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L-R smash products for bimodule algebras

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Progress in Natural Science:Materials International 2006年第6期16卷 580-587页

作者： ZHANG Liangyun (department of mathematics, nanjing Agricultural university, nanjing 210095, china department of mathematics, nanjing university, nanjing 210008, china) department of mathematics Nanjing Agricultural University Nanjing 210095 China department of mathematics Nanjing U-niversity Nanjing 210008 China

In this paper, we prove that the L-R smash product A(?)H is exactly the twisted smash product A * H if H is a finite dimensional cocommutative Hopf algebra, and give a sufficient and necessary condition for L-R smash products to be bialgebras (Hopf algebras) . For any finite dimensional coquasitriangular Hopf algebra (H,σ), we prove that the L-R smash product H(?)H is semisimple Artinian if H is semisimple and H * is unimodular. In particular, the L-R smash product D(H)* (?)D(H)* semisimple Artinian if the Drin-fel'd double D(H) is semisimple.

关键词： bimodule algebras L-R smash products coquasitriangular Hopf algebras Long bialgebras.

LIMIT CYCLES AND BIFURCATION CURVES FOR THE QUADRATIC DIFFERENTIAL SYSTEM (III)_(m=0) HAVING THREE ANTI-SADDLES (I)

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Chinese Annals of mathematics,Series B 1996年第2期17卷 167-174页

作者： YE YANQIAN department of mathematics, nanjing university, nanjing 210008, china. 南京大学数学系江苏南京

For the quadratic system: x=-y+δx + lx2 + ny2, y=x(1+ax-y) under conditions -10 the author draws in the (a, ()) parameter plane the global bifurcationdiagram of trajectories around O(0,0). Notice that when na2+l < 0 ... 详细信息

关键词： Quadrtic systen Anti-saddle Bifurcation curve Limit cycle

Maschke-type theorem and Morita context over weak Hopf algebras

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Science china mathematics 2006年第5期49卷 587-598页

作者： ZHANG Liangyun College of Science, nanjing Agricultural university, nanjing 210095, china department of mathematics, nanjing university, nanjing 210008, china College of Science Nanjing Agricultural University Nanjing China department of mathematics Nanjing University Nanjing China

This paper gives a Maschke-type theorem over semisimple weak Hopf algebras,extends the well-known Maschke-type theorem given by Cohen and Fishman and constructs a Morita context over weak Hopf algebras.

关键词： weak Hopf algebra, smash product, Maschke-type theorem, Morita context.

THE UNIQUENESS OF BIFURCATION TO SEPARATRIX LOOPS IN SUPERCRITICAL CASES

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Chinese Annals of mathematics,Series B 1994年第4期15卷 493-500页

作者： SUN JIANHUA (department of mathematics, nanjing university, nanjing 210008, china.) 南京大学数学系江苏南京

In paper[4]the existence of bifurcation to separatrir loops in supercritical cases on the planeis studied. This note is a continuation of [4].The author proves the uniqueness of limit cyclesin a neighborhood of the sa... 详细信息

关键词： Supercritical Separatrir loop Bifurcation Limit cycle Uniqueness.

IBN Rings and Orderings on Grothendieck Groups

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Acta Mathematica Sinica,English Series 1994年第3期10卷 225-230页

作者： Tong Wenting department of mathematics nanjing university nanjing,210008 china department of mathematics Nanjing University Nanjing China

Let R be a ring with an identity element.R∈IBN means that Rm■Rn implies m=n,R ∈IBN1 means that Rm ■Rn⊕K implies m≥n,and R ∈IBN2 means that Rm■Rm⊕K implies K=*** this paper we give some characteristic properties of IBN1 and IBN2,with orderings o the Grothendieck *** addition,we obtain the following results:（1）If R ∈IBM1 and all finitely generated projective left R-modules are stably free,then the Grothendieck group Ko（R）is a totally ordered abelian group.（2）If the pre-ordering of the Grothendieck group Ko（R）of a ring R is a partial ordering,then R ∈IBM1 or Ko（R）=0.

关键词： IBN Rings and Orderings on Grothendieck Groups Math PSF

Non-p-generic and Strongly Nonbranching Degree

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Acta Mathematica Sinica,English Series 1994年第1期10卷 30-41页

作者： Ding Decheng department of mathematics nanjing university nanjing,210008 china department of mathematics Nanjing University Nanjing China

It has been proved by the author that every p-generic degree is *** this paper we construct an *** which is strongly nonbranching and *** means that the class of nonbranching degrees does not coincide with the class o... 详细信息

关键词： Non-p-generic and Strongly Nonbranching Degree NB

Surface Billiards and Nonvanishing Lyapunov Exponents

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Acta Mathematica Sinica,English Series 1997年第1期13卷 21-34页

作者： Cheng Jian (department of mathematics,nanjing university,nanjing 210008,china) 南京大学数学系江苏南京

We study in this paper the billiards on surfaces with mix-valued Gaussian curvature and the condition which gives nonvanishing Lyapunov exponents of the *** introduce a criterion upon which a small perturbation of the... 详细信息

关键词： Billiards Lyapunov exponents Curvature

SUPPLEMENT　TO“PASSAGE，BLOCKADE，SINK　AND　SOURCE　OF　A　PLANAR　DYNAMICAL　SYSTEMS”

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Chinese Annals of mathematics,Series B 1994年第4期15卷 489-492页

作者： YE YANQIAN(department of mathematics, nanjing university, nanjing 210008,china.) 南京大学数学系江苏南京

A Theorem is given on the number of passages passing throgh a multiply-connected region,which corrects a wrong conjecture in a former paper of the author.

关键词： Passage Multiply-connected region Critical point Saddle point.

MULTIVALUED PERTURBATION TO NONLINEAR DIFFERENTIAL INCLUSIONS WITH MEMORY IN BANACH SPACES

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Chinese Annals of mathematics,Series B 1996年第2期17卷 237-244页

作者： XUEXINGMEI SONGGUOZHU departmentofMathemtics＆Mechanics SoutheastUniversityNanjing210018China. departmentofmathematics NanjingUniversityNanjing210008China.

The authors give the existence results to the nonlinear differential inclusion u'(t) ∈ Au(t) +F(t,ut), where A is a ganerator of equicontinuous semigroup and F is multivalued.

关键词： Differential inclusion with memory Equicontimuous semigroup Housdorff measure Kamke function