Lagrange方程的动力学本质

对广泛应用的Lagrange方程的动力学本质做了探讨,指出在引入速度变换矩阵后,Lagrange方程实际上是牛顿第二定律的一种表示方式;由于引入了速度变换矩阵,Lagrange方程可以方便地在任意的坐标系中建立,对动力学问题的求解提供了一个途径。     

基于矩阵初等变换的n元函数极值的快速判别法

给出了 n元函数极值的一个充分条件 ,并结合矩阵的初等变换建立了 n元函数极值的一种快速判别法 ,最后给出了一个例子     

A note on the complex semi‐definite matrix Procrustes problem

This note outlines an algorithm for solving the complex ‘matrix Procrustes problem’. This is a least‐squares approximation over the cone of positive semi‐definite Hermitian matrices, which has a number of applications in the areas of Optimization, Signal Processing and Control. The work generalizes the method of Allwright (SIAM J. Control Optim. 1988; 26 (3):537–556), who obtained a numerical solution to the real‐valued version of the problem. It is shown that, subject to an appropriate rank assumption, the complex problem can be formulated in a real setting using a matrix‐dilation technique, for which the method of Allwright is applicable. However, this transformation results in an over‐parametrization of the problem and, therefore, convergence to the optimal solution is slow. Here, an alternative algorithm is developed for solving the complex problem, which exploits fully the special structure of the dilated matrix. The advantages of the modified algorithm are demonstrated via a numerical example. Copyright © 2007 John Wiley & Sons, Ltd.     

Differential density matrix overlap: an index for assessment of electron correlation in atoms and molecules

Summary A new index, called the differential density matrix overlap (DDMO), is proposed for assessment of the electron correlation effects in atoms and molecules. DDMO can be easily calculated as the negative value of the correlation energy derivative with respect to the relative position of the occupied and virtual orbitals. DDMO is transparent to physical interpretation. It can serve as a tool for analyzing the accuracy of approximate electron correlation methods and the validity of the Hartree-Fock wavefunction as the zeroth-order approximation. The properties of DDMO are discussed using test calculations on 11 atoms and molecules as an example.     

GLOBAL WEAK SOLUTIONS OF THE RELATIVISTIC VLASOV-KLEIN-GORDON SYSTEM IN TWO DIMENSIONS

In this paper we consider the system of classical particles coupled with a Klein-Gordon field in two dimensions.We establish a-priori-bounds on the solutions of this system with initial data satisfying a size restriction derived from conservation of energy.This result,together with the smoothing of"velocity averaging",yields the existence of global weak solutions to the corresponding restricted initial value problem.The size restriction is necessary since energy of the system is indefinite.Finally,we show that the weak solutions preserve the total mass.     

正定矩阵标准型的复合矩阵的一般形式

实对称正定矩阵的复合矩阵正定性的研究已有结论,但对于一般意义下的正定矩阵的复合矩阵是否仍然是正定的研究需要利用一般的正定矩阵的标准形的复合矩阵进行讨论,给出了一般公式及具体算法,为讨论其复合矩阵的正定性提供了基础条件.     

Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise

A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance.     

表面细分技术在二维声辐射和声散射中的应用

把表面细分技术应用于求解边界积分方程，既能把CAD模型直接用于边界元分析，又能精确描述复杂的边界几何形状，实现网格自动加密和形函数自动升阶，满足误差要求。把它应用于简单的二维声辐射和声散射，结果表明对提高边界元方法的计算精度是有效的。     

Pascal矩阵与Vandermonde矩阵的关系

EI-Mikkawy M证明了对称Pascal矩阵Q_n和Vlandermonde矩阵V_n之间满足矩阵方程Q_n=T_nV_n,这里T_n是一个随机矩阵。本文证明了随机矩阵T_n能够分解成第一类Stirling矩阵和对角矩阵的乘积,得到了矩阵T_n的元素之间的递推关系,从而回答了EI-Mikkawy M的一个公开问题。同时得到了一些与Stirling数相关的组合恒等式。     

The weak pigeonhole principle for function classes in S 12

It is well known that S ¹₂ cannot prove the injective weak pigeonhole principle for polynomial time functions unless RSA is insecure. In this note we investigate the provability of the surjective (dual) weak pigeonhole principle in S ¹₂ for provably weaker function classes. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)