关于J－对称微分算子的J－自伴扩张的若干注记

本文给出了一条解析描述Ｊ－对称微分算子Ｊ－自伴扩张的新途径．我们借助方程Ｔ（ｙ）＝λｏｙ的解，而不是如文［３］利用方程＋（ｙ）＇＝－ｙ的解来描述Ｊ－对称微分算式的所有Ｊ－自伴域在奇异端点的边条件，不过我们假设生成的最小算子具非空正则域．我们对主要定理给出了若干有趣的注，得到了二阶极限圆情形的有趣结果．     

关于J－对称微分算子的J－自伴扩张的若干注记

本文给出了一条解析描述Ｊ－对称微分算子Ｊ－自伴扩张的新途径．我们借助方程Ｔ（ｙ）＝λｏｙ的解，而不是如文［３］利用方程＋（ｙ）＇＝－ｙ的解来描述Ｊ－对称微分算式的所有Ｊ－自伴域在奇异端点的边条件，不过我们假设生成的最小算子具非空正则域．我们对主要定理给出了若干有趣的注，得到了二阶极限圆情形的有趣结果．     

复系数2n阶微分算子的谱

本文研究了复系数２ｎ阶微分算式（２．１）生成的Ｊ－自伴微分算子谱,对两类微分算子的本质谱,离散谱作了定性研究,得到了所生成微分算子本质谱的存在范围,以及所生成微分算子的谱是离散的充分条件．     

关于一类具有中间亏指数的正系数的对称微分算子

本文研究了一类具有中间亏指数的正系数的对称微分算式＝０（－１）ｋＤｋｅａｎｘＤｋ及＝０（－１）ｋａｋＤｋｅａｎｘＤｋ,证明了它们的亏指数的值域是（ｎ,ｎ＋２,…,２ｎ－１）或｛ｎ,ｎ＋ ２,…,２ｎ－２ ｝,或是一个子集合,并给出了具中间亏指数的算式的例子·这些例子表明具正系数的对称微分算式不一定都是极限点的,从而对 Ｅｖｅｒｉｔｔ Ｗ． Ｎ．［１］提出的猜测又以一种新的方式给出了否定的回答．本文还得到了一类非对称的微分算式一些相应的结果．     

Hermite型插值算子对可微函数的逼近

Ｈｅｒｍｉｔｅ型插值算子对可微函数的逼近章仁江（中国计量学院，杭州３１００３４）关键词Ｈｅｒｍｉｔｅ型插值算子，Ｊａｃｏｂｉ多项式．分类号ＡＭＳ（１９９１）４１Ａ／ＣＣＬＯ１７４设（１）＞ｘ１＞ｘ２＞…＞ｘｎ＞（－１），ｘｋ＝ｃｏｓθｋ（ｋ＝１，２，...     

SL(n+1,R)/S(GL(1,R)×GL(n,R))上线丛的一个超几何方程

本文研究了伪黎曼对称空间SL（n+1,R）/S（GL（1,R）×GL（n,R））线丛上的微分方程.利用李代数方法,即Casimir算子得到这个微分算子.这个微分算子是一个超几何方程,这个结论推广了文献[1,3,5]中的微分方程.     

d维Bernstein算子加Jacobi权的收敛阶

１．引 言 设Ｓ＝Ｓｄ（ｄ＝１,２,…）是 Ｒｄ中的单纯形,即记ｋ＝（ｋ１,ｋ２,……,ｋｄ）∈Ｒｄ,ｋｉ为非负整数, ,则Ｓ上定义的函数ｆ所对应的ｄ维Ｂｅｒｎｓｔｅｉｎ算子定义为其中 Ｐｎ,ｋ（ｘ）＝是 Ｂｅｒｎｓｔｅｉｎ基函数．引进多维Ｊａｃｏｂｉ权函数, 这里 ．定义Ｂｅｒｎｓｔｅｉｎ权函数 表示微分算子． 记 是单位向量,即第ｉ个分量为１,其余ｄ－１个分量为０, ．定义函数ｆ在方向ｅ上的ｒ阶对称差分为Ｃ（Ｓ）中的加权Ｓｏｂｏｌｅｖ空间为其中Ｓ为Ｓ的内部．定义加权Ｋ－泛函及加权光滑模其中 为加权范数． …     

某类带参数4n－阶微分算子的一个同胚与线性同胚定理

本文对某类由考察一些物体的运动性状而引出的４ｎ－阶线性非对称或非线性微分算子给出了一个正则性定理。这个定理包含在实（非线性）情形下２个同胚与扩张同胚类，或者在复（线性）情形下３个线性同胚与扩张线性同胚类。这对于揭示某些物体（例如，某些飞行器）在它们运动过程中的双向平稳性是有用的。     

完全非线性混合可积微分算子解的正则性——献给陆善镇教授75华诞

本文介绍一类带有非对称正核的完全非线性混合可积微分算子并研究其解的正则性.具体地,本文建立关于该算子非局部A-B-P（Alexandroff-Bakelman-Pucci）估计、Harnack不等式以及解的Holder和C1,α正则性.     

广义微分算子的谱

本文利用经典的角度量的方法，研究了由Ｒ－Ｎ导数定义的广义微分算子Ｌ的谱性质，这种性质以前尚未被研究过。文章共分三部分：（一）给出广义微分算子Ｌ的定义，并介绍了文中涉及的一些概念；（二）给出文中要用到的一些已知定理；（三）通过讨论角度变量θ（ｘ，λ），得出算子Ｌ的一些谱性质．     

一个关于非负矩阵的不等式

证明:若(xij)是一个元素不全为零的m×n非负矩阵,则当0相似文献   

关于联图P_1VP_n的k-强优美性

本文研究了联图P_1VP_n的k-强优美性问题.利用K-强优美图的定义,获得了联图P_1VP_n是k-强优美图的必要条件,还得到了当n:2k-1时联图P_1VP_n是k-强优美图,亦是k-优美图,及当n≥3时联图P_1VP_n是2-强优美图,也是2-优美图的结果,推广了联图P_1VP_n是优美图的结果.     

Notes on D-optimal designs

The purpose of this paper is to exhibit new infinite families of D-optimal (0, 1)-matrices. We show that Hadamard designs lead to D-optimal matrices of size (j, mj) and (j − 1, mj), for certain integers j ≡ 3 (mod 4) and all positive integers m. For j a power of a prime and j ≡ 1 (mod 4), supplementary difference sets lead to D-optimal matrices of size (j, 2mj) and (j − 1, 2mj), for all positive integers m. We also show that for a given j and d sufficiently large, about half of the entries in each column of a D-optimal matrix are ones. This leads to a new relationship between D-optimality for (0, 1)-matrices and for (±1)-matrices. Known results about D-optimal (±1)-matrices are then used to obtain new D-optimal (0, 1)-matrices.     

Minimum vertex covers and the spectrum of the normalized Laplacian on trees

We show that, in the graph spectrum of the normalized graph Laplacian on trees, the eigenvalue 1 and eigenvalues near 1 are strongly related to minimum vertex covers.In particular, for the eigenvalue 1, its multiplicity is related to the size of a minimum vertex cover, and zero entries of its eigenvectors correspond to vertices in minimum vertex covers; while for eigenvalues near 1, their distance to 1 can be estimated from minimum vertex covers; and for the largest eigenvalue smaller than 1, the sign graphs of its eigenvectors take vertices in a minimum vertex cover as representatives.     

Simple assembly line balancing—Heuristic approaches

In this paper heuristics for Type 1 and Type 2 of the Simple Assembly Line Balancing Problem (SALBP) are described. Type 1 of SALBP (SALBP-1) consists of assigning tasks to work stations such that the number of stations is minimized for a given production rate whereas Type 2 (SALBP-2) is to maximize the production rate, or equivalently, to minimize the sum of idle times for a given number of stations. In both problem types, precedence constraints between the tasks have to be considered.We describe bidirectional and dynamic extensions to heuristic priority rules widely used for SALBP-1. For the solution of SALBP-2 we present search methods which involve the repetitive application of procedures for SALBP-1. Furthermore, improvement procedures for SALBP-2 are developed and combined with tabu search, a recent strategy to overcome local optimality. Several optional elements of tabu search are discussed. Finally, the application of a nontraditional tabu search approach to solve SALBP-1 is investigated. Computational experiments validate the effectiveness of our new approaches.     

THE EXISTENCE AND STABILITY OF THE HETEROCLINIC CYCLE IN A KIND OF BIOLOGICAL SYSTEM

IIntroductlonConsider the n－spedes biological systemlit\1．＝IJ!厂．＋》*i,工上D、忍＝上,’··。n．ti)Ifffi＝1,it is S S－SpSCllS LOthaka－VoltOOYY SystSS．Iftti＝2,It Is S S－sPeCieSKolmongorov system．As to the n－spedes Gause－Lotb－Volterra system矿ti 乙工．＝T;Ii、y Qiil．I。Ti 7 U,on M U,t6)174 AnnofDiff Eqs．VO18M叫 and Leonard[1],Ho凡aner and Sigmund问 have studied this system forthe case n二 3 respectlvelyand noted that thereprobably exists aheterocllnlccyclefor…     

一类抛物型方程边界条件的均匀化模型及证明

设伪抛物问题边界 Ω =Γ可表为Γ =Γ0 ∪Γ1,对任意ε>0 ,将Γ1分为Γε1和Γε1,并在其上给出不同的边界条件 ;讨论了几种当Γε1的每一连通分支的直径或沿某方向的直径随ε趋于零而趋于零时的相应解的极限性态 .     

共振条件下多点边值问题解的存在性

本文讨论多点边值问题x"(t)=f(t,x(t),x'(t))+e(t),t∈(0,1);x'(0)= x'(ξ),x(1)=sum from i=1 to m-3βix(ηi)解的存在性,其中βi∈R,sum from i=1 to m-3β=1,0<η1<η2< …<ηm-3<1,0<ξ<1,sum from i=1 to m-3βiηi=1.这时dimKer L=2.当βi取不同的符号 时,应用Mawhin重合度定理,证明了多点边值问题的一些存在性结果. 以前文章所 涉及的多点边值问题解的存在性都是在dim Ker L=1的情况下讨论的,所以我们的 工作是新的探索.     

给定顶点数和边数的连通图的Q-谱半径的界

图的无符号拉普拉斯矩阵是图的邻接矩阵和度对角矩阵的和,其特征值记为q1≥q2≥…≥qn.设C(n,m)是由n个顶点m条边的连通图构成的集合,这里1≤n-1≤m≤(n2).如果对于任意的G∈C(n,m)都有q1(G*)≥q1(G)成立,图G*∈C(n,m)叫做最大图.这篇文章证明了对任意给定的正整数a=m-n+1,如果n...     

On the analysis of a dynamic evolutionary algorithm

Evolutionary algorithms are applied as problem-independent optimization algorithms. They are quite efficient in many situations. However, it is difficult to analyze even the behavior of simple variants of evolutionary algorithms like the (1+1) EA on rather simple functions. Nevertheless, only the analysis of the expected run time and the success probability within a given number of steps can guide the choice of the free parameters of the algorithms. Here static (1+1) EAs with a fixed mutation probability are compared with dynamic (1+1) EAs with a simple schedule for the variation of the mutation probability. The dynamic variant is first analyzed for functions typically chosen as example-functions for evolutionary algorithms. Afterwards, it is shown that it can be essential to choose the suitable variant of the (1+1) EA. More precisely, functions are presented where each static (1+1) EA has exponential expected run time while the dynamic variant has polynomial expected run time. For other functions it is shown that the dynamic (1+1) EA has exponential expected run time while a static (1+1) EA with a good choice of the mutation probability has polynomial run time with overwhelming probability.