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The maximal super-singular integral operators on product spaces

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Science china mathematics 2011年第12期54卷 2615-2626页

作者： WANG Hui1 & CHEN JieCheng2.3, 1department of mathematics, Xidian University, Xi’an 710071, {2. 2.0} of mathematics, Zhejiang normal University, Jinhua 32.004, {2. 3department of mathematics, Zhejiang University, Hangzhou 31002., {2. department of mathematics Xidian University Xi’an China department of mathematics Zhejiang Normal University Jinhua China department of mathematics Zhejiang University Hangzhou China

We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2.0｜∫｜u｜〉ε1,｜v｜〉ε2.b1（｜u｜）b2.｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ∈ S（R^n ×R^m）, where 0 ≤ α,β〈∞, b1 b2.∈ L∞（R＋1 ）,Ω satisfies certain cancellation conditions and Ω∈L1（S^n-1×S^m-1）in the case α,β〉0;Ω∈L（log＋L）（S^n-1×S^m-1）in the case αβ=0 and α＋β 〉0. It is proved that, for 1〈p〈∞.T＊Ω,α,βis a bounded operator from the homogeneous Sobolev space Lα,β^p（R^n×R^m）to the Lebesgue space L^p（R^n×R^m）.

关键词： super-singular integral maximal operator product spaces

The multi-soliton solutions of the CH-γ equation

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Science china mathematics 2008年第2期51卷 314-320页

作者： CHEN ChunLi~(1+) LI YiShen~2.ZHANG JinE~3 1 department of mathematics,{2. Jiaotong University,{2. 2.02.0,china 2.department of mathematics,University of Science and Technology of china,Hefei 2.002.,china 3 SB and SEF,University of Hong Kong,Pokfulam Road,Hong Kong,china department of mathematics Shanghai Jiaotong University Shanghai China department of mathematics University of Science and Technology of China Hefei China SB and SEF University of Hong Kong Hong Kong China

This paper solves the integrable CH-γequation for analytical multiple soliton solutions with the Darboux transformation *** properties of the soliton solutions are different from the CH equation.

关键词： CH-γ equation multi-soliton solutions Darboux transformation 35Q35 35Q51

Weighted estimates for the multilinear singular integral operators with non-smooth kernels

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Science china mathematics 2011年第3期54卷 587-602页

作者： HU GuoEn1 & LU ShanZhen2.1department of Applied mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002. {2. 2.0} of mathematics, Beijing normal University, Beijing 100875, {2. department of Applied mathematics Zhengzhou Information Science and Technology Institute Zhengzhou China department of mathematics Beijing Normal University Beijing China

In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smoot... 详细信息

关键词： approximation to the identity weighted norm inequality singular integral operator non-smooth kernel Calderón-Zygmund decomposition

Extremal problems on the generalized Hua domain of the first type

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Progress in Natural Science:Materials International 2006年第4期16卷 352-358页

作者： SU Jianbing and YIN Weiping department of mathematics, Xuzhou {2. University, Xuzhou 2.1116, china department of mathematics, Capital {2. University, Beijing 100037, china department of mathematics Xuzhou Normal University Xuzhou 221116 China department of mathematics Capital Normal U-niversity Beijing 100037 China

Some extremal problems between the generalized Hua domain of the first type and the unit ball are studied. The extremal mapping and extremal value in explicit formulas are also obtained.

关键词： extremal problem generalized Hua domain of the first type minimal circumscribed Hermitian ellipsoid.

Extremal problems on the Hua domain of the first type

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Science china mathematics 2005年第Z1期48卷 343-354页

作者： SU Jianbing & YIN Weiping mathematics department, Xuzhou {2. University, Xuzhou 2.1116, china mathematics department, Capital {2. University, Beijing 100037, china mathematics department Xuzhou Normal University Xuzhou China mathematics department Capital Normal University Beijing China

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.

关键词： extremal problem, Hua domain of the first type, minimal circumscribed Hermitian ellipsoid.

A LINE SEARCH FILTER SECANT METHOD FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION

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Journal of Systems Science & Complexity 2010年第2期23卷 343-361页

作者： Zhujun WANG Detong ZHU department of mathematics Shanghai Normal University Shanghai 200234 China. Business College Shanghai Normal University Shanghai 200234 China.

This paper formulates and analyzes a line search method for general nonlinear equalityconstrained optimization based on filter methods for step acceptance and secant methods for *** feature of the new algorithm is that the secant algorithm is used to produce a searchdirection,a backtracking line search procedure is used to generate step size,some filtered rules areused to determine step acceptance,second order correction technique is used to reduce infeasibility andovercome the Maratos *** convergence properties of this method are analyzed:under mildassumptions it is showed that every limit point of the sequence of iterates generated by the algorithmis feasible,and that there exists at least one limit point that is a stationary point for the ***,it is also established that the Maratos effect can be overcome in our new approach by addingsecond order correction steps so that fast local superlinear convergence to a second order sufficient localsolution is ***,the results of numerical experiments are reported to show the effectivenessof the line search filter secant method.

关键词： Filter method nonlinear programming secant algorithm second order correction.

Particle tunnels across the horizon of Garfinkle-Horowitz-Strominger dilaton black hole

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Science china(Physics,Mechanics & Astronomy) 2007年第5期50卷 601-610页

作者： FANG HengZhong1 & ZHAO Zheng2.1 department of Physics, china University of Petroleum, Dongying 2.7061, china 2.department of Physics, Beijing normal University, Beijing 100875, china department of Physics China University of Petroleum Dongying China department of Physics Beijing Normal University Beijing China

We promote the work of Parikh and Wilczek on the black hole radiation to the emission of massive and charged particles from Garfinkle-Horowitz-Strominger black hole. The energy and charge of the space-time are conservational during the course of the evaporation. The calculation shows that the emission spectrum is not precisely thermal, while has a correction, and the conclusion supports the view- point of information conservation.

关键词： Hawking radiation, black body spectrum, barrier, information loss, entropy of black hole, Komar energy

Codes From Strongly Regular (α,β)-reguli

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Journal of shanghai Jiaotong university(Science) 2008年第4期13卷 491-494页

作者：李秀丽 department of mathematics Shanghai Jiaotong University

Strongly regular (α,β)-reguli are a class of incidence structures with given conditions which were introduced by Hamilton and Mathon. We introduce two classes of codes constructed from strongly regular (α,β)-regul... 详细信息

关键词： two-weight codes strongly regular (α,β)-reguli

GENERAL CAUCHY PROBLEM FOR THE LINEAR SHALLOW-WATER EQUATIONS ON AN EQUATORIAL BETA-PLANE

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Journal of Hydrodynamics 2006年第3期18卷 303-309页

作者： SHEN Chun SHI Wei-hui School of mathematics and Information Yantai Normal University Yantai 264025 China shanghai Institute of Applied mathematics and Mechanics Shanghai University Shanghai 200072 China department of mathematics Shanghai University Shanghai 200444 China

Based on the theory of stratification, the well-posedness of the initial value problem for the linear shallow-water equations on an equatorial beta-plane was discussed. The sufficient and necessary conditions of the existence and uniqueness for the local solution of the equations were presented and the existence conditions for formal solutions of the equations vere also given. For the Cauchy problem on the hyper-plane {t = O}, the local analytic solution were worked out and a special case was discussed. Finally, an example was used to explain the variety of formal solutions for the ill-posed problem.

关键词： stratification initial value problem,well-posedness shallow-water equations