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.     

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.      

ON A HYPER HILBERT TRANSFORM＊＊＊＊

The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an application of the above results, the authors give the Lp-boundedness for a class of the hyper singular integrals and the fractional integrals with variable kernel. Moreover, as another application of the above results, the authors prove the dimension free estimate for the hyper Riesz transform. This is an extension of the related result obtained by Stein.     

自共轭矩阵二项式的广义F-范数估计定理

将 Wielandt-Hoffman定理的一种对称形式推广到四元数体上 ,得到了自共轭矩阵二项式的广义F—范数估计定理和一个幂迹定理 .     

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.     

分布参数系统的最小Orlicz范数控制

本文对于状态空间为具无条件基的Banach空间、控制空间为Orlicz空间的单输入分布参数系统给出最小范数控制的表达式。     

模糊关系性质的模糊T-近似算子刻画

在定义一般模糊关系下的模糊T-近似的基础上，用模糊T-近似算子来刻画模糊关系的自反性、对称性、T-传递性等性质，并讨论了模糊T-粗糙集的一些性质。     

MATRIX NORM VERSIONS OF THE KANTOROVICH INEQUALITY AND ITS APPLICATIONS

In this paper we discuss the generalizations of the Kantorovich inequality and obtain some generalized Kantorovich inequalities in the sense of matrix norm. We further illustrate how to use these inequalities to determine the lower bound of relative efficiency of the parameter estimate in linear model.     

N—范数,M—最小二乘解的扰动理论

一 引言与预备知识 设A∈C~(mxn),M与N分别为m阶与n阶正定的Hermite矩阵。则存在唯一的矩阵X∈C~(n×m),满足     

关于矩阵Kronecker积的谱半径的不等式

本文证明了矩阵的 Kronecker积的谱半径的两个不等式