A THEOREM ON THE 1-FACTORS OF (m, n)-TREES

In this paper a necessary and sufficient condition for a (m, n)-tree to have a 1-factor is given. Tutte's theorem in which the given graph is a tree is generalized.     

THE EIGENVALUE PROBLEM EQUIVALENT TO MULTIVARIATE POLYNOMIAL SYSTEM

In this paper, the authors proved that finding all solutions of a given multivariate polynomial system is equivalent to solving a relative joint eigenvalue problem(Theorem 1) and in some cases one can find all solutions of the given system from the eigenvalues and vectors of one matrix or matrix pencil (Theorem 2). Especially the situation that the ideal generated by the given system is 0-dimensional is discussed.     

A NEW APPROACH TO SOLVE SYSTEMS OF LINEAR EQUATIONS

1. IntroductionThe new aPProaCh is based on the analysis of the motion of a damped harmonic oscillatorin the gravitational field 11]. The associated equation of motion ismXtt + oXt + aX = b (1)where X = X(t), is the one dimensions di8PlaCement of Of a mass m under a dissipation(o > 0), a ~nic potential (a > 0) and a constant acceleration (b, gravitational field). Thetotal energy variation is given by the equationwhereThe solution of the motion equation (1) is given by the sum of two contr…     

NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF PERIODIC SOLUTIONS OF RICCATI'S EQUATION WITH PERIODIC COEFFICIENTS

In this paper, the concept of generalized ω-periodic solution is given for Riccati's equationy'=a(t)y~2 b(t)y c(t)with perriodic coefficients, the relation between generalized ω-periodicsolutions and the characteristic numbers of system x'_1=c(t)x_2, x'_2=-a(t)x_1-b(t)x_2 is indicated, andseveral necessary and sufficient conditions are given using the coefficients. Moreover, in the case of a(t)without zero, the relation between the number of continuous ω-periodic solutions of y'=a(t)y~2 b(t)y c(t) δand the parameter δ is given; thus the problem on the existence of continuous ω-periodic.solutions is basically solved.     

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE ADVECTION-DIFFUSION EQUATIONS

1. IntroductionConsider the advection--diffusion equationin a bounded polygonal domain fl c IR2 with the boundary an, where o < K << 1 is thediffusion parameter, rr > 0 is a given positive constant, g(x) is a given vector field representingthe flow with V…     

GEOMETRY AND DIMENSION OF SELF—SIMILAR SET

The authors show that the self-similar set for a finite family of contractive similitudes (similarities, i.e., |fi(x) - fi(y)| = αi|x - y|, x,y ∈ RN, where 0 < αi < 1) is uniformly perfect except the case that it is a singleton. As a corollary, it is proved that this self-similar set has positive Hausdorff dimension provided that it is not a singleton. And a lower bound of the upper box dimension of the uniformly perfect sets is given. Meanwhile the uniformly perfect set with Hausdorff measure zero in its Hausdorff dimension is given.     

DNA labelled graphs with DNA computing

Let k≥2, 1≤i≤k andα≥1 be three integers. For any multiset which consists of some k-long oligonucleotides, a DNA labelled graph is defined as follows: each oligonucleotide from the multiset becomes a point; two points are connected by an arc from the first point to the second one if the i rightmost uucleotides of the first point overlap with the i leftmost nucleotides of the second one. We say that a directed graph D can be(k, i;α)-labelled if it is possible to assign a label(l_1(x),..., l_k(x))to each point x of D such that l_j(x)∈{0,...,a-1}for any j∈{1,...,k}and(x,y)∈E(D)if and only if(l_k-i 1(x),..., l_k(x))=(l_1(y),..., l_i(y)). By the biological background, a directed graph is a DNA labelled graph if there exist two integers k, i such that it is(k, i; 4)-labelled. In this paper, a detailed discussion of DNA labelled graphs is given. Firstly, we study the relationship between DNA labelled graphs and some existing directed graph classes. Secondly, it is shown that for any DNA labelled graph, there exists a positive integer i such that it is(2i, i; 4)-labelled. Furthermore, the smallest i is determined, and a polynomial-time algorithm is introduced to give a(2i, i; 4)-labelling for a given DNA labelled graph. Finally, a DNA algorithm is given to find all paths from one given point to another in a(2i, i; 4)-labelled directed graph.     

A new approximate proximal point algorithm for maximal monotone operator

The problem concerned in this paper is the set-valued equation 0 ∈T(z) where T is a maximal monotone operator. For given xk and βk > 0, some existing approximate proximal point algorithms take x~(k+1) = xk such thatwhere {ηk} is a non-negative summable sequence. Instead of xk+1 = xk , the new iterate of the proposing method is given bywhere Ω is the domain of T and PΩ(·) denotes the projection on Ω. The convergence is proved under a significantly relaxed restriction supk>0 ηk<1.     

SUPERPOSITION FORMULAE OF A FIFTH ORDER KdV EQUATION AND ITS MODIFIED EQUATION

The Backlund transformation (BT) for a fifth order KdV equation is presented in the bilinear form.Furthermore,a nonlinear superposition formula related to the BT obtained above is proved rigorously.By the way,a nonlinear superposition formula of a modified fifth order KdV equation is also given.     

First passage models for denumerable semi-Markov decision processes with nonnegative discounted costs

This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs.The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set.We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy.Then,we prove that the value function satisfies the optimality equation and there exists an optimal(or e-optimal) stationary policy under suitable conditions by using a minimum nonnegative solution approach.Further we give some properties of optimal policies.In addition,a value iteration algorithm for computing the value function and optimal policies is developed and an example is given.Finally,it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes.     

一种特殊规划的分块超松驰组合牛顿——乘子算法

本文给出了分块的超松驰组合牛顿－乘子（ＢＳＯＲ－Ｎ－Ｍ）方法，来求解一类约束函数可分块的规划问题，证明了其收敛性，进一步给出与理论相应的数值结果。     

一种两点迭代法

本文给出了一个求超越方程实根的新的两点格式ｘｋ＋１＝ｘｋ－ｘｋ－ｘｋ－１３ｆ（ｘｋ）－４ｆｘｋ＋ｘｋ－１２＋ｆ（ｘｋ－１）ｆ（ｘｋ），它集弦割法和抛物线法的优点于一身，具有更快的收敛速度，且收敛阶为二阶．     

降低风险措施有效性综合评价的一种非参数方法

针对风险评估中提出的以下3个问题：（1）当投入量不增时,能否继续降低风险层次,（2）在风险层次不升高的情况下,能否降低投入量,（3）对于某一方案投入指标和风险指标是否还有进一步改进的可能性,给出了一种用于评价降低风险措施有效性的非参数方法（RDEA）,并对文[1]中的有关模型进行了进一步分析,运用偏序集理论给出了DEA有效的一个充要条件.最后,探讨了该方法在船舶工程领域中的应用.     

解非线性方程组的一类离散的Newton算法

1．引言考虑非线性方程组设xi是当前的迭代点，为计算下一个迭代点，Newton法是求解方程若用差商代替导数，离散Newton法要解如下的方程其中这里为了计算J（；；h），需计算n‘个函数值．为了提高效能，Brown方法l‘］使用代入消元的办法来减少函数值计算量．它是再通过一次内选代从h得到下一个迭代点14＋1．设n；＝（《1，…，Zn尸，t二（ti，…，t＊”，t为变量．BfOWll方法的基本思想如下．对人（x）在X；处做线性近似解出然后代入第二个函数，得到这是关于tZ，…，tn的函数．当（tZ，…，t。尸一（ZZ，…，Z。厂时，由（1．4），…     

一类特殊的椭圆型问题的高效蒙特卡罗算法

针对求一类特殊的椭圆型问题在任意点的数值解问题,本文在把有限元方法与蒙 特卡罗方法相结合的基础上提出了一种新的高效蒙特卡罗算法,并用算例说明了该方法 的优越性.     

一个四阶收敛的牛顿类方法

A fourth-order convergence method of solving roots for nonlinear equation,which is a variant of Newton's method given.Its convergence properties is proved.It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end,numerical tests are given and compared with other known Newton and Newtontype methods.The results show that the proposed method has some more advantages than others.It enriches the methods to find the roots of non-linear equations and it ...     

A Ulm-like method for inverse eigenvalue problems

We propose a Ulm-like method for solving inverse eigenvalue problems, which avoids solving approximate Jacobian equations comparing with other known methods. A convergence analysis of this method is provided and the R-quadratic convergence property is proved under the assumption of the distinction of given eigenvalues. Numerical experiments as well as the comparison with the inexact Newton-like method are given in the last section.     

扩充偏微分方程(组)守恒律和对称的辅助方程方法及微分形式吴方法的应用

首先,我们给出了引入伴随方程(组)扩充原方程(组)的策略使给定偏微分方程(组)的扩充方程组具有对应泛瓯即,成为Lagrange系统的方法,以此为基础提出了作为偏微分方程(组)传统守恒律和对称概念的一种推广-偏微分方程(组)扩充守恒律和扩充对称的概念;其次,以得到的Lagrange系统为基础给定了确定原方程(组)扩充守恒律和扩充对称的方法,从而达到扩充给定偏微分方程(组)的首恒律和对称的目的;第三,提出了适用于一般形式微分方程(组)的计算固有守恒律的方法;第四,实现以上算法过程中,我们先把计算(扩充)守恒律和对称问题均归结为求解超定线性齐次偏微分方程组(确定方程组)的问题.然后,对此关键问题我们提出了用微分形式吴方法处理的有效算法;最后,作为方法的应用我们计算确定了非线性电报方程组在内的五个发展方程(组)的新守恒律和对称,同时也说明了方法的有效性.     

基于同伦分析方法的一种改进的试位法

应用同伦分析方法,提出了一种求解非线性方程改进的试位法．给出的一些数值例证显示了该运算法则的有效性．     

与积分有关的一个极限及其应用

将崔尚斌编著的《数学分析教程》(中册)的一个综合习题进行推广,得到求与积分有关的极限的几个实用性结果,并给出多个应用例子.