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.     

最小多项式矩阵与线性多变量系统(Ⅰ)

本文分为两部分:(Ⅰ)为关于最小多项式矩阵的理论:(Ⅱ)为最小多项式矩阵理论在线性多变量系统中的应用.在(Ⅰ)中,我们给出了线性变换在向量组的消失多项式矩阵与最小多项式矩阵的概念,给出了不变子空间的生成组与最小生成组的概念.在讨论了这些概念的基本性质之后,我们研究了它们与线性变换在任何不变子空间上诱导算子对应的特征矩阵之间的关系,给出了向量组的最小多项式矩阵类的特征,并给出了有相同生成空间的生成组之间的充分必要条件.利用这些结果,对于给定的矩阵A,给出了能使系统x=Ax+Bu完全可控的矩阵B的全体的集合的表达式.     

Battle-outcome prediction for an extended system of Lanchester-type differential equations

Battle-outcome-prediction conditions are given for an extended system of Lanchester-type differential equations for two different types of battle-termination conditions: (a) fixed-force-level-breakpoint battles, and (b) fixed-force-ratio-breakpoint battles. Necessary and sufficient conditions for predicting battle outcome are given in the former case for a fight to the finish, while sufficient conditions are given in the latter case. The former results are equivalent to those for the problem of classical analysis of determining (explicitly as a function of the initial conditions) the occurrence of a zero point for the solution to this extended system, although such results as given here have not appeared previously for nonoscillatory (in the strict sense) solutions.     

Intervals of 1-Lipschitz aggregation operators, quasi-copulas, and copulas with given affine section

Best lower and upper bounds for 1-Lipschitz aggregation operators with a given affine section are given. These are used to determine best bounds for quasi-copulas and copulas with a given affine section. However, in general there is no greatest copula with a given non-decreasing affine section. These results are used to study (quasi-)copulas with arbitrary affine sections.     

A note on linearized polynomials and the dimension of their kernels

Recently explicit representations of the class of linearized permutation polynomials and the number of such polynomials were given in Zhou (2008) [4] and Yuan and Zeng (2011) [3]. In this paper, we generalize this result to linearized polynomials with kernel of any given dimension, solving an open problem in Charpin and Kyureghyan (2009) [1]. Moreover, more explicit representations of such polynomials are given and several classes of explicit linearized polynomials with kernel of any given dimension are presented.     

The dual bases for the Bézier-Said-Wang type generalized Ball polynomial bases and their applications

A unifying representation for the existing generalized Ball bases and the Bernstein bases are given. Then the dual bases for the Bézier-Said-Wang type generalized bases (BSWGB for short) are presented. The Marsden identity and the mutual transformation formulas between Bézier curve and Bézier-Said-Wang type generalized curve (BSWGB curve) are also given. These results are very useful for the applications of BSWGB curves and their popularization in CAGD. Numerical examples are also given to show the effectiveness of our methods.     

The interpolation method of Sprague-Karup

The usual interpolation method is that of Lagrange. The disadvantage of the method is that in the given points the derivatives of the interpolating polynomials are not equal one to the other. In the method of Hermite, polynomials of a higher degree are used, whose derivatives in the given points are supposed to be equal to the derivatives of the function at the given points. This means that those derivatives must be known.If those derivatives are not known, then in the given points the derivatives may be replaced by approximative values, e.g. based on the interpolating polynomials of Lagrange. Such a method has been described by T. B. Sprague (1880) and in a simplified form by J. Karup (1898). In this paper the formulae are derived. Both methods are illustrated with an example. Some properties and theorems are stated. Tables to simplify the computational work are given. Subroutines for these interpolation methods will be published in a next article.     

Tikhonov solutions of approximately given systems of linear algebraic equations under finite perturbations of their matrices

The properties of a mathematical programming problem that arises in finding a stable (in the sense of Tikhonov) solution to a system of linear algebraic equations with an approximately given augmented coefficient matrix are examined. Conditions are obtained that determine whether this problem can be reduced to the minimization of a smoothing functional or to the minimal matrix correction of the underlying system of linear algebraic equations. A method for constructing (exact or approximately given) model systems of linear algebraic equations with known Tikhonov solutions is described. Sharp lower bounds are derived for the maximal error in the solution of an approximately given system of linear algebraic equations under finite perturbations of its coefficient matrix. Numerical examples are given.     

Lagrange multiplier characterizations of solution sets of constrained pseudolinear optimization problems

In this article, we study the minimization of a pseudolinear (i.e. pseudoconvex and pseudoconcave) function over a closed convex set subject to linear constraints. Various dual characterizations of the solution set of the minimization problem are given. As a consequence, several characterizations of the solution sets of linear fractional programs as well as linear fractional multi-objective constrained problems are given. Numerical examples are also given.     

On the expansion of confluent hypergeometric functions in terms of Bessel functions

For the confluent hypergeometric functions U (a, b, z) and M (a, b, z) asymptotic expansions are given for a → ∞. The expansions contain modified Bessel functions. For real values of the parameters rigorous error bounds are given.     

Sufficient conditions for Nash bargaining in differential games

Sufficient conditions for Nash bargaining in differential games are given. These conditions are compared with the sufficient conditions given by Liu (Ref. 1).     

A spline interpolation method for solving boundary value problems of potential theory from discretely given data

An interpolation procedure using harmonic splines is described and analyzed for solving (exterior) boundary value problems of Laplace's equation in three dimensions (from discretely given data). The theoretical and computational aspects of the method are discussed. Some numerical examples are given.     

FINITENESS CONDITIONS FOR GENERALIZED EXPONENTS OF DIGRAPHS

1.IntroductionR.A.BrualdiandBolianLiuintroducedin199011]theconceptofgeneralizedexponentsforprimitivedigraphs.Thisconceptisageneralizationofthetraditionalconceptoftheexponentsforprimitivedigraphsandhasbackgroundsinmemorylesscommunicationsystemsassociatedwithdigraphs.Inthispaperweshowthatgeneralizedexponentscanalsobedefinedfordigraphswhicharenotnecessarilyprimitive.WewillgivenecessaryandsufficientconditionsforthefinitenessofthegeneralizedexponentsexpD(k),f(D,k)andF(D,k).Theseideasandresultss…     

ON HERMITIAN POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATION X-A^＊X^-2 A=I

The Hermitian positive definite solutions of the matrix equation X-A^＊X^-2 A=I are studied. A theorem for existence of solutions is given for every complex matrix A. A solution in case A is normal is given. The basic fixed point iterations for the equation are discussed in detail. Some convergence conditions of the basic fixed point iterations to approximate the solutions to the equation are given.     

Management of periodic demands in distribution systems

The problem of the optimal scheduling of periodic demands for a given facility or commodity is presented and some properties of an integer programming model are discussed. Algorithms (both of implicit enumeration type and heuristic) are also given.     

非线性反应扩散方程的广义条件对称及其精确解

利用广义条件对称,考虑非线性反应扩散方程的精确解,对应于不同的参数讨论,得到相应的方程及其允许的广义条件对称,进而得到方程的精确解.     

Algebraic bounds on standardized sample moments

Best possible bounds are given for standardized sample (or finite population) moments and absolute moments of arbitrary order, generalizing those given by Cramér (1945) and Kirby (1974) on sample skewness and kurtosis.     

Centers of generic division algebras,the rationality problem 1965–1990

A survey is given of the rationality problem of the center of generic division algebras. Connections are given with Brauer groups of fields, geometric moduli problems and representation theory. An outline is given of recent results. Research associate of the NFWO (Belgium).     

Symmetric-triangular decomposition and its applications part II: Preconditioners for indefinite systems

As an application of the symmetric-triangular (ST) decomposition given by Golub and Yuan (2001) and Strang (2003), three block ST preconditioners are discussed here for saddle point problems. All three preconditioners transform saddle point problems into a symmetric and positive definite system. The condition number of the three symmetric and positive definite systems are estimated. Therefore, numerical methods for symmetric and positive definite systems can be applied to solve saddle point problems indirectly. A numerical example for the symmetric indefinite system from the finite element approximation to the Stokes equation is given. Finally, some comments are given as well. AMS subject classification (2000) 65F10     

对称拓扑分子格的直和

文章给出了对称拓扑分子格的直和概念,给出了拓扑分子格的直和的特征,证明了对称拓扑分子格的分离性Ti(i=-1,0,1,2)及可数性CⅠ,CⅡ是可和性质.