ON THE GLOBAL ASYMPTOTIC STABILITY OF THE EQUATION +f+h+g(x)=0

This paper gives a sufficient criterion of the global asymptotic stability of the zerosolution of the equation(?)+f((?))+h((?))+g(x)=0     

Wolstenholme定理的进一步推广

Ｗｏｌｓｔｅｎｈｏｌｍｅ定理巳被推广过．本文再作进一步推广，得到一般性的结果和几个重要的同余关系式．     

Computing A-optimal Designs for Weighted Polynomial Regression by Taylor Expansion

This article is concerned with the problem of constructing A-optimal design for polynomial regression with analytic weight function on the interval [m ? a, m + a], m, a > 0. It is shown that the structure of the optimal design depends on a and weight function only, as a close to 0. Moreover, if the weight function is an analytic function a, then a scaled version of optimal support points, and weights are analytic functions of a at a = 0. We make use of a Taylor expansion to provide a recursive procedure for calculating the A-optimal designs. Examples are presented to illustrate the procedures for computing the optimal designs.     

Directly-Riemann积分的收敛定理

本文着重研究了Directly－Riemann积分收敛问题，得到了几个重要的积分收敛定理。     

Persistent age distributions for an age‐structured two‐sex population model*

In this paper we formulate an age‐structured two‐sex population model which takes into account a monogamous marriage rule and the duration of marriage. We are mainly concerned with the existence of exponential solutions with a persistent age distribution. First we provide a semigroup method to deal with the time‐evolution problem of our two‐sex population model. Next, by constructing a fixed point mapping, we prove the existence of exponential solutions under homogeneity conditions.     

The generalized fluctuation test: A unifying view

In this paper, a general principle of constructing tests for parameter constancy without assuming a specific alternative is introduced. A unified asymptotic result is established to analyze this class of tests. As applications, tests based on the range of recursive and moving estimates are considered, and their asymptotic distributions are characterized analytically. Our simulations show that different tests have quite different behavior under various alternatives and that no test uniformly dominates the other tests.     

A Folk Theorem for Asynchronously Repeated Games

We prove a Folk Theorem for asynchronously repeated games in which the set of players who can move in period t, denoted by I_t, is a random variable whose distribution is a function of the past action choices of the players and the past realizations of I_τ's, τ=1, 2,…,t−1. We impose a condition, the finite periods of inaction (FPI) condition, which requires that the number of periods in which every player has at least one opportunity to move is bounded. Given the FPI condition together with the standard nonequivalent utilities (NEU) condition, we show that every feasible and strictly individually rational payoff vector can be supported as a subgame perfect equilibrium outcome of an asynchronously repeated game.     

自指、悖论与哥德尔定理

一般悖论都以自指概念为基础,然而自指并不必然导致悖论。受悖论启发,哥德尔定理最重要的步骤之一是构造了自指的语句,但并没有导致矛盾,关键在于哥德尔在构造自指语句时区分了真与可证、给定系统的可证性与系统外的可证性等概念。     

一类高阶非线性常微分方程组的正解存在性和多重性

利用锥上的不动点定理,研究了带有独立参数的非线性2p-2q阶常微分方程组正解的存在性和多重性.如果非线性项满足一定条件,而参数λ和μ分别属于适当的区间时,得到了方程组分别至少有一个正解及两个正解的存在性结果.这一结果从方程组的高阶与不同阶以及两参数的独立性两方面对已有结果进行了推广.