表有限域上矩阵为两个可逆矩阵的平方和

本文将有限域Ｆｑ（ｃｈａｒ Ｆｑ≠２）上的Ｄｉｃｋｓｏｎ方程：ｘ＾２＋ｙ＾２＝ａ（ａ≠０）当│Ｆｑ│≥７时在Ｆｑ＾－中有解的经典结果推广到ｎ阶方阵上，证明了只要Ｆ≠Ｆ２，除奇数阶纯量阵外每一ｎ阶方阵可表为两个可逆阵的平方和。     

An application of the capacitance matrix method to accommodate masked land areas and island circulations in a primitive equation ocean model

The capacitance matrix method has been implemented in a primitive equation ocean model to accommodate islands and portions of irregular coastal boundaries that cannot be treated adequately by boundary-fitted orthogonal curvilinear co-ordinates. The algorithm preserves the ability to solve the streamfunction equation using fast and accurate elliptic solvers that require a rectangular computational domain. By superposition of a set of island Green functions, the solution is adjusted to ensure continuity of pressure around each island. The implementation is tested by comparison with an analytic solution for wind-driven flow in a closed basin similar to the southwest Pacific Ocean.     

关于隐式LU分解算法分解算法求矩阵主子阵逆的注记（英）

ＡＲｅｍａｒｋｏｎｔｈｅＩｎｖｅｒｓｅｏｆＰｒｉｎｃｉｐａｌＭａｔｒｉｃｅｓｂｙＩｍｐｌｉｃｉｔＬＵＦａｃｔｏｒｉｚａｔｉｏｎＨｕａｎｇＫａｉｂｉｎＷｕＨｅｂｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＮａｎｊｉｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉ...     

关于K-分块循环矩阵及其对角化问题的讨论

给出了K-分块循环矩阵的概念,并探讨了K-分块循环矩阵的相似类及其对角化问题.     

A globally well-posed finite element algorithm for aerodynamics applications

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems. Of critical importance, essentially non-oscillatory solutions are uniformly attained for a range of supercritical flow situations with shocks.     

N维最弱受约束电子势模型的精确解

精确地求解了N维最弱受约束电子势模型束缚态的Schrodinger方程,得到了其能级和相对应的归一化径向波函数.在此基础上,运用广义拉盖尔多项式的级数展开得到了N维最弱受约束电子势模型径向矩阵元的通项表达式.     

The matrix equation AXB+CYD=Eover a simple artinian ring

This paper discussed the matrix equation AXB+CYD=Eover a simple Artinian ring, obtains several necessary and sufficient conditions for existence of a solution, gives the representation of solution by g-inverses, and extends a theorem of W.E. Roth's simple Artinian rings.     

Cosmological models with constant deceleration parameter in Nordtvedt’s theory

Exact solutions of the field equations of Nordtvedt’s theory for spatially flat FRW models with constant deceleration parameter have been obtained. Singular solutions with (i) power-law (ii) exponential expansion have been studied in Nordtvedt’s theory where the coupling parameterω is a function of the scalar fieldφ.     

退化时滞差分系统的通解

讨论具有时滞的退化差分系统，给出其初始函数的相容性条件，并给出其通解，最后举例说明之．     

由路段交通量推算OD矩阵的一种有效方法及其应用

针对现有OD矩阵估计方法的不足，本讨论了一种新的有效的估计方法，它包括一个路段流量的预处理过程，以消除路段观测流量的不相容，然后经过流量加载和卸载两个逆过程，进行反复迭代，最终得到再现路段交通量的OD矩阵，中例证了该方法的有效性。