巧用简谐运动的对称性解题

简谐运动的特点是具有往复性，相对平衡位置对称的两点，加速度、回复力、位移、均为等值反向，速度可能相同也可能等值反向，动能、势能一定相同．在实际问题中利用这些特点分析问题，往往会收到事半功倍的效果．     

HILBERTIAN INVARIANCE PRINCIPLE FOR EMPIRICAL PROCESS ASSOCIATED WITH A MARKOV PROCESS

The authors establish the Hilbertian invariance principle for the empirical process of a stationary Markov process, by extending the forward-backward martingale decomposition of Lyons-Meyer-Zheng to the Hilbert space valued additive functionals associated with general non-reversible Markov processes.     

对角因子循环矩阵的谱分解及其应用

在文「１」的基础上讨论对角因子循环矩阵。首先，我们给出对角因子循环矩阵的谱分解，然后，讨论对角因子循环矩阵的广义逆，最后，作为应用，求解一类偏微分方程。     

可补Hilbert C*-模及其有界模映射

给出了可补Hilbert C^*-模一系列等价刻画，获得了一类有界模映射的分解定理。     

用矩阵的谱分解研究线性矩阵方程

本利用矩阵的谱分解来研究线性矩阵方程，并给出当A，B为简单矩阵(即可对角化方阵)时，方程AX-XB=C和X=AXB=C有解的充要条件及通解形式。     

On the Decomposition of Hopf Module Coalgebra

In1969,Sweedler[1]giventhedecompositiontheoreyofcoalgebraswhicharecocommu-tative.In1975,Kaplansky[2]showedthatanycoalgebracanbeuniquelydecomposedintoadirectsumofitsindecomposablesubcoalgebras.From1978to1992,Shudo[3]andXu[4]consructuredtheindecomposabledirectsumcomponentsofacoalggebra,viadefineequivalenceralationforthesetofsimplesubcoalgebras.Asweknow,themodolecoalgebraisthennaturalgeneralizationofcoalgebra.AndittakesplayanimportentroleintheDrinfelddouble.Inthispaper,wediscussthedecompositio…     

有向S—回路和有向S—迹

本文给出了有向生成回路和有向生成迹的几个充分条件。 设G为强连通1—图,无环,n阶。对于G的任两不相邻顶点x,y。①如果 d(x)+d(y)≥2n+1。那么对于G的任两顶点u和v,或有u-v有向S-迹,或有v-u有向S-迹。②如果 d(x)+d(y)≥2n-3。那么G含有向S-回路。     

满意正交表及其判别方法

本文提出了满意正交表的概念，并且利用正交表和投影矩阵的正交分解之间的关系给出了满意正交表的一种判别方法。     

对合的分解

Using the notion of biconnected sum we define the biconnected sum (T₁, M₁)§(T₂,M₂) of two involutions (T1M1) and (T2,M2) which is an involution on the biconnected sum M₁,§M₂. A connected involution is said to be reducible if it can be expressed as a biconnected sum of two connected involutions.Theorem Each connected involution (T, M) can be decomposed into a bi-connected sum of connected irreducible involutions (T, M)=(T₁, M₁)§…§(T_q,M_q),and (?) where the coefficients of H_{n_1}(M) are in Z/2 Z if M is unoriented, in Z if is oriented .