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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, china 2department of mathematics, Zhejiang normal university, Jinhua 321004, china 3department of mathematics, Zhejiang university, Hangzhou 310027, china 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

ON LOCAL STABILIZATION OF NONLINEAR CONTROL SYSTEMS

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Systems Science and Mathematical Sciences 1992年第4期5卷 289-298页

作者： ZHENG Yufan (department of mathematics,east china normal university,shanghai 200062,china)

Based on the notion of maximal absolute observability and its normalforms,a new method for studying the local stabilization for a kind of nonlinearcontrol systems is *** from the previous results given by Byrnes-Isitori and others,this new method can deal with more general systems,and hasmuch simpler way to prove the stabilization conditions and to design the feedbacklaws.

关键词： Nonlinear control absolute observability zero dynamics minimumphase

Bifurcations of Rough Heteroclinic Loops with Three Saddle Points

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Acta Mathematica Sinica,English Series 2002年第1期18卷 199-208页

作者： JIN Yin Lai ZHU De Ming department of mathematics. Linyi Teachers university. Shandong 276005. P. R. china department of mathematics. east china normal university. shanghai 200062. P. R. china department of mathematics. east china normal university. shanghai 200062. P. R. china department of mathematics Linyi Teachers' University Shandong P. R. China department of mathematics East China Normal University Shanghai P. R. China

In this paper, we study the bifurcation problems of rough heteroclinic loups cormecting threc saddle points for a higher-dimensional system. Under some transversal conditions and the nontwisted condition. the existence. uniqueness. nd incoexistencc of thc l-heteroclinic loop with threc or two saddle pomts. l-homoclinic orbit and l-periodic orbit near T are obtained. Nleanwhile, the bifurcation surfaces and existence regions are also given. Moreover. the above bifurcation results are extended to the case for heteroclinic loop with l saddle points.

关键词： Local coordinates Heteroclinic loop Homoclinic orbit Periodic orbit Bifurcation surface

Rose solutions with three petals for planar 4-body problems

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Science china mathematics 2010年第12期53卷 3085-3094页

作者： DENG ChunHua 1,2 , ZHANG ShiQing 1, & ZHOU Qing 3 1 Yangtze Center of mathematics and College of mathematics, Sichuan university, Chengdu 610064, china 2 Faculty of mathematics and Physics, Huaiyin Institute of Technology, Huai’an 223001, china 3 department of mathematics, east china normal university, shanghai 200062, china Yangtze Center of mathematics and College of mathematics Sichuan University Chengdu China Faculty of mathematics and Physics Huaiyin Institute of Technology Huai’an China department of mathematics East China Normal University Shanghai China

For planar Newtonian 4-body problems with equal masses, we use variational methods to prove the existence of a non-collision periodic choreography solution such that all bodies move on a rose-type curve with three pet... 详细信息

关键词： 4-body problems with Newtonian potentials rose solutions with three petals winding numbers variational minimization methods

Note on the number of integral ideals in Galois extensions

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Science china mathematics 2010年第9期53卷 2417-2424页

作者： L GuangShi1,& WANG YongHui2 1School of mathematics,Shandong university,Jinan 250100,china 2department of mathematics,Capital normal university,Beijing 100048,china School of mathematics Shandong University Jinan China department of mathematics Capital Normal University Beijing China

Let K be an algebraic number field of finite degree over the rational filed *** ak be the number of integral ideals in K with norm *** this paper we study the l-th integral power sum of ak,i.e.,∑k≤ x akl(l = 2,3,...).We are able to improve the classical result of Chandrasekharan and *** an application we consider the number of solutions of polynomial congruences.

关键词： Dedekind zeta-function integral ideal congruences

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 normal university, Xuzhou 221116, china department of mathematics, Capital normal 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 normal university, Xuzhou 221116, china mathematics department, Capital normal 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 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 university , shanghai 200433 , china department of mathematics , Henan normal university, 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.

ON THE UNIQUE SOLVABILITY OF THE NONLINEAR SYSTEMS IN MDBM

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Journal of Computational mathematics 1994年第1期12卷 55-60页

作者： Kuang Jiao-xun Lu Lian-hua (department of mathematics, shanghai normal university, shanghai, china) 上海师范大学数学系上海

To obtain the approximate solution of the nonlinear ordinary differential equations requires the solution to systems of nonlinear equations. The authors study the conditions for the existence and uniqueness of the sol... 详细信息

关键词： DL ON THE UNIQUE SOLVABILITY OF THE NONLINEAR SYSTEMS IN MDBM