关于圈的完全正矩阵实现

本文给出了一个关联图为圈的非负、半正定矩阵A为完全正的一个充要条件.我们还证明了这样的矩阵A（当A为完全正时）的分解指数即为A的阶数.     

On completely irreducible operators

Let T be a bounded linear operator on Hilbert space H, M an invariant subspace of T. If there exists another invariant subspace N of T such that H = M + N and M ∩ N = 0, then M is said to be a completely reduced subspace of T. If T has a nontrivial completely reduced subspace, then T is said to be completely reducible; otherwise T is said to be completely irreducible. In the present paper we briefly sum up works on completely irreducible operators that have been done by the Functional Analysis Seminar of Jilin University in the past ten years and more. The paper contains four sections. In section 1 the background of completely irreducible operators is given in detail. Section 2 shows which operator in some well-known classes of operators, for example, weighted shifts, Toeplitz operators, etc., is completely irreducible. In section 3 it is proved that every bounded linear operator on the Hilbert space can be approximated by the finite direct sum of completely irreducible operators. It is clear that a completely irreducible operator is a rather suitable analogue of Jordan blocks in L(H), the set of all bounded linear operators on Hilbert space H. In section 4 several questions concerning completely irreducible operators are discussed and it is shown that some properties of completely irreducible operators are different from properties of unicellular operators. __________ Translated from Acta Sci. Nat. Univ. Jilin, 1992, (4): 20–29     

完全正矩阵的整数分解

n阶矩阵A称为完全正的,如果A有分解:A=BB^T,其中B为元素非负矩阵,B的最小可能列数称为A的分解指数.本文考察低阶双非负矩阵在整数环上的完全正分解及其分解指数.     

确定线性偏微分方程组可积系统的对合特征集方法

基于Ritt-Wu特征集方法和Riquier-Janet理论,给出一种将线性微分方程组化成简单标准形式的有效算法．该算法通过消去冗余和添加可积条件获得线性微分方程组的完全可积系统(有形式幂级数解)或不相容判定．该算法不仅适用于常系数的线性偏微分方程组,而且对于变系数(以函数为系数)仍然有效．作者还给出了完全可积系统判定定理及其严格证明．     

完全Rees矩阵半群的分解及性质

用等价关系Q^~出了完全Rees矩阵半群的一种分解．而且得到了它的每个Q^~一类的表示．     

小球与均质自由杆的碰撞

讨论了小球与自由杆碰撞过程中所遵从的物理规律,明确了完全非弹性碰撞过程的能量特征,指出完全非弹性碰撞后两物体不一定粘在一起共同运动的事实.     

完全可分的三元系TS(v,4)的支撑集

§ 1　 IntroductionA triple system of order v and indexλ,denoted by TS(v,λ) ,is a collection of3- ele-mentsubsets Aof a v- set X,so thatevery 2 - subsetof X appears in preciselyλ subsets of A.L etλ≥ 2 and (X,A) be a TS(v,λ) .If Acan be partitioned into t(≥ 2 ) parts A1,A2 ,...,Atsuch that each (X,Ai) is a TS(v,λi) for 1≤ i≤ t,then (X,A) is called de-composable.Otherwise it is indecomposable.If t=λ,λi=1for 1≤ i≤ t,the TS(v,λ) (X,A) is called completely decomposable.It …     

The completely positive and doubly nonnegative completion problems

We prove the following. Let G be an undirected graph. Every partially specified symmetric matrix, the graph of whose specified entries is G and each of whose fully specified submatrices is completely positive (equal to BB^T for some entrywise nonnegative matrix B), may be completed to a completely positive matrix if and only if G is a block-clique graph (a chordal graph in which distinct maximal cliques overlap in at most one vertex). The same result holds for matrices that are doubly nonnegative (entrywise nonnegative and positive semidefinite).     

A note on δ-I-sets

We characterize δ-I-sets, discuss the relation between δ-sets, δ-I-sets and I _δ-sets and generalize some of the results.     

Electrochemical synthesis of 1,2,3,4,4,5,6-substituted 1,4-dihydropyridines

It has been shown that chemical oxidation of the methyl ester of 3,4,5-trimethoxycarbonyl-1,2,6-trimethyl-1,4-dihydropyridine to the pyridinium salt, requiring forcing experimental conditions, may be replaced by electrochemical oxidation. On electrochemical reduction of 3,4,5-trimethoxycarbonyl-1,2,6-trimethylpyridinium perchlorate in the presence of alkylating agents 1,2,3,4,4,5,6-substituted 1,4-dihydropyridines are obtained. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 226–237, February, 2007.