疲劳与断裂中细观损伤的群体响应

实验中观察到，在疲劳短裂纹损伤阶段，损伤累积由众多的短裂纹萌生和发展而构成。对于韧性材料裂纹起始，实验中观察到裂尖前方孔洞群体损伤累积．依据损伤以群体方式发生和发展的特征，分别采用裂纹数密度守恒和孔洞数密度守恒的分析方法，探讨了疲劳短裂纹和裂尖前方孔洞群体损伤的演化过程和损伤累积行为。     

非线性积分算子的泰勒级数展开式

本文讨论了Banach空间中的泰勒级数,并给出了非线性Volterra积分算子的泰勒级数展开式。     

随机测度的收敛性

本文研究了随机共轭算子的值域及随机测度空间的度量性     

一个三阶拟线性方程解的局部存在性

本文应用半群无穷小生成算子稳定族所构造的发展系统讨论较广一类Kdv方程Cauchy问题解的局部存在性。     

高阶变系数线性微分方程的新算子解法

本文将常系数线性微分方程的算子解法推广到变系数线性微分方程中，用新的方法──算子解法求解某些变系数的线性微分方程，给出了常系数线性方程特解公式．     

关于p-凸泛函族的共鸣定理

共鸣定理是泛函分析中重要的基础定理之一,其形式也有多种变化。在[1]—[5]中讨论了一类共鸣定理,即所谓凸泛函族的共鸣定理。由于凸分析的广泛运用性,凸性的概念有必要进一步推广。本文首先给出p-凸性的概念,p-凸集和p-凸泛函具有完全类似于凸集和凸泛函的性质,然后导出了在拓扑向量空间及赋范空间中p-凸泛函族的几个共鸣定理,推广了文[1]—[5]中的相应结果。     

单模电磁场的位相性质

本文利用Pegg—Barnett位相算符形式引入了有限维Hilbert空间的位相算符和位相态基，详细讨论了二态系统的位相算符表示及性质。     

一般约束优化问题的摄动梯度投影法

利用梯度投影法与罚函数技巧，将带等式和不等式约束优化问题化成一个无约束问题，提出了求解不等式、等式约束优化问题的摄动梯度投影算法。考虑到计算的误差因素，在搜索方向上进行摄动，得到一个方向不精确的梯度投影法。参数δｋ取不同的数还可以得到一类梯度投影法。从而保证了在实际应用中更容易实现，在较弱的条件下，证明了该算法的全局收敛性。     

Some notes on Church's thesis and the theory of games

This paper considers games in normal form played by Turing Machines. The machines are fed as input all the relevent information and then are required to play the game. Some impossibility results are derived for this set-up. In particular, it is shown that no Turing Machine exists which will always play the correct strategy given its opponent's choice. Such a result also generalizes to the case in which attention is restricted to economically optimizing machines only. The paper also develops a model of knowledge. This allows the main results of the paper to be interpreted as stemming out of the impossibility of always deciding whether a player is rational or not in some appropriate sense.     

A First-Order Spatial Integer-Valued Autoregressive SINAR(1, 1) Model

Binomial thinning operator has a major role in modeling one-dimensional integer-valued autoregressive time series models. The purpose of this article is to extend the use of such operator to define a new stationary first-order spatial non negative, integer-valued autoregressive SINAR(1, 1) model. We study some properties of this model like the mean, variance and autocorrelation function. Yule-Walker estimator of the model parameters is also obtained. Some numerical results of the model are presented and, moreover, this model is applied to a real data set.