二阶三点边值问题正解的存在性

利用锥拉伸和压缩不动点定理，得到了二阶非线性三点边值问题u″（t）＋a（t）u’（t）＋b（t）u（t）＋h（t）f（t，u,（t））=0，t∈（0，1）u（O）=βu（δη），u（1）=au（η）的正解存在性的充分条件，其中α，β∈[0，＋∞），0〈η〈1     

左端刚性固定右端简单支撑的奇异梁方程正解的存在性

设E[0,1]是一个零测度的闭子集。对于左端刚性固定右端简单支撑的非线性梁方程u^（（4））（t）=f（t,u（t））,t∈[0,1]／E,u（0）=u（1）=u′（0）=u″（1）=0,证明了一个新的正解存在定理,其中允许非线性项f（t,u）是非单调的并且在t=0,t=1及u=0处是奇异的.主要工具是全连续算子的逼近定理和锥压缩锥拉伸型的Guo-Krasnoselskii不动点原理。     

二阶系统边值问题的正解

本文以关于非线性全连续算子的锥不动点定理为工具，研究以下二阶系统边值问题x"（t）＋λa（t）f（x（t），y（t）＝0，y"（t）＋λb（t）g（x（t），y（t））＝0，x（0）＝x（1）＝y（0）＝y（1）＝0．在不假定f单调的情况下，本文得出了上述问题存在正解的若干充分条件．     

一类非线性算子方程的可解性

一类非线性算子方程的可解性王守田（黑龙江大庆石油学院数学系，安达１５１４００）专著［１］把非线性算子方程ｘ＝Ａ（ｘ，…，ｘ）的迭代求解问题列为非线性分析的基本问题之一，文［２］在Ｂａｎａｃｈ空间的锥中讨论了方程ｘ＝Ａ（ｘ，ｘ）的可解性问题，该文中对算...     

变分方法与反向上下解

本文在非线性方程的下解不小于上解这一条件（即反向上下解条件）下研究了其解的存在性．我们证明了，如果非线性算子方程有变分结构，有一对反向上下解，对应的算子映某个锥入锥并且满足一定的辅助条件，那么这一方程在锥中至少有两个解．另外，本文还研究了反向上下解条件下非线性椭圆边值问题正解的存在性．     

高维非自治系统非平凡周期解的存在性

本文利用非线性泛函分析中锥的理论，讨论了ｎ维非自治系统ｘ＝Ａ（ｔ）ｘ＋ｇ（ｔ，ｘ）ｘ∈Ｒ＾ｎ产工得到了系统（１）存在非平凡ω周期解的充分条件。     

四阶边值问题正解的存在性与多解性

本文讨论了非线性四阶边值问题u^(4)(t)=φ（t）f(u(t),u“(t),t∈(0,1),u(0)=u(1)=u“(0) =u“(1)=0正确的存在性，其中φ（t)∈C([0,1],[0,∞)),f(u,v)∈C（[0,∞],[0,∞))。利用锥压缩与锥拉伸不动点定理，给出了该问题正解存在与多个正解存在的充分条件。     

序区间上(-φ)-凸减算子的不动点定理及其应用

本文引入序区间上（－φ）－凸减算子，统一处理了一般凹（凸）的一类减算子，利用锥理论和新的叠代技巧在非紧非连续的假设下得到了不动点的存在唯一性和叠代收敛性。并将所得结果应用于非线性偏微分方程。     

向量值最优化问题的最优性条件与对偶性

本文我们首先给出一类向量值优化问题（VP）的正切锥真有效解的定义，在锥方向导数的假设下，讨论了一类单目标问题 的最优性必要条件；然后利用正切锥方向导数定义一类正切锥F－凸函数类，并给出了（VP）正切锥真有效解的充分性条件，最后我们亦讨论了（VP）在正切锥真有效解意义下的对偶性质。     

Banach空间中一类混合型非线性微分-积分方程的最大最小解的存在性

用单调迭代的方法和一些新的比较结果，研究了Banach空间中一类事型非线性微分－积分方程的最大最小解，我们用空间E的弱完备性和锥P的正规性（这时可推出P是正则的）来代替紧性条件。     

时间随机环境中一维紧邻随机游动的常返性质

设环境q={q(n)}∞0是取值于[0,1]上一列独立同分布的随机变量列,且Eq(0)=p;{Sn}∞0是随机环境q中取整数值随机游动,S0=0,且满足:对任意的整数xi(i≥0),x,y,P(Sn+1=y|S1=x1,…,Sn-1=xn-1,Sn=x,q)={q(n),y=x+1,1-q(n),y=x-1,0,其他.我们证明了:p>1/2时,Sn→+∞,a.e.,n→∞;p<1/2时,Sn→-∞,a.e.,n→∞;p=1/2时,-∞=(lim infSn)/(n→+∞)<(lim supSn)/(n→+∞)=+∞,a.e.,n→∞.     

A dynamic programming approach to the complete set partitioning problem

The complete set partitioning (CSP) problem is a special case of the set partitioning problem where the coefficient matrix has 2 ^m –1 columns, each column being a binary representation of a unique integer between 1 and 2 ^m –1,m1. It has wide applications in the area of corporate tax structuring in operations research. In this paper we propose a dynamic programming approach to solve the CSP problem, which has time complexityO(3 ^m ), wheren=2 ^m –1 is the size of the problem space.     

On the divergence of Nörlund logarithmic means of Walsh-Fourier series

It is well known in the literature that the logarithmic means 1/logn ^n-1∑k=1 Sk（f）/k of Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function on the unit interval. This is not the case if we take the partial sums. In this paper we prove that the behavior of the so-called NSrlund logarithmic means 1/logn ^n-1∑k=1 Sk（f）/n-k is closer to the properties of partial sums in this point of view.     

Strong Arens irregularity of Beurling algebras with a locally convex topology

Let G be a locally compact group with a weight function ω. Recently, we have shown that the Banach space L₀^∞ (G,1/ω) can be identified with the strong dual of L¹(G, ω)equipped with some locally convex topologies τ. Here we use this duality to introduce an Arens multiplication on (L¹(G, ω), τ)**, and prove that the topological center of (L¹(G, ω), τ)** is (L¹(G, ω); this enables us to conclude that (L¹(G, ω), τ) is Arens regular if and only if G is discrete. We also give a characterization for Arens regularity of L₀^∞ (G, 1/ω)¹. Received: 8 March 2005     

AN APPROXIMATION THEOREM OF A M-P INVERSE BY OUTER INVERSES

Let H1 and H2 be separable Hilbert spaces, and B(H1,H2) all of boundedlinear operators from H1 into H2. In this note, we prove the following theorem: for any positive integer N and T ε B(H1, H2) with a closed range, there exists an outerinverse TN^# with finite rank N such that T y = lim TN^#y for any y ε H2, where T N→∞ denotes the Moore-Penrose inverse of T. Thus computing T is reduced to computingouter inverses TN^# with finite rank N. Moreover, because of the stability of boundedouter inverse of a T ε B(H1,H2), this is very useful.     

On Shellsort and the frobenius problem

A boundO(N ^1+1/k ) for the running time of Shellsort, withO(logN) passes, is proved very simply by application of a Frobenius basis withk elements.     

Selection on rectangular meshes with multiple broadcasting

One of the fundamental algorithmic problems in computer science involves selecting thekth smallest element in a setS ofn elements. In this paper we present a fast selection algorithm which runs inO(n ^1/8 logn) time on a mesh with multiple broadcasting of sizen ^3/8 ×n ^5/8. Our result shows that, just like semigroup computations, selection can be done much faster on a suitably chosen rectangular mesh than on square meshes. We also show that if every processor can storen ^1/9 items, then our selection algorithm runs inO(n ^1/9 logn) time on a mesh with multiple broadcasting of sizen ^1/3 ×n ^5/9.Work supported by NASA under grant NCC1-99.This author was partly supported by NSF grant CCR-8009996.     

Inverse scattering up to smooth functions for the Dirac-ZS-AKNS system

We consider the Dirac-ZS-AKNS system (1) where (the space of functions with n derivatives in L ¹), (2) We consider for (1) the transition matrix and, in addition, for the case of the Dirac system (i.e. for the selfadjoint case the scattering matrix We can divide main results of the present work into three parts. I. We show that the inverse scattering transform and the inverse Fourier transform give the same solution, up to smooth functions, of the inverse scattering problem for (1). More preciseley, we show that, under condition (2) with , the following formulas are valid: (3) and, in addition, for the case of the Dirac system (4) where denotes the factor space. II. Using (3), (4), we give the characterization of the transition matrix and the scattering matrix for the case of the Dirac system under condition (2) with III. As applications of the results mentioned above, we show that 1) for any real-valued initial data , the Cauchy problem for the sh-Gordon equation has a unique solution such that and for any t > 0, 2) in addition, for , for such a solution the following formula is valid: where denotes the space of functions locally integrable with n derivatives. We give also a review of preceding results.     

Stable minimum space partitioning in linear time

In the stable0–1 sorting problem the task is to sort an array ofn elements with two distinct values such that equal elements retain their relative input order. Recently, Munro, Raman and Salowe gave an algorithm which solves this problem inO(n log*n) time and constant extra space. We show that by a modification of their method the stable0–1 sorting is possible inO(n) time andO(1) extra space. Stable three-way partitioning can be reduced to stable0–1 sorting. This immediately yields a stable minimum space quicksort, which sorts multisets in asymptotically optimal time with high probability.