关于域上矩阵广义逆的加法映射

假设F是特征不为2的域,令Mn(F)是F上n×n矩阵的集合.本文证明了f是Mn(F)到自身的矩阵{1}-逆或{1,2}-逆的加法保持算子当且仅当f有:(a)f=0;(b)f(A)=εPAτP-1对任意A∈Mn(F),其中P∈GLn(F),τ-为域F的某个单自同态且x(1)=1,ε=±1;(c)f(A)=εP(Aτ)TP-1对于任意A∈Mn(F),其中τ,ε,P如(b)中一样意义.     

格矩阵半群的Euler-Fermat公式

给出并证明格矩阵半群的Euler-Fermat公式:A(n-1)2 1 = A(n-1)2 1 [n], A ∈ Mn(L)其中L是任意的分配格,Mn(L)是L上所有n阶矩阵构成的半群.这是布尔矩阵半群的Euler-Fermat公式的一种推广.     

双格半群在模糊逻辑中的典例

分析了n元模糊逻辑函数集合中的偏序结构,论证了该集合M-={f|f:[0,1]n→[0,1],(A)x∈[0,1]n,f(x)∈[0,1]}是一个双格半群.并且M-关于其上定义的等值关系构成的商集W={Cf|(A)g∈Cf(∈)M-,f(x)=g(x),f,g∈M,x∈[0,1]n}也构成一个双格半群.     

任意域上n×n矩阵半群的积性函数

设 F 是任意域,M_n 记 F 上 n×n(n≥2)矩阵全体构成的乘法半群.熟知,行列式映射是 M_n 到 F 的乘法同态.本文考虑其反问题,即决定全部从 M_n 到 F 的半群乘法同态,亦即 M_n 的全部积性函数.我们以 Hom(M_n,F)记 M_n 到 F 的乘法同态全体构成的集,即若(?)∈Hom(M_n,F),则有(?)(AB)=(?)(A)(?)(B) (?)A、B∈M_n又我们用 GL_n(F)及 SL_n(F)记 F 上一般线性群与特殊线性群.I_n 记 M_n 中单位阵,E_(ij)记 M_n 中(i,j)位置是1,其余位置是0的矩阵。当λ为 F 中非零元素时,F_(ij)(λ)记     

Homomorphisms Between Multiplicative Semigroups of Matrices Over Fields

Suppose F is a field, and n, p are integers with 1 ≤ p 〈 n. Let Mn（F） be the multiplicative semigroup of all n × n matrices over F, and let M^Pn（F） be its subsemigroup consisting of all matrices with rank p at most. Assume that F and R are subsemigroups of Mn（F） such that F M^Pn（F）. A map f ： F→R is called a homomorphism if f（AB） = f（A）f（B） for any A, B ∈F. In particular, f is called an endomorphism if F = R. The structure of all homomorphisms from F to R （respectively, all endomorphisms of Mn（F）） is described.     

关于变量个数的几个单调函数

目前 ,人们对比较变量大小之间关系的不等式较为关注 ,但是 ,笔者发现 ,有一些不等式在变量的定义域内 ,经过变量置换 ,可以得到关于变量个数的一些单调函数 .为了讨论方便 ,设实函数 f(x)的定义域为x∈(a ,b) ,实数Pi>0 (1≤i≤n) ,n∈N .记λn=∑ni=1Pi,An=∑ni=1Pixi/λn,Bn=∑ni=1Pif(xi) /λn.定理　若 f(x)在区间 (a ,b)上为凸函数 ,则φ(n) =λn[f(An) -Bn]是n的递增函数 .证　设x′i∈ (a ,b) ,根据凸函数定理有f(A′n)≥B′n (1)A′n=∑ni=1Pix′i/λn,B′n=∑ni=1Pif(x′i) /λn.令x′1=x′2 =… =x′n - 1=An - 1,x′n=xn…     

Some Conditions for K_0(B(X))=0

Let A be an unital Banach algebra with the unital element I. We denote the set of (n×n)-matrices over A by Mn(A). The set of idempotent elements of A is denoted by P1(A):={P∈A: P2=P}, and accordingly the set of idempotent elements of Mn(A) is denoted by Pn(A):=P1(Mn(A)). We define P∞(A) :=∪n∈N Pn(A). In the set of P∞(A), for P,Q ∈ Pn(A), we say that P is (algebraic) equivalent to Q, if there exist A,B∈ Mn(A) such that     

高三数学期中自测题

选择题　 (每小题 5分 ,12小题共 6 0分 .在每小题给出的四个选项中 ,只有一项是符合题目要求的 )1.集合M ={x|x =2n ,n∈Z} ,N ={x|x =2n +1,n∈Z} ,P ={x|x =4n +1,n∈Z} ,x∈M ,y∈N ,则必有 (　　 )(A)x +y∈M .(B)x +y∈N .(C)x +y∈P .(D)x +y M ,N ,P任何一个 .2 .已知集合M =- 1,0 ,1,f是从M到M的映射 ,则满足 f(- 1) +f(0 ) +f(1) =0的映射有(　　 )(A) 6个 .　 (B) 7个 .　 (C) 8个 .　 (D) 9个 .3.已知f0 (x ) =f (x ) =x +1(x≤ 1) ,-x +3(x >1) ,fn +1(x) =f [fn (x ) ],则f2 (- 12 ) = (　　 )(A) - 12 . (B) 32 …     

TO SOLVE MATRIX EQUATION sum (A~iXBi=c) BY THE SMITH NORMAL FORM

§ 1　IntroductionLet F be a field,F[λ] be the polynomial ring over F,Fm× n( or Fm× n[λ] ) be the setofall m×n matrices over F( or F[λ] ) .Let M(i) be the ith column of M∈Fm× m[λ] ,i=1 ,...,n.A g-inverse of M∈Fm× n will be denoted by M- and understood as a matrix for whichMM- M=M.In this paper,we discuss the linear matrix equation ki=0Ai XBi =C, ( 1 )where A∈Fm× m,Bi∈Fn× q,i=0 ,1 ,...,k,and C∈Fm× q.Equation( 1 ) is called universally solvable if ithas a solution f…     

一类l-半群的l-自同构

设R有1的全序环。记Mn(R)为R上n×n矩阵乘法半群,则Mn(R)在通常格序下成为l-半群。本文对l-半群Mn(R)的∨-自同构,∧-自同构以及l-自同构给出了详细的刻画。     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

<正>~~     

Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.