具p-Laplace算子型边值问题解的存在性

将具p-Laplace算子的边值问题转化成算子方程,对于p的不同取值给出适当的条件.利用Mawhin连续引理的推广形式,证明了一类具p-Laplace算子的微分方程边值问题解的存在性,得到了一系列解存在的充分条件.     

Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case

We study the problem of the existence and uniqueness of solutions to the Bellman equation in the presence of unbounded returns. We introduce a new approach based both on consideration of a metric on the space of all continuous functions over the state space, and on the application of some metric fixed point theorems. With appropriate conditions we prove uniqueness of solutions with respect to the whole space of continuous functions. Furthermore, the paper provides new sufficient conditions for the existence of solutions that can be applied to fairly general models. It is also proven that the fixed point coincides with the value function and that it can be approached by successive iterations of the Bellman operator.     

考虑边界条件影响的差分格式的稳定性分析

本文对一类抛物型方程的初边值问题建立了相应的有限差分格式,在考虑边界条件影响的前提下,通过Gerschgorin定理对该格式的稳定性进行了分析,得到了差分格式稳定性的一个必要条件。最后通过数值算例对文中所得结果及差分格式的收敛性作了进一步的分析。     

中值定理“中间点”渐近性研究的新进展(I)

综述了近年来在中值定理“中间点”渐近性方面取得的若干新成果 ,同时 ,提出了笔者认为值得进一步讨论的问题     

谈几类中值定理辅助函数的构造方法

给出三类中值定理辅助函数的构造方法.     

对共同基金定理的重新认识——不完整市场研究

本文就不完整市场提出了对连续时间共同基金定理的重新认识。这一新认识的提出同样摆脱了以往研究中对投资者消费和最终财富效用函数的假设。同样的，这些效用函数也都是可时间累加的、非减的函数。这项理论延伸也是基于离散过程和线性代数的简单属性。本文的研究结果适用于不完整市场。另外，以往只适用于包含单一风险资产的完整市场的最优投资策略自动延伸至包含多个风险资产的不完整市场。文中举出了一个实例。     

When an Event Makes a Difference

For (S, Σ) a measurable space, let and be convex, weak^* closed sets of probability measures on Σ. We show that if ∪ satisfies the Lyapunov property , then there exists a set A ∈ Σ such that min_μ1∈ μ₁(A) > max_μ2 ∈ (A). We give applications to Maxmin Expected Utility (MEU) and to the core of a lower probability.     

Scoring of web pages and tournaments—axiomatizations

Consider a set of elements which we want to rate using information about their bilateral relationships. For instance sports teams and the outcomes of their games, journals and their mutual citations, web sites and their link structure, or social alternatives and the tournament derived from the voters' preferences. A wide variety of scoring methods have been proposed to deal with this problem. In this paper we axiomatically characterize two of these scoring methods, variants of which are used to rank web pages by their relevance to a query, and academic journals according to their impact. These methods are based on the Perron–Frobenius theorem for non-negative matrices.

Strong convergence properties for partial sums of asymptotically negatively associated random vectors in Hilbert spaces

Abstract

In this paper, we investigate the almost sure convergence for partial sums of asymptotically negatively associated (ANA, for short) random vectors in Hilbert spaces. The Khintchine-Kolmogorov type convergence theorem, three series theorem and the Kolmogorov type strong law of large numbers for partial sums of ANA random vectors in Hilbert spaces are obtained. The results obtained in the paper generalize some corresponding ones for independent random vectors and negatively associated random vectors in Hilbert spaces.