关于大几何参数的开顶扁球壳屈曲问题的奇摄动*

本文利用修正多重尺度法研究了大几何参数的具有刚性中心的边缘铰接的开顶扁球壳,在复合载荷作用下的非线性稳定问题。求得了扁壳几何参数h值较大时,本问题的一致有效的渐近解。     

多重尺度法应用于变厚度开顶扁球壳在复合载荷下的非线性稳定问题

利用改进多重尺度法研究了大几何参数的变厚度的具有刚性中心的开顶扁球壳,在复合载荷作用下的非线性稳定问题,求得了扁壳几何参数k值较大时,本问题的一致有效的渐近解,并进行了余项误差估计。     

扁球壳在均布压力与均匀温度场联合作用下的屈曲

根据扁壳几何非线性理论,推导了均布压力与均匀温度场联合作用下的扁球壳的位移型几何非线性控制方程.考虑夹紧边界条件,采用打靶法得到了扁球壳轴对称弯曲与屈曲的数值结果.讨论了壳体几何参数对平衡路径、临界荷载的影响.给出了壳体临界几何参数.当几何参数大于临界几何参数时,上、下临界荷载都随几何参数增加而增加.给定几何参数时,考察了不同均匀温度场对壳体上、下临界荷载、临界几何参数以及平衡构型的影响.均匀升温会使上临界荷载显著增加,会使下临界荷载略有减小.均匀变温会使临界几何参数改变.     

扁球壳在热-机械荷载作用下的稳定性分析

基于扁壳几何非线性理论,应用虚功原理和变分法推导了均匀变温场中圆底扁薄球壳在均布外侧压力作用下的位移型几何非线性控制方程.考虑周边不可移简支边界条件,运用打靶法计算获得了不同几何参数的扁球壳轴对称弯曲变形的数值结果.定义了壳体临界几何参数.考察了壳体几何参数对平衡路径和临界荷载的影响.当壳体几何参数大于壳体临界几何参数时,上临界荷载随几何参数的增加单调增加,下临界荷载在很小范围内随几何参数的增加而增加,之后随几何参数的增加而减小.给定几何参数时,考察了不同均匀温度变化对壳体临界几何参数、临界荷载和平衡构型的影响.均匀升温使上临界荷载显著增加,使下临界荷载和临界几何参数显著减小.     

双层网格圆底扁球壳的非线性稳定问题

从基于等效夹层壳思想的双层网格扁壳,非线性弯曲理论的变分方程出发,利用坐标变换方法和驻值余能原理,导出双层网格圆底扁球壳,在均布压力作用下的轴对称大挠度方程和边界条件．采用修正迭代法,求得了两类边界条件下双层网格圆底扁球壳的非线性载荷-位移关系式和临界屈曲载荷的解析表达式,并讨论了几何参数对临界屈曲载荷的影响．     

线布载荷作用下碟形扁壳的非线性稳定*

本文对轴对称线布载荷作用下碟形扁壳的非线性稳定问题进行了分析,得到了各种常见边界条件下碟形扁壳特征关系的二次近似表达式.讨论了几何参数β,γ和k对非线性特性的影响.     

变厚度夹层截顶扁锥壳的非线性稳定性分析

对具有变厚度夹层截顶扁锥壳的非线性稳定问题进行了研究。利用变分原理导出表层为等厚度而夹心为变厚度的夹层截顶扁锥壳的非线性稳定问题的控制方程和边界条件,采用修正迭代法求得了具有双曲型变厚度夹层截顶扁锥壳的非线性稳定性问题的解析解,得到了内边缘与一刚性中心固结而外边缘为可移夹紧固支的变厚度夹层截顶扁锥壳临界屈曲载荷的解析表达式,讨论了几何参数和物理参数对壳体屈曲行为的影响。     

静载荷作用下正交各向异性旋转扁壳的非线性自由振动

本文用加权残值法和Lindstedt－Poincare摄动法研究了圆柱型正交各向异性扁薄球壳和锥壳在均布静载荷作用下的轴对称非线性自由振动问题，得到了其非线性固有频率和振幅间的特征关系，并讨论了静载荷及壳体的几何参数和材料参数对其振动特性的影响。     

带有集中激励的一类非线性边值问题的奇摄动

本文综合利用近代分析和奇异摄动方法，讨论了一类具有集中激励的非线性向量微分方程组初值总是 的渐近性质，构造了这类问题的一致有效渐近解。并利用这个方法求解几何参数的扁球壳在集中力作用下的非线性稳定性问题，得到了较好的结果。     

在边缘线布载荷作用下开顶扁球壳的非线性稳定问题的奇摄动解

本文利用奇异摄动方法计算了在内边缘线布载荷作用下无刚性中心的开顶扁球壳的非线性稳定问题,得到了几何参数k值较大时本问题的一致有效的渐近解.     

On the convergence of uncertain sequences

Uncertain variables are measurable functions from uncertainty spaces to the set of real numbers. In this paper, a new kind of convergence, convergence uniformly almost surely (convergence uniformly a.s.), is presented. Then, relations between convergence uniformly almost surely and convergence almost surely (convergence a.s.), convergence in measure, convergence in mean, and convergence in distribution are discussed.     

平衡随机模型中方差分量的非负估计

众所周知, 对于平衡随机模型, 方差分量的方差分析估计为一致最小方差无偏估计. 本文基于方差分量的方差分析估计, 构造了一个二次不变估计类, 它包含了一些常用重要估计. 证明了该估计类在一定条件下在均方误差意义下一致优于方差分析估计, 并在此估计类基础上, 给出了方差分量的两种非负估计, 它们在均方误差意义下分别一致优于方差分析估计和限制极大似然估计, 且有显式解、容易计算.     

Attractivity properties of α-contractions

It is known that if T:X → X is completely continuous where X is a Banach space, then point dissipative and compact dissipative are equivalent, and imply the existence of a maximal compact invariant set which is uniformly asymptotically stable and attracts bounded sets uniformly. If T is an α-contraction, it is not known whether point dissipative and compact dissipative are equivalent. However, it is known that if T is an α-contraction and compact dissipative, then there exists a maximal compact invariant set which is uniformly asymptotically stable and attracts a neighborhood of any compact set uniformly. In this paper we show that for most practical examples which give rise to α-contraction, point dissipative and compact dissipative are equivalent. For example, we show this is true for stable neutral functional differential equations, retarded functional differential equations of infinite delay, and strongly damped nonlinear wave equations. We conjecture that this should be true for almost any practical application which gives rise to an α-contraction.     

On the compactly locally uniformly rotund points of Orlicz spaces

In this paper, locally uniformly rotund points and compactly locally uniformly rotund points are introduced. Moreover, criteria for compactly locally uniformly rotund points in Orlicz spaces are given.     

Convergence Properties of the DFP Algorithm for Unconstrained Optimization

In this article, the convergence properties of the DFP algorithm with inexact line searches on uniformly convex functions are investigated. An inexact line search is proposed and the global convergence and superlinear convergence of the DFP algorithm with this line search on uniformly convex functions are proved.     

Topologically weakly mixing homeomorphisms of the Klein bottle that are uniformly rigid

In this paper we prove that there is a large family of topologically weakly mixing homeomorphisms of the Klein bottle that are uniformly rigid. We do this by viewing the Klein bottle as the quotient of the two-torus by an appropriate group action and producing topologically weakly mixing homeomorphisms of the two-torus that are uniformly rigid and equivariant with respect to the action.     

A non-symmetric singular cauchy problem

In this paper we replace uniformly convex (or reflexive and normal structure) as required by Browder and Kirk, by uniformly normal structure to obtain a fixed point theorem for non-expansive self mappings. Examples are given to show that spaces with uniformly normal structure are not all uniformly convex and spaces with normal structure do not all have uniformly normal structure.

AMS (MOS) subject classification (1970) Primary 47410.     

Generalization performance of least-square regularized regression algorithm with Markov chain samples

The previously known works describing the generalization of least-square regularized regression algorithm are usually based on the assumption of independent and identically distributed (i.i.d.) samples. In this paper we go far beyond this classical framework by studying the generalization of least-square regularized regression algorithm with Markov chain samples. We first establish a novel concentration inequality for uniformly ergodic Markov chains, then we establish the bounds on the generalization of least-square regularized regression algorithm with uniformly ergodic Markov chain samples, and show that least-square regularized regression algorithm with uniformly ergodic Markov chains is consistent.     

随机脉冲泛函微分方程的{\boldmath p}阶矩有界性

随机脉冲泛函微分方程是一个具有广泛应用前景的数学模型. 该文利用带Razumikhin条件的Liapunov直接法和比较原理, 得到了随机脉冲泛函微分方程的解的一致(一致且最终、一致且一致最终) p阶矩有界的充分条件, 其中在获得一致有界性和一致最终有界性时, 对dV(t, x(t))/dt 的限制条件也较少, 因此研究结果非常便于应用.     

一致星象和凸象超几何函数的一些性质

介绍了(高斯)超几何函数属于一致星象函数和一致凸函数的某些子类的一些性质.还考虑了与超几何函数相关的算子.