A note onQ-matrices

This paper concerns three classes of matrices that are relevant to the linear complementarity problem. We prove that within the class ofP ₀-matrices, theQ-matrices are precisely the regular matrices.Research supported by Department of Energy, Contract EY-76-S-03-0326 PA # 18.     

Matrices with convolutions of binomial functions and Krawtchouk matrices

We introduce a class S_N of matrices whose elements are terms of convolutions of binomial functions of complex numbers. A multiplication theorem is proved for elements of S_N. The multiplication theorem establishes a homomorphism of the group of 2 by 2 nonsingular matrices with complex elements into a group G_N contained in S_N. As a direct consequence of representation theory, we also present related spectral representations for special members of G_N. We show that a subset of G_N constitutes the system of Krawtchouk matrices, which extends published results for the symmetric case.     

矩阵的加权Moore—Penrose逆

利用矩阵的广义奇异值分解，给出了复数域上矩阵的Moore—Penrose逆存在的充要条件及其表达式．     

Remarks on Stable Range for Matrices

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关于环上的块循环矩阵环

定义了环R上的块循环矩阵环A，主要证明了下列结论：(1)若J是A的理想，d1，d2，…，dn是R的可逆元，则存在R的理想I使得J=I[σ1，σ2，…，σn]．(2)若d1，d2，…，dn是R的可逆元，则(i)R是单环当且仅当A是单环；(ii)R是局部环当且仅当A是局部环；(iii)J(A)=J(R)[σ1，σ2，…，σn]；(iv)R是半本原环当且仅当A是半本原环．(3)若d1，d2，…，dn都是R的幂零元，则J(A)=J(R) ( (i1,i2,…,im)∈r＼(0,0，…．0n)}RO2 2^1 O2 2^3…O2 2^3.(4)R是左Artin(Noether)环当且仅当A是左Artin(Noether)环．(5)若R有左Morita对偶(自对偶)，则A有左Morita对偶(自对偶)．     

Integrally Closed Domains,Minimal Polynomials,and Null Ideals of Matrices

Abstract

We show that every element of the integral closure D′ of a domain D occurs as a coefficient of the minimal polynomial of a matrix with entries in D. This answers affirmatively a question of Brewer and Richman, namely, if integrally closed domains are characterized by the property that the minimal polynomial of every square matrix with entries in D is in D[x]. It follows that a domain D is integrally closed if and only if for every matrix A with entries in D the null ideal of A, N _D (A)?=?{f?∈?D[x]?∣?f(A)?=?0} is a principal ideal of D[x].     

基于相对熵的多粒度语言判断矩阵的群决策方法

针对多粒度语言判断矩阵的群决策问题提出基于相对熵的最优化模型的排序方法.在多粒度语言偏好信息的导出函数基础上定义了语言判断矩阵对应的导出模糊互补判断矩阵,并给出其排序向量的计算式;同时采用语言判断矩阵的一致性指标来确定专家重要性程度的权向量;在相对熵的意义下构建了群决策排序向量的最优化模型,探讨了模型的求解方法.实例分析表明该模型是可行和有效的.     

ICP-MS测定超高纯钽铌及其化合物中痕量杂质元素

以 HF- HNO3 微波消解试样 ,直接用 ICP- MS测定高纯钽铌化合物中 19个杂质元素 ,选择了仪器的工作参数 ,考查了质谱干扰及基体干扰的情况 ,选择内标元素 Ga、In校正 ,克服了基体效应。检出限为0 .0 0 5— 0 .2μg/ g,回收率为 87%— 110 % ,方法快速准确 ,灵敏度高。     

Unusual degradation behavior of citric acid-crosslinked gelatin in vitro and in vivo

The aim of this study was to evaluate the biodegradability and biocompatibility of gelatin matrices designed for drug-eluting stents (DESs). The matrices were prepared by crosslinking alkali-treated gelatin (AlGelatin) with a citric acid-based crosslinker, trisuccinimidyl citrate (TSC), to form AlGelatin-TSC. The biodegradation behavior of the matrices was evaluated in vitro and in vivo. An in vitro enzymatic degradation test showed that AlGelatin-TSC prepared at a TSC concentration of 20 mM is the most stable in collagenase solution compared to AlGelatin-TSC prepared at TSC concentrations higher or lower than 20 mM. Then, AlGelatin-TSC were implanted subcutaneously in rats to evaluate their biodegradability and tissue reaction in vivo. Similar to the in vitro degradation behavior, AlGelatin-TSC with TSC concentration of 20 mM exhibited the lowest biodegradable rate in vivo among all AlGelatin-TSC. In addition, strong inflammation and calcification were not observed for AlGelatin-TSC at any TSC concentration. From an analysis of the crosslinking density of the resulting AlGelatin-TSC, the lowest biodegradability of AlGelatin-TSC with TSC concentration of 20 mM was due to the highest crosslinking density of the matrix. These results suggest that AlGelatin-TSC is suitable for use as matrices in DESs because of its excellent biocompatibility and biodegradability.