整环上Moore-Penrose逆的刻画

若A为整环上的n阶可逆矩阵,则X=A-1是满足方程rank■=rank(A)的唯一矩阵.把它推广到满足Rao条件的整环上得到关于矩阵A的Moore-Penrose逆A+的刻画.     

A(X,M)-c-内射性

本文研究了X-扩张模.利用A( X,M)-c-内射模的概念,获得了A( X,M)-c-内射模的有限直和仍是A( X,M)-c-内射模的一个充分必要条件,并推广了相应的结果.     

汽车行驶的时间问题

就d>2R的情形解决如下组合几何极值问题:某平原地区有一个很大的湖泊.湖泊周围有两个村庄A,B.村庄A到村庄B的直线距离为已知.一辆汽车从A村庄出发以已知匀速速度驶向村B庄.问:若这辆汽车以最短路径行驶到达B村庄至多需要多少时间?     

最优带仲裁认证码

本文研究带仲裁认证码（亦称A^2-码）。一个A^2-码，当它的欺骗攻击成功概率达到信息论下界且密钥长度也达到最小时称为是最优的。本文给出最优A^2-码的组合结构的特征，从而将构造最优A^2-码的问题归结为构造相应的一类组合设计的问题。     

On Symmetric Cayley Graphs of Valency Eleven

A Cayley graph Γ=Cay(G,S)is said to be normal if G is normal in Aut Γ.In this paper,we investigate the normality problem of the connected 11-valent symmetric Cayley graphs Γ of finite nonabelian simple groups G,where the vertex stabilizer Av is soluble for A=Aut Γ and v ∈ VΓ.We prove that either Γ is normal or G=A5,A10,A54,A274,A549 or A1099.Further,11-valent symmetric nonnormal Cayley graphs of A5,A54 and A274 are constructed.This provides some more examples of nonnormal 11-valent symmetric Cayley graphs of finite nonabelian simple groups after the first graph of this kind(of valency 11)was constructed by Fang,Ma and Wang in 2011.     

Complete intersection points on affine varieties

This paper addresses the following problem: given a commutative ring A, what is the structure of the set of “CI points,” i.e., those maximal ideals generated by dim(A) elements? When A is finitely generated over an algebraically closed field, we conjecture that this set is a countable union of closed subsets of Max(A). When A is regular of dimension ? or 3, we verify this conjecture, as well as an analogous set-theoretic conjecture.     

代数A在子代数A^H上投射的若干充分条件

假设Ｈ是域ｋ上的有限维Ｈｏｐｆ代数,Ａ是Ｈ－模代数,本文刻画了Ａ＾ＨＡ的投射性并给出了Ａ＾ＨＡ是投射的若干充分条件,其中Ａ＾Ｈ是Ａ的Ｈ－不变子代数。     

M-P逆和加权M-P逆的有限迭代计算公式

本文，对于任意给定的矩阵A，我们给出了计算其M—P逆和加权M—P逆的有限迭代计算公式．根据这一迭代公式，当我们选取初始矩阵为X0=A^#，则矩阵A的加权M—P逆A^＋MN在不考虑舍入误差的情况下，可以在有限迭代的情况得到，同样当我们选取初始矩阵X0=A^＊，其M—P逆A^＋亦可以在有限迭代下获得．最后我们用数值例子检验了我们算法的正确性。     

On a Plus-Construction for Algebras over an Operad

We prove a analogous to Quillen's plus-construction in the category of algebras over an operad. For that purpose we prove that this category is a closed model category and prove the existence of an obstruction theory. We apply further this plus-construction for the specific cases of Lie algebras and Leibniz algebras which are a noncommutative version of Lie algebras: let sl(A) be the kernel of the trace map gl(A)A/[A,A], where A is an associative algebra with unit and gl(A) is the Lie algebra of matrices over A. Then the homotopy of slA)⁺ in the category of Lie algebras is the cyclic homology of A whereas it is the Hochschild homology of A in the category of Leibniz algebras.     

二维核废料污染问题的一个二阶差分格式

本文研究了多孔介质中含分子弥散的不可压核废料污染问题,此模型由一非线性抛物-椭圆耦合偏微分方程组的初边值问题来描述,对此问题利用降阶法给出了一个关于时间和空间均具有二阶精度的差分格式,并对所构造的格式进行了理论分析,得到了离散的l2模误差估计结果.     

矩阵moore—penrose逆的一种简捷求法

本文结出了利用AA~H或A~HA的特征多项式求矩阵A的moore-peuroxe逆的方法。     

Nontrivial Attractors in a Model Related to the Three-Body Quantum Problem

A model of a quantum mechanical system related to the three-body problem is studied. The model is defined in terms of a symmetric pseudo-differential operator (PDO) with unbounded symbol. The entire family of self-adjoint extensions of this operator is studied using harmonic analysis. A regularization procedure for this PDO is introduced and the spectral properties of the operators obtained in this way are investigated. The limit behavior of the regularized operators when the regularization parameter is removed is analyzed and a nontrivial attractor is exhibited.     

On the consistency of linear and quadratic systems

A system of linear inhomogeneous inequalities is examined. An algorithm is presented for isolating all the consistent subsystems in this system that are maximal with respect to inclusion, and justification of this algorithm is given. A criterion for the consistency of a system of quadratic inhomogeneous equations and inequalities is proposed.     

A new defect‐correction method for the stationary Navier‐Stokes equations based on pressure projection

A new defect‐correction method based on the pressure projection for the stationary Navier‐Stokes equations is proposed in this paper. A local stabilized technique based on the pressure projection is used in both defect step and correction step. The stability and convergence of this new method is analyzed detailedly. Finally, numerical examples confirm our theory analysis and validate high efficiency and good stability of this new method.     

The asymptotically best method for synthesizing limited-depth Boolean recursive schemes

A model of limited-depth recursive schemes for the functions of Boolean algebra (Boolean functions), constructed from multi-output functional elements, is considered. A lower estimate of the Shannon function for the complexity of schemes of this class is derived. Upper estimates for the complexity of some specific functions and systems of functions in this class of schemes are obtained. A method is proposed for synthesizing schemes of this class for arbitrary functions that allow us (using the derived lower estimate) to determine the asymptotics of the Shannon function for their complexity.     

无和数列的倒数和

设A={a1,a2,...}是一个严格递增的正整数数列,如果每一个an都不能写成它前面一些不同项的和,则称A为无和数列.令ρ(A)=∑∞k=11ak.1962年,Erds证明了,对任意无和数列A,有ρ(A)103.1977年,Levine和O’Sullivan改进为ρ(A)3.9998.最近,Chen进一步改进为ρ(A)3.0752.本文证明了,对于无和数列A={a1,a2,...}(a1a2···),当a12时,有ρ(A)2.526.     

PERMANENCE OF A NONAUTOMONOUS POPULATION MODEL

1.IntroductionPersistenceofpopulationsplaysanimportantroleinmathematicalecology.Inrecentyears)muchattentionhasbeengiventothepersistenceofnonautomonouspopulationmodelsll--6].[1]proposedtheconceptofpersistenceinthemeanofpopulations.Thisisofimportancebecausenotonlyitprovidesawaytocharacterizethepersistenceofpopula-nons,butalsothereareonlythresholdsbetweenpersistenceinthemeanandtheextinctionofpopulationsforgeneralnonautomonouspopulationmodels.In[2]thethresholdwasestablishedforone-dimensionalnonaut…     

求矩阵广义逆的另一种初等变换方法

讨论了当矩阵A为满秩矩阵时求其广义逆的一种方法,并将此方法推广,给出当A为非满秩矩阵时求其广义逆的一般方法,同时给出算例.本文推广了文献[1]的结果.     

A series solution of nonlinear injection–extraction well equation

In this paper, the groundwater flow will be investigated. The tracer concentration is calculated for the saturated–unsaturated aquifer. A nonlinear diffusion equation is derived in a single injection–extraction well. A numerical procedure based on Adomian-decomposition method (ADM) is proposed for solving this nonlinear diffusion equation and finally this method is examined for some test problems.     

局部域上的仿交换算子

本文的主要结果是:当A(ξ,η)满足A0,A1,A2,A3,A4时,则T_b在L~2(K)中有界的充要条件是b∈BMO(K).并用此结果推出带符号b的分数次积分交换子,奇异积分交换子在L~2(K)中有界的充要条件,和带符号b的乘子交换子在L~2(K)中有界的一个充分条件.