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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 {2., Xidian university, Xi’an 710071, china 2.1} of {2., Zhejiang normal university, Jinhua 32.004, china 3department of {2., Zhejiang university, Hangzhou 31002., china 1. department of mathematics Xidian University Xi’an 710071 China2. Department of Mathematics Zhejiang Normal University Jinhua 321004 China3. Department of Mathematics Zhejiang University Hangzhou 310027 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

Quenched moderate deviations principle for random walk in random environment

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Science china mathematics 2010年第8期53卷 1947-1956页

作者： HONG WenMing 1 & wang HuaMing 1,2.1 Key Laboratory of mathematics and Complex Systems of Ministry of Education & School of Mathematical Sciences,{2. normal university,{2. 100875,china 2.department of Basic Courses,Business College,{2. Union university,{2. 10002.,china 1. Key Laboratory of mathematics and Complex Systems of Ministry of Education & School of Mathematical Sciences Beijing Normal University Beijing 100875 China2. Department of Basic Courses Business College Beijing Union University Beijing 100025 China

We derive a quenched moderate deviations principle for the one-dimensional nearest random walk in random environment,where the environment is assumed to be stationary and *** approach is based on hitting time decompos... 详细信息

关键词： random walk in random environment moderate deviations principle hitting time

The influence of laser pulse on the photoabsorption spectra of Li atom in strong external field

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Science china(Physics,Mechanics & Astronomy) 2006年第2期49卷 178-186页

作者： wang Dehua1 & LIN Shenglu2.1. School of Physics and Electronic Engineering, Yantai normal {2., Yantai 2.402., china 2. department of Physics, Shandong normal {2., Jinan 2.0014, china 1. School of Physics and Electronic Engineering Yantai Normal University Yantai 264025 China 2. department of Physics Shandong Normal University Jinan 250014 China

Using the time-dependent perturbation theory and the calculation formula of the single- and double-pulse absorption spectra of the atom in strong external fields, we calculate the single- and double-pulse absorption spectra of Li atom in strong magnetic field for different pulse widths. The results show that a pulse of some width can reduce the contribution of the short period closed orbits and eliminate the contribution of the long period orbits. Compared with the single-pulse absorption spectra, we found that for some phase differences, the double-pulse laser absorption spectra are strengthened; while for others, they are reduced. Therefore, we can use the pulse laser to control the oscillation of the absorption spectra and obtain the optimization object.

关键词： laser pulse closed orbit absorption spectra.

A categorical interpretation of Yetter-Drinfel'd modules

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Chinese Science Bulletin 1999年第9期44卷 771-778页

作者： KAN Haibin and wang ShuanhongInstitute of mathematics , Fudan {2. , Shanghai 2.0433 , china department of mathematics , Henan normal {2., Xinxiang 453002. china Institute of mathematics Fudan Univrrsity Shanghai China Dcpartment of mathematics Henun Normal University Xinxiang China

It is known that any strict tensor category （C, I） can determine a strict braided tensor category Z （ C）, the centre of C. When A is a finite Hopf algebra, Drinfel’d has proved that Z（AM） is equivalent to D（A）M as a braided tensor category, where AM is the left A-module category, and D （A） is the Drinfel’d double of A. This is the categorical interpretation of D （A）.Z（4M） is proved to be equivalent to the Yetter-Drinfel’ d module category AY D4 as a braided tensor category for any Hopf algebra A. Furthermore, for right A-comodule category MA , Z（MA） is proved to be equivalent to the Yetter-Drinfel’ d module category AY D4 as a braided tensor category. But, in the two cases, the Yetter-Drinfel’ d module category AY DA has different braided tensor structures.

关键词： Yetter-Drinfel’d module tensor category equivalence.

Optimal value functions of generalized semi-infinite min-max programming on a noncompact set

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Science china mathematics 2005年第2期48卷 261-276页

作者： wang Changyu, YANG Xiaoqi & YANG Xinmin Institute oi Operations Research, Qufu normal {2., Qufu 2.3165, china department of Applied mathematics, Dalian {2. of Technology, Dalian 11602., china department of Applied mathematics, The Hong Kong Polytechnic {2., Hong Kong, china department of mathematics, Chongqing normal {2., Chongqing 400047, china 1. Institute of Operations Research Qufu Normal University 273165 Qufu China 2. department of Applied mathematics Dalian University of Technology 116024 Dalian China 3. department of Applied mathematics The Hong Kong Polytechnic University Hong Kong China 4. department of mathematics Chongqing Normal University 400047 Chongqing China

In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subdifferential characterizations of optimal value functions are given. Using these properties,we establish first order optimality conditions for unconstrained generalized semi-infinite programming problems.

关键词： optimal value function, directional derivative, subdifferential, semi-infinite programming, first order optimality condition.

LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES

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Acta Mathematica Scientia 2010年第3期30卷 968-974页

作者：王路生尹景学王泽佳 department of mathematics Jilin University department of mathematics South China Normal University

This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration equations ｜x｜λ＋Эt^-Эu=div（｜x｜^k∨u^m）＋｜x｜λ＋ku^p with 0 〈 m 〈 1,p 〉 1,λ≥0, k ∈ R. An interesting phenomenon is that there exist two thresholds k∞ and kl for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k E （k∞, k1）, otherwise, pc is infinite or does not exist.

关键词： Newtonian filtration equation critical exponent exterior problem Thresh -old

RECOGNITION AND CLASSIFICATION FOR O(n)-EQUIVARIANT BIFURCATIONS WITH O(n)-CODIMENSION LESS THAN 5

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Chinese Annals of mathematics,Series B 1998年第4期19卷 391-400页

作者： wang XIAOFENG (department of Applied {2., Tsinghua university, beijing 100084, china.)TANG YUN (department of Applied {2., Tsinghua university, beijing 100084, china.)wang DUO (School of Mathematical Science, Peking universityl Beliing 10 Tsing Hua Univ Dept Appl Math Beijing 100084 Peoples R China Peking Univ Sch Math Sci Beijing 100080 Peoples R China

Bifurcation problems equivariant under the standard action of the orthogonal group O(n) up to O(n)-codimension 4 are classified into 19 classes. For each class the normal form and one universal unfolding are calculate... 详细信息

关键词： O(n)-equivariant bifurcation normal form Universal unfolding Recognition problem

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 {2., Qufu 2.3165, china 2.4} of mathematics, East china normal {2., Shanghai 2.02.1, 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

Lifting Minimal Resolutions over Zariskian Filtered Rings

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Acta Mathematica Sinica,English Series 1997年第4期13卷 513-516页

作者： wang Zhixi department of {2., Capital normal university, beijing 100037, china

The correlation between the resolution for a Zariskian filtered ring R and that for its associated graded ring G(R) is discussed in this note. Then we show some examples satisfying the condition of the theorem.

关键词： Zariskian filtered ring Minimal filt--projective resolution Gr-semiperfect ring