ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Sufficient conditions are established for the asymptotic behavior of solutionsof nonlinear delay differential equations x′(t)+sum from i=1 to m(pi(t)x(t-т_i))=F(t,x_t),t≥0where 0<т_1<т_2<…<т_m≤r,pi∈C([0,∞)),i=1,2,…,m,F∈C([0,∞)×C_0,R).C_0=C([-r,0],R)equipped with the sup norm ||·|| forsome r>0. A new result is established, some known results are improved.     

单调全局最优化问题的凸化外逼近算法

单调优化是指目标函数与约束函数均为单调函数的全局优化问题．本文提出一种新的凸化变换方法把单调函数化为凸函数，进而把单调优化问题化为等价的凸极大或凹极小问题，然后采用Hoffman的外逼近方法来求得问题的全局最优解．我们把这种凸化方法同Tuy的Polyblock外逼近方法作了比较，通过数值比较可以看出本文提出的凸化的方法在收敛速度上明显优于Polyblock方法．     

On a Generalized Cochrane Sum and Its Hybrid Mean Value Formula

The main purpose of this paper is to use a mean value theorem of Dirichlet L-functions to study the asymptotic property of a hybrid mean value of a generalized Cochrane sum, and give an interesting mean value formula.2000 Mathematics Subject Classification: Primary—11F20; Secondary—11F99     

反对称正交对称矩阵反问题

本文讨论一类反对称正交对称矩阵反问题及其最佳逼近．研究了这类矩阵的一些性质，利用这些性质给出了反问题解存在的一些条件和解的一般表达式，不仅证明了最佳逼近解的存在唯一性，而且给出了此解的具体表达式．     

Decomposition Methods for Differentiable Optimization Problems over Cartesian Product Sets

This paper presents a unified analysis of decomposition algorithms for continuously differentiable optimization problems defined on Cartesian products of convex feasible sets. The decomposition algorithms are analyzed using the framework of cost approx imation algorithms. A convergence analysis is made for three decomposition algorithms: a sequential algorithm which extends the classical Gauss-Seidel scheme, a synchronized parallel algorithm which extends the Jacobi method, and a partially asynchronous parallel algorithm. The analysis validates inexact computations in both the subproblem and line search phases, and includes convergence rate results. The range of feasible step lengths within each algorithm is shown to have a direct correspondence to the increasing degree of parallelism and asynchronism, and the resulting usage of more outdated information in the algorithms.     

Large deviations and the generalized processor sharing scheduling for a two-queue system

We establish the optimal asymptotic decay rate of per-session queue length tail distributions for a two-queue system where a single constant rate server serves the two queues using the Generalized Processor Sharing (GPS) scheduling discipline. The result is obtained using the sample-path large deviation principle and has implications in call admission control for high-speed communication networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

一类新的插值结点

有界单连通区域Ｇ，其边界θＧ＝Г∈（１，α），α〉０。本计算节以广义Ｆａｂｅｒ多项式φｎ（ｚ）的零点为插值结点的Ｌａｇｒａｎｇｅ插值多项式的逼近性质，得到了它对Ａ（Ｇ↑－）中的函数的一致逼近阶和平均逼近阶的估计，并且得到了它对Ｅ＾ｐ（Ｇ）中函数的平均逼近阶的估计，还指出关于平均逼近阶的估计是不可改进的。     

Stationary Distribution Function Estimation for Ergodic Diffusion Process

The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound.     

三系数有限元向量尺度函数的构造

The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.     

Browder-Petryshyn 型的严格伪压缩映射的粘滞迭代逼近方法

主要研究Browder-Petryshyn型的严格伪压缩映射的粘滞迭代逼近过程,证明了Browder-Petryshyn型的严格伪压缩映射的不动点集F(T)是闭凸集．在q-一致光滑且一致凸的Banach空间中,对于严格伪压缩映射T,利用徐洪坤在2004年引进的粘滞迭代得到的序列弱收敛于T的某个不动点．同时证明了Hilbert空间中Browder-Petryshyn型的严格伪压缩映射的相应迭代序列强收敛到T的某个不动点,其结果推广与改进了徐洪坤2004年的相应结果．