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Boundedness for commutators of fractional Hardy operators on Herz spaces

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Progress in Natural Science:Materials International 2007年第1期17卷 20-25页

作者： FU Zunwei, LIU Zongguang and LU Shanzhen ( School of Mathematical Sciences, Beijing normal university, Beijing 100875, china department of mathematics, Linyi normal university, Linyi 276005, china department of mathematics, china university of Mining and Technology, Beijing 100083, china) [a]School of Mathematical Sciences Beijing Normal University Beijing China [b]Departhent of mathematics Linyi Normal University Linyi China [c]Departhent of mathematics China University of Mining and Technology Beijing China

Some boundedness results are established for commutators generated by classical fractional Hardy operators and one-sided CMO functions on the homogeneous Herz spaces, which extends some known results.

关键词： fractional Hardy operator Hardy’s integral inequality commutator one-sided CMO function homogeneous Herz space.

A differentiable sphere theorem with positive Ricci curvature and reverse volume pinching

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Science china mathematics 2011年第3期54卷 603-610页

作者： WANG PeiHe1 & WEN YuLiang2 1School of Mathematical Sciences, Qufu normal university, Qufu 273165, china 2department of mathematics, east china normal university, shanghai 200241, china 1. School of Mathematical Sciences Qufu Normal University Qufu 273165 China2. Department of Mathematics East China Normal University Shanghai 200241 China

Let Mn be a compact, simply connected n (≥3)-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned satisfies that the sectional curvature KM is not larger than 1, while Ric(M)≥n+2 4 and the volume V (M) is not larger than (1 + η)V (Sn) for some positive number η depending only on n.

关键词： k-th Ricci curvature Hausdorff convergence differentiable sphere theorem harmonic coordinate harmonic radius

SEMI-DEFINITE RELAXATION ALGORITHM FOR SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES

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Chinese Annals of mathematics,Series B 2005年第1期26卷 153-158页

作者： CHENFENG ZHANGLIANSHENG departmentofmathematics ShanghaiUniversityShanghai200436China／／DepartmentofIndustrialEngineeringandManagementShanghaiJiaotongUniversityShanghai200030China. departmentofmathematics ShanghaiUniversityShanghai200436China

The authors present a semi-definite relaxation algorithm for the scheduling problem with controllable times on a single machine. Their approach shows how to relate this problem with the maximum vertex-cover problem with kernel constraints (MKVC).The established relationship enables to transfer the approximate solutions of MKVCinto the approximate solutions for the scheduling problem. Then, they show how to obtain an integer approximate solution for MKVC based on the semi-definite relaxation and randomized rounding technique.

关键词： Scheduling with controllable times Semi-definite programming Approximation algorithm

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Saturated models

Chinese Science Bulletin 1998年第7期43卷 562-564页

作者： CHEN Guolong department of mathematics, Beijing normal university, Beijing 100875, china department of mathematics Beijing Normal University Beijing China

An equivalent description of saturated models is given, and some properties of countable saturated models, almost saturated models and full models are discussed. New proofs of two important theorems of the related doc... 详细信息

关键词： almost saturated model full model power type.

Optimal Control of Semilinear Elliptic Variational Bilateral Problem

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Acta Mathematica Sinica,English Series 2000年第1期16卷 123-140页

作者： Qihong Chen Institute of mathematics,Fudan university,shanghai 200433,P.R.china shanghai normal university,shanghai 200023,P.R.china Institute of mathematics Fudan University Shanghai 200433 P.R. China shanghai normal university Shanghai 200023 P.R. China

This paper is concerned with an optimal control problem for semilinear elliptic variational inequalities associated with bilateral *** and optimality conditions of the optimal pair are established.

关键词： Elliptic bilateral variational inequality Optimal control Existence Optimality condition

Lp integrability of trigonometric series with special varying coefficients

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Applied mathematics:A Journal of Chinese Universities 2009年第4期24卷 402-410页

作者： WEI Bao-rong department of mathematics,Hangzhou normal university,Zhejiang 310036,china department of mathematics Hangzhou Normal University Zhejiang 310036 China

Very recently,Yu,Le and Zhou introduced the so called Δ*B1 and Δ*B2 conditions,which are generalizations of the monotone *** applying these two new conditions,the author essentially generalizes the classical results of Chen on the necessary and sufficient conditions of the Lp integrability of trigonometric *** fact,the present paper gives the first result on the necessary and sufficient conditions of the Lp integrability of trigonometric series,where coefficients may have diffierent signs.

关键词： Lp integrability trigonometric series special varying coefficients

The pointwise dimension of self-similar measures

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Chinese Science Bulletin 1999年第23期44卷 2136-2140页

作者： CHEN Ercai and XIONG Jincheng department of mathematics , Nanjing normal university , Nanjing 210097, china department of mathematics , South china normal university, Guangzhou 510631 , china department of mathematics Nanjing Normal University Nanjing China department of mathematics South China Normal University Guangzhou China

The problem about the existence of pointwise dimension of self-similar measure has been discussed. The Hausdorff dimension of the set of those points for which the pointwise dimension does not exist equals the dimenti... 详细信息

关键词： self-similar measure point wise dimension Hausdorff dimension multifractal symbolic space.

METHOD OF NONCONFORMING MIXED FINITE ELEMENT FOR SECOND ORDER ELLIPTIC PROBLEMS METHOD OF NONCONFORMING MIXED FINITE ELEMENT FOR SECOND ORDER ELLIPTIC PROBLEMS

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Journal of Computational mathematics 2000年第5期18卷 449-456页

作者： Zhen-dong Luo (department of mathematics, Capital normal university, Beijing 100057, china) 首都师范大学北京 100037

In this paper, the method of non-conforming mixed finite element for second order elliptic problems is discussed and a format of real optimal order for the lowest order error estimate.

关键词： Non-conforming mixed finite element Error estimate Second order elliptic problems.

Spectral Radius of Non-negative Matrices and Digraphs

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Acta Mathematica Sinica,English Series 2002年第2期18卷 293-300页

作者： ZHANG Xiao Dong department of mathematics.east china normal university,shanghai 2.0062.P.R.china E-mail:xdzhang2@hotmail.comLI Jiong Sheng department of mathematics.university of Science and Technology of china,Hefei 230026,P.R china department of mathematics East China Normal University Shanghai P. R. China department of mathematics University of Science and Technology of China Hefei P. R. China

We present,an upper and a lower bound for the spectral radius of non-negative matrices. Then we give the bounds for the spectral radius of digraphs.

关键词： Non-negative matrix Digraph Spectral radius