B(X)上保持约当积的固定点的满射

设B(X)是维数大于等于3的复Banach空间X上有界线性算子全体构成的代数.设A∈B(X),若Ax=x,则称x∈X是算子A的固定点.Fix(A)表示A的所有固定点的集合.本文刻画了B(X)上保持算子的Jordan积的固定点的满射.     

Group inverse and core inverse in Banach and C*-algebras

Abstract

In this paper, we have focused our study on the acute perturbation of the group inverse for the elements of Banach algebra with respect to the spectral radius. We also give perturbation analysis for the core inverse in C*- algebra. The perturbation bounds for the core inverse under some conditions are presented. Additionally, this paper extends the results obtained in [11, 14].     

Fast computation of generic bivariate resultants

We prove that the resultant of two “sufficiently generic” bivariate polynomials over a finite field can be computed in quasi-linear expected time, using a randomized algorithm of Las Vegas type. A similar complexity bound is proved for the computation of the lexicographical Gröbner basis for the ideal generated by the two polynomials.     

不同调光方式LED照射下的人体非视觉效应

分别采用模拟调光和PWM调光方式实现LED光调节。采用生理参数法,以在校大学生为研究对象,选择3种色温(3 000,5 600,6 500 K)LED光源,在3种照度(300,500,800 lx)水平下,对8名(5男,3女)受测者在实验前后的脉搏和瞳孔进行测量。选择同样3种色温LED光源,分别采用两种调光方式添加蓝光(464nm,20 lx)实现300 lx的照明环境,对12名(8男,4女)受测者在实验前后的脉搏和瞳孔进行测量。结果表明:两种调光方式实现的LED光环境对人体脉搏变化率和瞳孔收缩率的影响均没有显著性差异;在测试照明环境中添加蓝光,可引起人体脉搏变化率和瞳孔收缩率增大,峰值处分别增加约6%和9%。     

一道行列式证明题的多种证明方法

针对线性代数教材中一道行列式证明题，利用行列式的性质，给出多种证明方法，旨在启发学生对相关行列式计算或证明题的解题方法进行探索．     

Invertible Linear Maps on the General Linear Lie Algebras Preserving Solvability

Let Mn be the algebra of all n × n complex matrices and gl(n,C) be the general linear Lie algebra,where n ≥ 2.An invertible linear map ?:gl(n,C) →gl(n,C) preserves solvability in both directions if bot...