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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.

A GOLDSTEIN'S TYPE PROJECTION METHOD FOR A CLASSOF VARIANT VARIATIONAL INEQUALITIES

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Journal of Computational mathematics 1999年第4期17卷 425-434页

作者： Bing-sheng He(department of mathematics, nanjing university, nanjing 210008, china) department of mathematics Nanjing University Nanjing 210008 China

Some optimization problems in mathematical programming can be translated to a variant variational inequality of the following form: Find a vectoru*, such that This paper presents a simple iterative method for solving this class of variational inequalities. The method can be viewed as an extension of theGoldstein's projection method. Some results of preliminary numerical experiments are given to indicate its applications.

关键词： Variational inequality Goldstein projection method.

GLOBAL CONVERGENCE AND IMPLEMENTATION OF NGTN METHOD FOR SOLVING LARGE-SCALE SMARSE NONLINEAR PROGRAMMING PROBLEMS

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Journal of Computational mathematics 2001年第4期19卷 337-346页

作者： Qin Ni (department of mathematics, nanjing university of Aeronautics and Astronautics, nanjing 210016, china) 南京航空航天大学江苏南京 210016

An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable for handling sparse data structure and pos sesses Q-quadratic convergence rate. The global convergence of this new method is proved, the convergence rate is further analysed, and the detailed implementation is discussed in this paper. Some numerical tests for solving truss optimization and large sparse problems are reported. The theoretical and numerical results show that the new method is efficient for solving large-scale sparse NLP problems.

关键词： Nonlinear programming Large-scale problem Sparse.

(1.2)INVERSES OF OPERATORS BETWEEN BANACH SPACES AND LOCAL CONJUGACY THEOREM

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Chinese Annals of mathematics,Series B 1999年第1期20卷 57-62页

作者： MA JIPU(department of mathematics,nanjing university,nanjing 210093,china) department of mathematics Nanjing University Nanjing 210093 China

Let E and F be Banach spaces and f non-linear C1 map from E into F. The main result isTheorem 2.2, in which a connection between local conjugacy problem of f at x0E and a localfine property of f'(x) at x0(see the Definition 1.1 in this paper) are obtained. This theoremincludes as special cases the two known theorems: the finite rank theorem and Berger's Theoremfor non-linear Fredholm operators. Moreover, the thcorem gives rise the further results for somenon-linear semi-Fredholm maps and for all non-linear semi-Wedholm maps when E and F areHilbert spaces. Thus Theorem 2.2 not only just unifies the above known theorems but alsoreally generalizes them.

关键词： Nonlinear semi-Fredholm maps Conjugacy problem Banach space

Regular n-simplices in R^n with vertices in Z^(n)

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Science china mathematics 2004年第1期47卷 104-113页

作者： XIA Jianguo & QIN Hourongdepartment of mathematics, nanjing Normal university, nanjing 210097, china (email: jgxia@***) department of mathematics, nanjing university, nanjing 210093, china Dept. of Math. Nanjing Normal Univ. Nanjing 210097 China Dept. of Math. Nanjing Univ. Nanjing 210093 China

In this paper the Ⅰ and Ⅱ regular n-simplices are introduced. We prove that the sufficient and necessary conditions for existence of an Ⅰ regular n-simplex in Rn are that if n is even then n = 4m(m + 1), and if n is odd then n = 4m + 1 with that n + 1 can be expressed as a sum of two integral squares or n = 4m - 1, and that the sufficient and necessary condition for existence of a Ⅱ regular n-simplex in Rn is n = 2m2 - 1 or n = 4m(m+1)(m 6 N). The connection between regulars-simplex in Rn and combinational design is given.

关键词： regular n-simplex in Rn, quadratic form.

Extension of isometries on the unit sphere of l^p (Γ) space

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Science china mathematics 2010年第4期53卷 1085-1096页

作者： FANG XiNian 1,& WANG JianHua 2 1 School of mathematics and Statistics,nanjing audit university,nanjing 210029,china 2 department of mathematics,Anhui Normal university,Wuhu 241000,china School of mathematics and Statistics Nanjing Audit University Nanjing China department of mathematics Anhui Normal University Wuhu China

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 < p < ∞,p≠2) onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto ... 详细信息

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 2) onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto E,so,we give an affirmative answer to the corresponding Tingley’s problem.

关键词： isometric extension l p (Γ) space isometry 1-Lipschitz mapping

A COLUMN RECURRENCE ALGORITHM FOR SOLVING LINEAR LEAST SQUARES PROBLEM

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Journal of Computational mathematics 1996年第4期14卷 301-310页

作者： J.X. Zhao(department of mathematics, nanjing university, nanjing china) 南京大学数学系江苏南京

A new column recurrence algorithm based on the classical Greville method and modified Huang update is proposed for computing generalized inverse matrix and least squares solution. The numerical results have shown the ... 详细信息

关键词： Math A COLUMN RECURRENCE ALGORITHM FOR SOLVING LINEAR LEAST SQUARES PROBLEM ABS

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

A MODIFIED PROJECTION AND CONTRACTION METHOD FOR A CLASS OF LINEAR COMPLEMENTARITY PROBLEMS

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Journal of Computational mathematics 1996年第1期14卷 54-63页

作者： B.S. He(department of mathematics, nanjing university, nanjing, china) 南京大学数学系江苏南京

Recently, we have proposed an iterative projection and contraction (PC) method for a class of linear complementarity problems (LCP)([4]). The method was showed to be globally convergent, but no statement could be made about the rate of convergence. In this paper, we develop a modified globally linearly convergent PC method for linear complementarity problems. Both the method and the convergence proofs are very simple. The method can also be used to solve some linear variational inequalities. Several computational experiments are presented to indicate that the method is surprising good for solving some known difficult problems.

关键词： Th Pn A MODIFIED PROJECTION AND CONTRACTION METHOD FOR A CLASS OF LINEAR COMPLEMENTARITY PROBLEMS II