多元统计分析中一类矩阵迹函数最小化问题的有效算法

研究来源于多元统计分析中的一类矩阵迹函数最小化问题minc+tr(AX)+∑mj=1tr(BjXCjXT),s.t.XTX = Ip,其中C为常数,A∈Rpxn(n ≥ p),Bj∈Rnxn,Cj∈Rpxp为给定系数矩阵.数值实验表明已有的Majorization算法虽可行,但收敛速度缓慢且精度不高.本文从黎曼流形的角...     

关于Finsler几何中的Hadamard定理

本文利用陈省身最近在Ｆｉｎｓｌｅｒ几何中引进的一个特殊仿射联络，把Ｒｉｅｍａｎｎ几何中关于非正曲率流形的Ｈａｄａｍａｒｄ定理推广到Ｆｉｎｓｌｅｒ几何中．     

调和映射在线性非平衡热力学中的应用

本文将一类线性非平衡热力学系统归结为调和映射问题.文中将昂塞格系数从常数推广成状态变量的函数,并应用调和映射讨论了系统的定态及其稳定性问题,给出了判定系统定态稳定性的判据.最后讨论了这些结果与原有的最小熵产生定理间的关系.     

EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS INVOLVING m CRITICAL HARDY-SOBOLEV EXPONENTS AND m SIGN-CHANGING WEIGHT FUNCTION

In this article, we consider a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and one sign- changing function. The existence and multiplicity results of positive solutions are obtained by variational methods.     

Smooth equivalence of differential equations and linear automorphisms

For systems of ordinary differential equations admitting linear automorphisms, we consider the problems of smooth equivalence and linearization preserving these automorphisms. Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 567–578, October, 1999.     

局部对称的黎曼流形中的极小子流形

主要研究了局部对称的黎曼流形中的定向紧致无边极小子流形的内蕴刚性问题,利用一个矩阵不等式,得到了这类子流形的一个刚性定理．所得结果部分改进了已有的一个结论．     

On doubly warped product Finsler manifolds

In this paper, we introduce horizontal and vertical warped product Finsler manifolds. We prove that every C-reducible or proper Berwaldian doubly warped product Finsler manifold is Riemannian. Then, we find the relation between Riemannian curvatures of doubly warped product Finsler manifold and its components, and consider the cases that this manifold is flat or has scalar flag curvature. We define the doubly warped Sasaki-Matsumoto metric for warped product manifolds and find a condition under which the horizontal and vertical tangent bundles are totally geodesic. We obtain some conditions under which a foliated manifold reduces to a Reinhart manifold. Finally, we study an almost complex structure on the tangent bundle of a doubly warped product Finsler manifold.     

时滞惯性流形及近似时滞惯性流形族

时滞惯性流形是对耗散系统惯性流形、近似惯性流形的最新发展,它基于对 大小涡分量间相互作用更细致的观察,即改变了惯性流形和近似惯性流形方法中大小 涡分量间相互作用为瞬时行为的隐含假定,而认为这种作用与系统的历史相关的．本 文结出了一类耗散系统时滞惯性流形的存在性证明,由于其存在性不需要“谱间隔条 件”保证,因而时滞惯性流形是广泛存在的．随后我们引出了一类离散的时滞惯性流 形,并在此基础上构造了一种近似时滞惯性流形族,分别给出了它们近似时滞惯性流 形的误差估计,结果显示这种新方法为构造稳定和高精度的算法提供了可能．     

流形元法固定边界约束处理研究

在数值流形方法中,对于材料的固定边界,一般采用罚函数的方法进行处理,即在固定边界上设置刚性弹簧约束其位移来实现固定约束条件的近似满足。罚函数法在理论上不是严格的固定约束处理方法,罚弹簧的布置与弹簧刚度的大小对模拟的效果都会产生影响。基于流形单元上位移函数的组成提出了流形方法固定边界约束处理的新方法,在组成流形单元的物理覆盖上,通过取消相应的覆盖函数在流形单元位移函数中的组成来实现双向固定的约束条件,通过使用只包含单方向位移的覆盖函数使x向固定约束条件和y向固定约束条件得到实现,推导了相应固定约束条件下的流形单元刚度矩阵的数值计算格式。该方法严格满足固定约束的物理意义,简化了固定边界的处理,并经算例证明是有效和准确的,有利于数值流形方法的程序实现和工程应用。     

Stability for manifolds of equilibrium states of generalized Birkhoff system

<正>Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied.A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized Birkhoffian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained.An example is given to illustrate the application of the results.