赋Orlicz范数的Musielak Orlicz序列空间的Gateaux可微点

该文给出赋Orlicz 范数的Musielak Orlicz序列空间中Gateaux可微点（光滑点）与Frechet可微点（强光滑点）的判定准则.在此基础上推出了该空间具有光滑性或强光滑性的充分必要条件.      

A NOTE ON THE BACKWARD ERRORS FOR INVERSE EIGENVALUE PROBLEMS

In this note,we consider the backward errors for more general inverse eigenvalus prob-lems by extending Sun‘‘‘‘s approach.The optimal backward errors defined for diagonal-ization matrix inverse eigenvalue problem with respect to an approximate solution,and the upper and lower bounds are derived for the optimal backward errors.The results may be useful for testing the stability of practical algorithms.     

Hilbert空间中最终范数连续半群的特征条件

本文给出了Hilbert空间中当t>t0(t0≥0)时,按一致算子拓扑连续C0半 群T(t)的四个特征条件.     

THE INVERSE PROBLEM FOR PART SYMMETRIC MATRICES ON A SUBSPACE

In this paper, the following two problems are considered:Problem Ⅰ. Given S∈E Rn×p,X,B 6 Rn×m, find A ∈ SRs,n such that AX = B, where SR8,n = {A∈ Rn×n|xT(A - AT) = 0, for all x ∈ R(S)}.Problem Ⅱ. Given A* ∈ Rn×n, find A ∈ SE such that ||A-A*|| = minA∈sE||A-A*||, where SE is the solution set of Problem Ⅰ.The necessary and sufficient conditions for the solvability of and the general form of the solutions of problem Ⅰ are given. For problem Ⅱ, the expression for the solution, a numerical algorithm and a numerical example are provided.     

一种矢量量化编码的快速搜索算法

提出了一种矢量量化编码的快速匹配算法。利用码书的拓扑结构和柯西 施瓦兹不等式的性质推导出了消除不必要匹配操作的条件,并根据这个条件提出了快速搜索算法。实验结果表明,该算法不仅明显降低了矢量编码过程的复杂程度,同时也保证了与全搜索编码相同的图像编码质量。与其它搜索方法的操作次数和存储空间进行了比较。     

THE EIGENVALUE PERTURBATION BOUND FOR ARBITRARY MATRICES

In this paper we present some new absolute and relative perturbation bounds for theeigenvalue for arbitrary matrices, which improves some recent results. The eigenvalueinclusion region is also discussed.     

线性流形上矩阵方程AXAT=B的极小Frobenius范数对称正交对称解

利用矩阵对的商奇异值分解,给出了线性流形上矩阵方程AXAT=B存在极小Frobe- nius范数对称正交对称解的充要条件及其解的表达式．     

Bergman空间和q-Bloch空间之间的复合算子

本文讨论了Bergman空间和q-Bloch空间(小q-Bloch空间)之间的复合算子Cφ的有界性和紧性特征,得到了以下结论:(1)Cφ是q-Bloch空间(小q-Bloch空间)到Bergman空间的有界算子或紧算子之充要条件; (2)Cφ是Bergman空间到q-Bloch空间的有界算子或紧算子之充要条件; (3)Cφ是Bergman空间到小q-Bloch空间的有界算子或紧算子之充要条件,还给出了算子 Cφ0的范数估计,此处Cφ0(f)(z)=foφ(z)-f(φ(0))．     

Navier-Stokes方程带Backtracking技巧的两重网格算法

1 引 言考虑二维不可压 Navier-Stokes方程:     

Lp范数下多元正系数代数多项式倒数对非负连续函数的逼近

设d≥1为正整数,S为Rd中的单纯形,C(S)为S上连续函数类,f(x)∈C(S),f(x)≥0,f(x) 0,p＞1,‖@‖p为通常的Lp范数,‖@‖为一致范数,则存在Pn(x)∈∏+n,d={Pn(x)Pn(x)=ak≥0},常数C＞0使‖f-1/Pn‖p≤C[ω2φ(f,/4n)+‖f‖/n],这里对k,x∈Rd,k=(k1,k2,…,kd),x=(x1,x2,…,xd),记|k|=k1+k2+…+kd,|x|=x1+x2+…+xd,xk=xk11xk22…xk11dk22,ω24(f,t)为单纯形S上关于一致范数的二阶Ditzian-Totik光滑模.