The solvability conditions for inverse eigenproblem of symmetric and anti‐persymmetric matrices and its approximation

The problem of generating a matrix A with specified eigen‐pair, where A is a symmetric and anti‐persymmetric matrix, is presented. An existence theorem is given and proved. A general expression of such a matrix is provided. We denote the set of such matrices by ??????_Eⁿ. The optimal approximation problem associated with ??????_Eⁿ is discussed, that is: to find the nearest matrix to a given matrix A* by A∈??????_Eⁿ. The existence and uniqueness of the optimal approximation problem is proved and the expression is provided for this nearest matrix. Copyright © 2002 John Wiley & Sons, Ltd.     

氯柱硼镁石在氯化镁水溶液中相转化平衡液相的红外光谱分析

采用差示FTIR光谱技术,研究了氯柱硼镁石在30℃下浓度为0.5,12和18％MgCl_2水溶液中溶解及相转化平衡饱和水溶液中硼氧配阴离子的FTIR光谱。给出了溶液中硼氧配阴离子的FTIR光谱振动频率的归属,515cm~(-1)为单和二硼氧配阴离子特征峰,630cm~(-1)为三硼氧配阴离子特征峰,550cm~(-1)为四硼氧配阴离子特征峰。对饱和水溶液中硼氧配阴离子的存在形式及其相互作用以及与相转化析出固相的关系进行了讨论。     

马科维兹资产组合选择模型的旋转算法

提出线性不等式组的一种旋转算法，并用其求解马科维兹资产组合选择模型，此算法每次迭代约需n^2次乘法和加法，其中n是模型中变量的数目，在微机上运行Delphi程序的实验结果表明，从上海和深圳股市1072支股票70期周末收盘价计算出20个最优投资组合仅需314次迭代和45s。     

New Exact Solutions to the Combined KdV and mKdV Equation

The modified mapping method is developed to obtain new exact solutions to the combined KdV and mKdV equation. The method is applicable to a large variety of nonlinear evolution equations, as long as odd- and even-order derivative terms do not coexist in the equation under consideration.     

求解非线性规划问题的光滑路径跟踪方法

通过对非线性规划问题的K-T点的光滑路径跟踪方法研究，得出一种针对于既有不等式约束条件又有等式约束条件的优化问题光滑路径跟踪方法，证明了光滑跟踪路径的存在性。     

On Quasiclassical Field Theories Invariant with Respect to a Lie Group

Mathematical Notes -     

三阶非线性时滞差分方程解的渐近性

研究了一类三阶非线性变滞量差分方程解的渐近性,给出了该类方程的非振动解当n→+∞时渐近趋于零或趋于某有限数值的几个充分条件.     

渐近周期Lotka-Volterra互惠系统的持久性

讨论了一类系数是渐近周期的连续函数的两种群Lotak-Volterra互惠系统的全局渐近性。     

关于Diophantine方程xp+2p=Dy2

设p是奇素数,D是无平方因子正整数。文章证明了:当p>3时,如果D不能被p或2kp+1形之素数整除,则方程xp+2p=Dy2没有适合gcd(x,y)=1的正整数解。     

排序向量的三个近似解系研究

AHP排序向量的"近似解法"至少可导出三个解系:K阶行平均法解系、K阶规范列平均法解系和K阶列平均倒数法解系.均在给定的比例判断矩阵的前提下,进行归一化处理,获得各自的排序向量.而当判断矩阵不一致时,其排序向量的结果也存在着差异.同时还存在继续研究的"真序"向量和AHP排序向量的其它近似解法.