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The isometric extension of “into” mappings on unit spheres of AL-spaces

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Science china Mathematics 2008年第10期51卷 1904-1918页

作者： ding guanggui school of Mathematics Science, Chern Institute of Mathematics and lpmc, nankai university, tianjin 300071, china school of Mathematics Science Chern Institute of Mathematics and LPMC Nankai University Tianjin China

In this paper, we show that if V0 is an isometric mapping from the unit sphere of an AL-space onto the unit sphere of a Banach space E, then V0 can be extended to a linear isometry defined on the whole space.

关键词： isometric extension (atomic) AL-space

THE UNIFORM BOUNDEDNESS PRINCIPLE IN SOME TOPOLOGICAL VECTOR GROUPS

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Systems Science and mathematical sciences 2000年第3期13卷 292-301页

作者： ding guanggui(Department of Mathematics, nankai university, tianjin 300071, china) 南开大学数学系天津 300071

It is shown that the famous Banach-Steinhaus theorem can be generalized to some families of nonlinear functionals defined on some topological groups and topological vector space, e.g. the F-spaced lβ(0 <β < 1) and S... 详细信息

关键词： Binary fissionable topological group locally pseudo-bounded second category uniform boundedness principle

A NOTE ON THE EQUICONTINUITY IN SOME TOPOLOGICAL GROUPS

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Systems Science and mathematical sciences 1999年第3期12卷 270-272页

作者： ding guanggui(Department of Mathematics, nankai university, tianjin 300071, china) 南开大学数学系天津 300071

In this paper, we show that a theorem concerning the equicontinuity of theoperators in F-spaces can be generalized to a class of operators defined on the binaryfissionable topological groups.

关键词： Binary fissionable topological group quasi-additive operator equicontinuity.

VORTEX DYNAMICS OF THE ANISOTROPIC GINZBURG-LANDAU EQUATION

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Acta Mathematica Scientia 2010年第3期30卷 949-962页

作者：温焕尧丁时进 school of mathematical sciences South China Normal University

In this article, using coordinate transformation and Gronwall inequality, we study the vortex motion law of the anisotropic Cinzburg-Landau equation in a smooth bounded domain Ω （R^2,that is ,Эtuε=j,k=1∑2（ajkЭxkuε）xj＋ε^2^-b（x）（1-｜uε｜^2）uε,x∈Ω,and conclude that each vortex,bj（t）（j=1,2,…,N）satisfies dt^-dbj（t）=-（a（bj（t））^-a1k（bj（t））Эxka（bj（t））,a（aj（t））^-a2k（bj（t））Эxka（bj（t）））,where a（x）=√a11a22-a12^2. We prove that all the vortices are pinned together to the critical points of a（x）. Furthermore, we prove that these critical points can not be the maximum points.

关键词： Anisotropic Ginzburg-Landau equation Gronwall inequality vortex dynamics

Simplest Normal Forms of Generalized Neimark-Sacker Bifurcation

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Transactions of tianjin university 2009年第4期15卷 260-265页

作者：丁玉梅张琪昌 school of Mechanical Engineering Tianjin University school of sciences Tianjin University of Science and Technology

The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system. It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation are expressed in polar coordinates, then all odd order terms must, in general, remain in the normal forms. In this paper, five theorems are presented to show that the conventional Neimark-Sacker bifurcation can be further simplified. The simplest normal forms of generalized Neimark-Sacker bifurcation are calculated. Based on the conventional normal form, using appropriate nonlinear transformations, it is found that the generalized Neimark-Sacker bifurcation has at most two nonlinear terms remaining in the amplitude equations of the simplest normal forms up to any order. There are two kinds of simplest normal forms. Their algebraic expression formulas of the simplest normal forms in terms of the coefficients of the generalized Neimark-Sacker bifurcation systems are given.

关键词： generalized Neimark-Sacker bifurcation simplest normal form near identity nonlinear transformations

Littlewood-Paley operators with variable kernels

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Science china Mathematics 2006年第5期49卷 639-650页

作者： CHEN Jiecheng, ding Yong & FAN Dashan Department of Mathematics, Zhejiang university (Xixi Campus), Hangzhou 310028, china school of mathematical sciences, Beijing Normal university, Beijing 100875, china Department of Mathematics, university of Wisconsin-Milwaukee, Milwaukee WI 53201, USA Department of Mathematics, Central china Normal university, Wuhan 430074, china Department of Mathematics Zhejiang University (Xixi Campus) Hangzhou China school of mathematical sciences Beijing Normal University Beijing China Department of Mathematics University of Wisconsin-Milwaukee Milwaukee USA Department of Mathematics Central China Normal University Wuhan China

In this paper we study a certain directional Hilbert transform and the boundedness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels... 详细信息

关键词： directional Hilbert transform, Sobolev spaces, Littlewood-Paley operator,variable kernel.

Impulsive Homoclinic Chaos in Van der Pol Jerk System

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Transactions of tianjin university 2010年第6期16卷 457-460页

作者：丁玉梅张琪昌 school of Mechanical Engineering Tianjin University school of sciences Tianjin University of Science and Technology

A 3D continuous autonomous chaotic system is reported, which contains a cubic term and six system parameters. Basic dynamic properties of the new Van der Pol Jerk system are studied by means of theoretical analysis and numerical simulation. Based on the Silnikov theorem, the chaotic characterisitics of the dynamic system are discussed. Using Cardano formula and series solution of differential equation, eigenvalue problem and the existence of homoclinic orbit are studied. Furthermore, a rigorous proof for th...

关键词： chaotic system homoclinic orbit Silnikov theorem

Antioxidant Effects of Dehydroepiandrosterone Are Related to Up-regulation of Thioredoxin in SH-SY5Y Cells

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Acta Biochimica et Biophysica Sinica 2005年第2期37卷 119-125页

作者： Jing GAO Hui-Ying SUN Zeng-Rong ZHU Zhen ding Li ZHU school of Medicine.school of Life sciences,Nanjing university.Nanjing 210093.china Institute of Nautical Medicine,Nantong university.Nantong 226001,china school of Medicine School of Life Sciences Nanjing UniversityNanjing 210093 China Institute of Nautical Medicine Nantong UniversityNantong 226001 China

Neuroprotective effects of dehydroepiandrosterone（DHEA）have been shown to be associatedwith its antioxidant properties,but the mechanisms remain *** that the thioredoxin（Trx）system,an important cellular redox modulation system,changes under oxidative stress and could exertprotective effects,the relationship between the antioxidant effects of DHEA and the Trx system regulationwas *** MTT assay and morphological observation,the effects of DHEA in the model of H2O2-induced oxidative stress in SH-SY5Y cells were analyzed,then RT-PCR and Western blot assay were used todetect the alteration in mRNA and protein level of Trx,The results showed that a pre-treatment of DHEA（10-100nM）protected cells against the toxicity induced by H2O2in a dose-dependent manner,which could beconfirmed in morphological observation by phase-contract *** addition,Trx mRNA transcriptionwas inhibited by H2O2（300μM）,which could be reversed by the pre-administration of DHEA in variousconcentrations（0.1-100nM）.Western blot assay confirmed that protein level of Trx could be elevated by thepre-treatment of DHEA（10-100nM）with the exposure of *** together,these data suggest thatDHEA may be useful in treating age-related neurodegenerative diseases based on its up-regulating effects onan antioxidant and neuroprotective protein thioredoxin,a substrate in the Trx redox system.

关键词： dehydroepiandrosterone(DHEA) thioredoxin(Trx) H2O2 SH-SY5Y cell

The isometrical extensions of 1-Lipschitz mappings on Gteaux differentiability spaces

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Science china Mathematics 2011年第4期54卷 711-722页

作者： ding guanggui school of mathematical sciences and lpmc Nankai UniversityTianjin 300071China

Let X and Y be real Banach *** that the subset sm[S1(X)] of the smooth points of the unit sphere [S1(X)] is dense in S1(X).If T0 is a surjective 1-Lipschitz mapping between two unit spheres,then,under some condition,T... 详细信息

关键词： 1-Lipschitz mapping linearly isometric extension Ga teaux differentiability space smooth point