几乎齐次函数的刻划定理

给出了几乎齐次函数的一个新的刻划定理，这一刻划是齐次函数欧拉定理的拓广。     

Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices

The sum of the largest eigenvalues of a symmetric matrix is a nonsmooth convex function of the matrix elements. Max characterizations for this sum are established, giving a concise characterization of the subdifferential in terms of a dual matrix. This leads to a very useful characterization of the generalized gradient of the following convex composite function: the sum of the largest eigenvalues of a smooth symmetric matrix-valued function of a set of real parameters. The dual matrix provides the information required to either verify first-order optimality conditions at a point or to generate a descent direction for the eigenvalue sum from that point, splitting a multiple eigenvalue if necessary. Connections with the classical literature on sums of eigenvalues and eigenvalue perturbation theory are discussed. Sums of the largest eigenvalues in the absolute value sense are also addressed.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.The work of this author was supported by the National Science Foundation under grants CCR-8802408 and CCR-9101640.The work of this author was supported in part during a visit to Argonne National Laboratory by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under contract W-31-109-Eng-38, and in part during a visit to the Courant Institute by the U.S. Department of Energy under Contract DEFG0288ER25053.     

凸集的广义Reuleaux三角形

常宽凸集的面积最小者为Reulaux三角形，而非常宽凸集的面积最小者为何呢？它就是本文将给出的广义Reuleaux三角形△R。     

一些部分差集和相对差集的构造

In this paper, we give a construction of RDS in Galois ring by using some bent function, and obtain the equivalent relationship between RDS and a kind of bent function. At the same time, its existence is demonstrated.     

Banach空间中凸映照的增长定理

本文利用凸映照的几何特征证明了一般复Banach空间中单位球上正规化双全纯凸映照的增长定理，即||f(x)||≤||x||/(1-||x||),A↓x∈B，对复内积空间，上述估计是最佳的。     

Differential subordinations concerning starlike functions

Denote byS ^* (⌕), (0≤⌕<1), the family consisting of functionsf(z)=z+a ₂z²+...+a_nzⁿ+... that are analytic and starlike of order ⌕, in the unit disc ⋎z⋎<1. In the present article among other things, with very simple conditions on μ, ⌕ andh(z) we prove the f’(z) (f(z)/z)^μ−1<h(z) implies f∈S^*(⌕). Our results in this direction then admit new applications in the study of univalent functions. In many cases these results considerably extend the earlier works of Miller and Mocanu [6] and others.     

球约束凸二次规划的一个新算法

首先利用Lagrange对偶 ,将球约束凸二次规划问题转化为无约束优化问题 ,然后运用单纯形法求解无约束优化问题 ,从而获得原问题的最优解     

Fixed Point Theorems on Product Topological Spaces and Applications

A new collectively fixed point theorem for a family of set-valued mappings defined on product spaces of non-compact topological spaces without linear structure is proved and some special cases are also discussed. As applications, some non-empty intersection theorems of sets with convex sections and equilibrium existence theorem of abstract economies are obtained under much weaker assumptions. Our results includes a number of known results as many special cases.     

一个含有和、积、幂结构的新不等式

本利用一个凸函数的凸性，并结合Jensen加权不等式，导出一个含和、积、幂结构的新不等式，它包含了一些名不等式。     

测定汞原子塞曼谱线相对强度

在原塞曼效应实验基础上，测定了塞曼分裂各谱线的相对强度，以作为原实验的补充．