实Banach空间中点到有限余维子空间的距离问题

讨论了点到有限余维子空间或者仿射集的最短距离问题.应用对偶化方法,得到了点到满足一定条件的有限余维子空间(或者仿射集)的距离公式,以及此时最佳逼近元的计算式,并给出了它们在某些具体的最优控制问题上的应用.     

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR NEUTRAL PERTURBED DYNAMIC EQUATIONS ON TIME SCALES

In this paper,we discuss the oscillatory behavior of a class of nonlinear neutral perturbed dynamic equations on time scales.Some new oscillation criteria are obtained for such dynamic equations.Finally,an example that dwells upon the sharp conditions of our result is also included.     

重积分和线面积分中的一个典型题目

针对授课班级出错率较高的一道曲面积分题目,给出四种解法.分析出错的原因在于练习不够外,主要是对重积分概念理解不够透彻.     

On the Ferrers property of valued interval orders

We study the relationship between the Ferrers property and the notion of interval order in the context of valued relations. Given a crisp preference structure without incomparability, the strict preference relation satisfies the Ferrers property if and only if the associated weak preference relation does. These conditions characterize a total interval order. For valued relations the Ferrers property can be written in two different and non-equivalent ways. In this work, we compare these properties by finding the kind of completeness they imply. Moreover, we study whether they still characterize a valued total interval orders.     

奇完全数的几个命题

本文证明形如3m-1的正整数不是完全数,由此推出当所有的qi≡-1(mod 3)时,奇数n=p~αП_(i=1)~sq_i~(2β_i)若是完全数,那么1/2σ(p~α)必是合数.指出k倍完全数的素因子必须满足一个不等式.运用此不等式证明当a≥n-2时形如a~(2~n)+b~(2~n)(a>b>0,a,b,n∈N~+)的奇数不是完全数.还指出当a与b都与3互素时,对于任意的正整数m,n,奇数a~(2~n)+b~(2~m)不是完全数.     

由Levy过程驱动的倒向随机微分方程在随机单调条件下解的存在唯一性

本文讨论了如下的由Levy过程驱动的倒向随机微分方程适应解的存在唯一性■其中W_s是一Wiener过程,H_s为由Levy过程构成Teugels鞅.我们通过构造函数逼近序列的方法证明了,在漂移系数f关于Y满足随机单调,f关于Z和U满足随机Lipschitz条件下,方程存在唯一适应解.     

有限群的Sylow-子群的弱s-可补极大子群(英文)

假设G是一个有限群,H是G的一个子群.称H在G是s-置换的,若对G的任意的Sylow-子群Gp,有HG_p=G_pH:称H在G是弱s-可补的,若存在G的子群T使得G=HT且H∩T≤H_(sG),其中H_(sG)是所有包含在H中的G的s-置换子群生成的子群.本文给出了下列定理:设F是一个包含超可解群系u的饱和群系,有限群G有一个正规子群H使得G/H∈F.若F~*(H)的每个Sylow子群的所有极大子群在G中是弱s-可补的,其中F~*(H)是H的广义Fitting子群,则G∈F.它是J.Algebra,2007,315:192-209一文中的Skiba公开问题在极大子群情形下的肯定回答.     

ASYMPTOTIC STABILITY OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH CONSTANT DELAYS:A DESCRIPTOR SYSTEM APPROACH

In this article,we establish some new delay-dependent and delay-independent stability criteria for all solutions to a nonlinear neutral differential equation,using Lyapunov-Krasovskii functional.     

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS TO A DISCRETE TIME NON-AUTONOMOUS COMPETING SYSTEM WITH FEEDBACK CONTROLS

In this paper,a class of discrete time non-autonomous competing system with feedback controls is considered. With the help of differential equations with piecewise constant arguments,we first propose a discrete model of a continuous non-autonomous competing system with feedback controls. Then,using the coincidence degree and the related continuation theorem as well as some priori estimations,a suficient condition for the existence of positive solutions to difference equations is obtained.     

OSCILLATION OF SOLUTIONS TO SECOND ORDER NEUTRAL PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Some new oscillation criteria are established for a second order neutral partial functional differential equation.Assumptions in our theorems are less restrictive,also the proofs are simpler than those in Li and Cui [11].We remove some assumptions that are required for the related results in the previous papers,thus our results generalize and improve many known conclusions.