应的梯度单调性等价,只有函数强伪凸和梯度强伪单调的等价性是否成立作为公开问题.其后,Schaible又在[2]中通过一个例子否定了两者的等价性,并引入了较弱的函数强伪凸和映射强伪单调的概念,在函数二次可微的条件下证明了函数强伪凸和梯度强伪单调等价.我们将引入强于[2]中概念的强伪凸和强伪单调性,对给出的定义,不附加条件便可保证函数强伪凸性和梯度强伪单调性等价.同时,对[2]中的一个错误予以指出,并给出正确的反例.还就[1]中问题给出远比[2]中简…     

Banach空间中一类非线性算子Ishikawa迭代序列收敛定理

在一般的Banach空间中,研究了Ishikawa迭代序列收敛问题,去掉了通常文献中关于空间X的一致光滑或S-一致光滑的严格要求,此外,还去掉或减弱了其它某些条件。因而本质地改进了近期文献的一系列相应定理。     

Generalized exponential dichotomy and global linearization

Hartman's linearization theorem says that if all eigenvalues of matrix A have no zero real part and f(x) is small Lipschitzian, then nonlinear system x^′=Ax+f(x) and its linear system x^′=Ax are topologically equivalent. In 1970s Palmer extended the theorem to nonautonomous systems. In this paper we extend Hartman's theorem to the systems with generalized exponential dichotomy.     

Strongly FP-injective modules

A module M is called strongly FP-injective if Extⁱ(P,M) = 0 for any finitely presented module P and all i≥1. (Pre)envelopes and (pre)covers by strongly FP-injective modules are studied. We also use these modules to characterize coherent rings. An example is given to show that (strongly) FP-injective (pre)covers may fail to be exist in general. We also give an example of a module that is FP-injective but not strongly FP-injective.     

On Strongly Copure Flat Modules and Copure Flat Dimensions

Let R be a left coherent ring. We first prove that a right R-module M is strongly copure flat if and only if Ext ⁱ (M, C) = 0 for all flat cotorsion right R-modules C and i ≥ 1. Then we define and investigate copure flat dimensions of left coherent rings. Finally, we give some new characterizations of n-FC rings.     

Strongly topological linearization with generalized exponential dichotomy

It has been proved that if x^′=A(t)x$x^{\prime }=A\left(t\right)x$ has a generalized exponential dichotomy and f(t,x)$f(t,x)$ satisfies certain conditions, then the nonlinear system x^′=A(t)x+f(t,x)$x^{\prime }=A\left(t\right)x+f(t,x)$ is topologically equivalent to its linear system x^′=A(t)x$x^{\prime }=A\left(t\right)x$. In this paper, we prove that if the condition |A(t)|≤M⋅a(t)$\left|A\left(t\right)\right|\le M\cdot a\left(t\right)$ is added, then x^′=A(t)x+f(t,x)$x^{\prime }=A\left(t\right)x+f(t,x)$ is strongly topologically equivalent to x^′=A(t)x$x^{\prime }=A\left(t\right)x$, where M$M$ is some positive number and a(t)$a\left(t\right)$ is the eigenfunction of the generalized exponential dichotomy, and therefore the corresponding solutions of x^′=A(t)x+f(t,x)$x^{\prime }=A\left(t\right)x+f(t,x)$ and x^′=A(t)x$x^{\prime }=A\left(t\right)x$ have the same stability.     

一秩算子和三角代数

Abstract, In this paper, a necessary condition for a maximal triangular algebra to be closed is given, A necessary and sufficient condition for a maxima] triangular algebra to he strongly reducible is obtained,     

Criterions for detecting the existence of the exponential dichotomies in the asymptotic behavior of the solutions of variational equations

We prove that the admissibility of any pair of vector-valued Schäffer function spaces (satisfying a very general technical condition) implies the existence of a “no past” exponential dichotomy for an exponentially bounded, strongly continuous cocycle (over a semiflow). Roughly speaking the class of Schäffer function spaces consists in all function spaces which are invariant under the right-shift and therefore our approach addresses most of the possible pairs of admissible spaces. Complete characterizations for the exponential dichotomy of cocycles are also obtained. Moreover, we involve a concept of a “no past” exponential dichotomy for cocycles weaker than the classical concept defined by Sacker and Sell (1994) in [23]. Our definition of exponential dichotomy follows partially the definition given by Chow and Leiva (1996) in [4] in the sense that we allow the unstable subspace to have infinite dimension. The main difference is that we do not assume a priori that the cocycle is invertible on the unstable space (actually we do not even assume that the unstable space is invariant under the cocycle). Thus we generalize some known results due to O. Perron (1930) [14], J. Daleckij and M. Krein (1974) [7], J.L. Massera and J.J. Schäffer (1966) [11], N. van Minh, F. Räbiger and R. Schnaubelt (1998) [26].     

强n-凝聚环

设R是一个环,n是一个正整数.右R-模M称为强n-内射的,如果从任一自由右R-模F的任一n-生成子模到M的同态都可扩张为F到M的同态;右R-模V称为强n-平坦的,如果对于任一自由右R-模F的任一n-生成子模T,自然映射VT→VF是单的;环R称为左强n-凝聚的,如果自由左R-模的n-生成子模是有限表现的;环R称为左n-半遗传的,如果R的每个n-生成左理想是投射的.本文研究了强n-内射模,强n-平坦摸及左强n-凝聚环.通过模的强n-内射性和强n-平坦性概念,作者还给出了强n-凝聚环和n-半遗传环的一些刻画.     

On Copure Projective Modules and Copure Projective Dimensions

Let R be any ring. A right R-module M is called n-copure projective if Ext¹(M, N) = 0 for any right R-module N with fd(N) ≤ n, and M is said to be strongly copure projective if Ext ⁱ (M, F) = 0 for all flat right R-modules F and all i ≥ 1. In this article, firstly, we present some general properties of n-copure projective modules and strongly copure projective modules. Then we define and investigate copure projective dimensions of modules and rings. Finally, more properties and applications of n-copure projective modules, strongly copure projective modules and copure projective dimensions are given over coherent rings with finite self-FP-injective dimension.