Quantale矩阵的行列式的若干性质

基于Q uan ta le矩阵的定义,本文讨论了Q uan ta le矩阵的行列式的若干性质。在交换Q uan ta le情形下,得到AB≥A B,AB≤A B,AA*≤A,其中A*表示Q uan ta le上的矩阵A的伴随矩阵。     

格矩阵的行列式与伴随矩阵

研究了格矩阵的行列式与伴随矩阵,给出了它们的一些代数性质,同时给出了由一个格矩阵构造一个传递矩阵的方法.     

范德蒙行列式推广形式的多项式证法

本文给出了范德蒙行列式推广形式的多项式证明，其方法不同于文［１］的定理１证明方法。     

Wronsky行列式及其一阶微分的关系

证明了n阶行列式一阶微分为其逐次微分之和,进而得到了Wronsky行列式及其一阶微分的关系．     

实四元数矩阵行列式函数的几点注记

分别对实四元数矩阵理论中出现的几种行列式函数在三个初等变换下的改变性作一些讨论,得出几种满足一定性质的行列式函数的不存在性或唯一存在性。     

On the Relation Between the Determinant and the Permanent on Symmetric Matrices

Let H n ( F ) be the space of n -square symmetric matrices over the field F . We generalize the main result of [M.H. Lim (1979). A note on the relation between the determinant and the permanent. Linear and Multilinear Algebra , 7 , 145-147], proving that the determinant is not convertible into the permanent on H n ( F ), provided that n ? 3, F has at least n elements and the characteristic of F is not 2. The case n = 2 is also studied.     

关于剩余类环的扩展的研究

作者对非结合环给出扩展的概念,即给定2个非结合环A和B,对任一非结合环R,称R是A被B的扩展,当且仅当A是R的理想且R/A≌B.对非结合环的扩展,文中证明了一个类似于Schreier群扩张定理的结果.作为应用,对给定的自然数m≥2,n≥2,文章刻画了模n的剩余类环Z_n被模m的剩余类环Z_m扩展所得到的有限环R的构造,证明了R可以用满足一定条件的自然数对(u,r)来描述,同时写出了R的理想和单侧理想的具体形状.作者还进一步证明,R是结合的当且仅当R=Z_nZ_m,且当R=Z_nZ_m时,R的每个理想都是Z_n的一个理想与Z_m的一个理想的直和,即此时R的理想是相对平凡的.     

On the Relation Between the Determinant and the Permanent on Symmetric Matrices

Let H n ( F ) be the space of n -square symmetric matrices over the field F . We generalize the main result of [M.H. Lim (1979). A note on the relation between the determinant and the permanent. Linear and Multilinear Algebra , 7 , 145-147], proving that the determinant is not convertible into the permanent on H n ( F ), provided that n ≥3, F has at least n elements and the characteristic of F is not 2. The case n = 2 is also studied.     

计算周期三对角矩阵行列式和逆矩阵的新算法

给出了一种计算周期三对角矩阵行列式和逆矩阵的新递推算法,它们的运算复杂度分别为O(n)和O(n2),该算法是文献[5]和[6]中相关算法的拓广.     

The Dixmier trace and asymptotics of zeta functions

We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup. We prove our results in a general semi-finite von Neumann algebra. We find for p>1 that the asymptotics of the zeta function determines an ideal strictly larger than Lp,∞ on which the Dixmier trace may be defined. We also establish stronger versions of other results on Dixmier traces and zeta functions.     

The Dirichlet divisor problem,traces and determinants for complex powers of the twisted bi-Laplacian

Estimating the counting function for the eigenvalues of the twisted bi-Laplacian leads to the Dirichlet divisor problem, which is then used to compute the trace of the heat semigroup and the Dixmier trace of the inverse of the twisted bi-Laplacian. The zeta function regularizations of the traces and determinants of complex powers of the twisted bi-Laplacian are computed. A formula for the zeta function regularizations of determinants of heat semigroups of complex powers of the twisted bi-Laplacian is given.     

Positivity of matrices with generalized matrix functions

Using an elementary fact on matrices we show by a unified approach the positivity of a partitioned positive semidefinite matrix with each square block replaced by a compound matrix, an elementary symmetric function or a generalized matrix function. In addition, we present a refined version of the Thompson determinant compression theorem.     

Ricci Flow and the Determinant of the Laplacian on Non-Compact Surfaces

On compact surfaces with or without boundary, Osgood, Phillips and Sarnak proved that the maximum of the determinant of the Laplacian within a conformal class of metrics with fixed area occurs at a metric of constant curvature and, for negative Euler characteristic, exhibited a flow from a given metric to a constant curvature metric along which the determinant increases. The aim of this paper is to perform a similar analysis for the determinant of the Laplacian on a non-compact surface whose ends are asymptotic to hyperbolic funnels or cusps. In that context, we show that the Ricci flow converges to a metric of constant curvature and that the determinant increases along this flow.     

迹与行列式的相互表示

应用牛顿恒等式,得到矩阵的特征值的对称多项式与等幂和之间的关系,以此为基础给出行列式的迹表示,另由克莱姆法则导出迹的行列式表示。     

环与剩余类环的同调维数

Ｓａｎｄｏｍｉｅｒｓｋｉ Ｆ．Ｌ,Ｓｍａｌｌ Ｌ．Ｗ,和 Ｆｉｅｌｄｓ Ｋ．Ｌ．［１－２］在“幂零”条件下研究了环与约化环的同调维数．然而对一些环（如交换 Ｖｏｎ Ｎｅｕｍａｎｎ正则环）,“幂零’的条件是不成立的．因此,在本文中我们考虑非“幂零”条件下（如Ｒ（Ｒ／Ｉ）（（Ｒ／Ｉ）Ｒ）是Ｒ－投身的或Ｒ（Ｒ／Ｉ）Ｒ是Ｒ－平坦的）,环与约化环的同调维数．     

A Priori Estimations of a Global Homotopy Residue Continuation Method

This work is concerned with the a priori estimations of a global homotopy residue continuation method starting from a disjoint initial guess. Explicit conditions ensuring the quadratic convergence of the underlying Newton–Raphson algorithm are proved.     

关于正交矩阵特征值与行列式的两个定理

以两种证明思路给出了正交矩阵特征值与行列式关系的定理,并在此基础之上提出了对称正交矩阵行列式的迹定理.     

η Forms and determinant lines

We construct a canonical zeta function (Quillen) connection on the determinant line bundle for a family of APS elliptic boundary value problems and show that its curvature is the 2-form component of a relative eta form.     

Cardinalities of Residue Fields of Noetherian Integral Domains

We determine the relationship between the cardinality of a Noetherian integral domain and the cardinality of a residue field. One consequence of the main result is that it is provable in Zermelo–Fraenkel Set Theory with Choice (ZFC) that there is a Noetherian domain of cardinality ?₁ with a finite residue field, but the statement “There is a Noetherian domain of cardinality ?₂ with a finite residue field” is equivalent to the negation of the Continuum Hypothesis.     

泛Clifford分析中的Laurent展式和留数定理

该文由泛Clifford分析中在特异边界上的Cauchy积分式得出了具有孤立奇点的LR正则函数在其相应的Laurent域上的Laurent展式，并由此给出了留数的定义，得出了类似于经典函数理论的留数定理。