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MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

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Acta Mathematica Scientia 2010年第4期30卷 1257-1268页

作者：丁协平 college of mathematics and software Science Sichuan Normal University Chengdu

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.

关键词： Maximal element system of generalized vector quasi-equilibrium problems Mathematical program Ci(x)-FC-partially diagonally quasiconvex Ci(x)-FC-quasiconvex Ci(x)-FC-quasiconvex-like FC-space

Some basic inequalities in higher dimensional non-Euclid space

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Science China mathematics 2007年第3期50卷 423-438页

作者： Ding-hua yang college of mathematics and software sciences, sichuan normal university, chengdu 610066, China chengdu Institute of Computer Applications, Chinese Academy of sciences, chengdu 610041, China college of mathematics and software sciences Sichuan Normal University Chengdu China chengdu Institute of Computer Applications Chinese Academy of Sciences Chengdu China

In this paper, the concept of a finite mass-points system∑N(H(A))(N>n) being in a sphere in an n-dimensional hyperbolic space Hn and a finite mass-points system∑N(S(A))(N>n) being in a hyperplane in an n-dimensional spherical space Sn is introduced, then, the rank of the Cayley-Menger matrix AN(H)(or a AN(S)) of the finite mass-points system∑∑N(S(A))(or∑N(S(A))) in an n-dimensional hyperbolic space Hn (or spherical space Sn) is no more than n+2 when∑N(H(A))(N>n) (or∑N(S(A))(N>n)) are in a sphere (or hyperplane). On the one hand, the yang-Zhang’s inequalities, the Neuberg-Pedoe’s inequalities and the inequality of the metric addition in an n-dimensional hyperbolic space Hn and in an n-dimensional spherical space Sn are established by the method of characteristic roots. These are basic inequalities in hyperbolic geometry and spherical geometry. On the other hand, some relative problems and conjectures are brought.

关键词： higher dimensional Euclid space simplex volume radius of circumscribed sphere metric addition yang-Zhang’s inequality Neuberg-Pedoe’s inequality.

SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

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Acta Mathematica Scientia 2007年第3期27卷 522-534页

作者：丁协平 college of mathematics and software Science Sichuan Normal University

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.

关键词： Maximal element generalized game equilibrium system of generalized vector quasi-equilibrium problems FC-spaces

The complete principal divisor lattices

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Science China mathematics 2010年第8期53卷 2159-2172页

作者： WANG XuePing & QU XiaoBing college of mathematics and software Science,sichuan normal university,chengdu 610066,China college of mathematics and software Science Sichuan Normal University Chengdu China

In this paper,we introduce a concept of principal divisor lattice and describe the structure of its *** first give a necessary and sufficient condition for the existence of irredundant join irreducible decompositions in complete principal divisor distributive lattices,and prove that the complete lower continuous,principal divisor lattices have irredundant join irreducible *** the end,we show the descriptions of lattices that have unique(***) irredundant join irreducible decompositions in complete lower continuous principal divisor lattices.

关键词： complete lattice principal divisor lattice distributive lattice irredundant join irreducible decomposition

EQUILIBRIUM PROBLEMS WITH LOWER AND UPPER BOUNDS IN TOPOLOGICAL SPACES

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Acta Mathematica Scientia 2005年第4期25卷 658-662页

作者：丁协平 college of mathematics and software Science Sichuan Normal University Chengdu 610066 China

By employing a fixed point theorem due to Ding, Park and Jung, some existence theorems of solutions for equilibrium problems with lower and upper bounds are proved in noncompact topological spaces. These results furth... 详细信息

关键词： Equilibrium problem fixed point theorem contractible space acyclic space,topological space

NEW SYSTEMS OF GENERALIZED QUASI-VARIATIONAL INCLUSIONS IN FC-SPACES AND APPLICATIONS

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Acta Mathematica Scientia 2011年第3期31卷 1142-1154页

作者：丁协平 college of mathematics and software Science sichuan normal university

In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity *** applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.

关键词： maximal element system of generalized quasi-variational inclusion problems system of quasi-optimization problems mathematical programs with systems of generalized quasi-variational inclusion constraints F C-space

On (2~m + 1)-variable symmetric Boolean functions with submaximum algebraic immunity 2^(m-1)

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Science China mathematics 2009年第1期52卷 17-28页

作者： LIAO QunYing1, LIU Feng2 & FENG KeQin2 1 college of mathematics and software sciences, sichuan normal university, chengdu 610066, China 2 Department of Mathematical sciences, Tsinghua university, Beijing 100084, China college of mathematics and software sciences Sichuan Normal University Chengdu China Department of Mathematical sciences Tsinghua University Beijing China

All (2m +1)-variable symmetric Boolean functions with submaximal algebraic immunity 2m-1 are described and constructed. The total number of such Boolean functions is 32 ·22m-3 +3m-2 · 24 - 2 for m≥2.

关键词： symmetric Boolean function algebraic immunity cryptography

MATHEMATICAL ANALYSIS OF THE COLLAPSE IN BOSE-EINSTEIN CONDENSATE

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Acta Mathematica Scientia 2009年第1期29卷 56-64页

作者：李晓光张健吴永洪 software Laboratory Sichuan Normal University college of mathematics and software Science Sichuan Normal University Department of mathematics and Statistics Curtin University of Technology

In this article, the authors consider the collapse solutions of Cauchy problem for the nonlinear Schrdinger equation iψt + 1/2 △ ψ - 1/2 ω2|x|2ψ + |ψ|2ψ = 0, x ∈ R2, which models the Bose-Einstein condensate with attractive interactions. The authors establish the lower bound of collapse rate as t → T . Furthermore, the L2-concentration property of the radially symmetric collapse solutions is obtained.

关键词： Nonlinear Schrdinger equation attractive Bose-Einstein condensates col-lapse rate L2-concentration

TRANSIENT QUEUE SIZE DISTRIBUTION SOLUTION OF GEOM/G/1 QUEUE WITH FEEDBACK-A RECURSIVE METHOD

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Journal of Systems Science & Complexity 2009年第2期22卷 303-312页

作者： Chuanyi LUO Yinghui TANG Cailiang LI Department of Economic mathematics Southwestern University of Finance and Economics Chengdu 610074China. School of mathematics and software Science Sichuan Normal University Chengdu 610066 China. Department of Information and Computer Science Chengdu Electron-Mechanical College Chengdu 610031China.

This paper considers the Geom/G/1 queueing model with feedback according to a latearrival system with delayed access (LASDA).Using recursive method,this paper studies the transientproperty of the queue size from the initial state N(0^+)=*** new results about the recursiveexpression of the transient queue size distribution at any epoch n^+ and the recursive formulae of theequilibrium distribution are ***,the recursive formulae of the equilibrium queuesize distribution at epoch n,and n are obtained,*** important relations between stationaryqueue size distributions at different epochs are discovered (being different from the relations given inM/G/1 queueing system).The model discussed in this paper can be widely applied in all kinds ofcommunications and computer network.

关键词：递归方法大小分布队列 m/G/1排队模型反馈暂态计算机网络初始状态