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D(β)-vertex-distinguishing total coloring of graphs

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Science china mathematics 2006年第10期49卷 1430-1440页

作者： ZHANG Zhongfu,LI Jingwen,CHEN Xiang’en,YAO Bing, WANG Wenjie & QIU Pengxiang institute of applied Mathematic,{2., lanzhou 730070, china College of mathematics and Information Science, Northwest Normal university, lanzhou 730070, china College of Information and Electrical Engineering,{2., lanzhou 730070, china institute of applied Mathematic Lanzhou Jiaotong University Lanzhou 730070 China College of mathematics Information Science Northwest Normal University Lanzhou 730070 China College of Information Electrical Engineering Lanzhou Jiaotong University Lanzhou 730070 China

A new concept of the D(β)-vertex-distinguishing total coloring of graphs, i.e., the proper total coloring such that any two vertices whose distance is not larger than β have different color sets, where the color set of a vertex is the set composed of all colors of the vertex and the edges incident to it, is proposed in this paper. The D(2.-vertex-distinguishing total colorings of some special graphs are discussed, meanwhile, a conjecture and an open problem are presented.

关键词： graph, total coloring, D(β)-vertex-distinguishing total coloring, D(β)-vertexdistinguishing total chromatic number.

On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengrong 2.and YU Yuanhong 3 1. Department of applied mathematics, Beijing {2. of Technology, Beijing 100081, china 2. Department of mathematics, Yunnan university, Kunming 650091, china 3. institute of applied mathematics, C Department of applied mathematics Beijing Institute of Technology Beijing China Department of mathematics Yunnan University Kunming China institute of applied mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.

Quantitative result on stability for delay difference systems

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Chinese Science Bulletin 1997年第22期42卷 1858-1861页

作者： ZHANG ShunianDepartment of applied mathematics, Shanghai {2. university, Shanghai 2.02.0, china Department of applied mathematics Shanghai Jiaotong University Shanghai China

IN ref. [1] we have established the stability criteria for the finite delay difference systems ofthe general form in terms of the discrete Liapunov functionals as well as Liapunov *** then, some other results have app... 详细信息

关键词： quadratic delay difference systems uniform stability uniform asymptotic stability stability region asymptotic stability region.

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2.1. Department of mathematics, Beijing Normal university, Beijing 100875,{2. 2. institute of applied Physics and Computational mathematics, Beijing 100080,{2. 1. Department of mathematics Beijing Normal University Beijing 100875 China 2. institute of applied Physics and Computational {2. Beijing 100080 China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

On some tests-based projection pursuit for elliptical symmetry of a high-dimensional distribution

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Chinese Science Bulletin 1998年第6期43卷 450-458页

作者： JING Ping 1 and ZHU Lixing 2.1. mathematics Lab, china {2. of Mining & Technology, Beijing 100083, china 2. Probability Lab, institute of applied mathematics, Chinese Academy of Sciences, Beijing 100080, china mathematics Lab China University of Mining & Technology Beijing China Probability Lab Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.

关键词： bootstrap approximation projection pursuit type statistic elliptical symmetry.

Theory of truth degrees of propositions in the logic system Ln^＊

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Science in china(Series F) 2006年第4期49卷 471-483页

作者： LI Jun1,2.& WANG Guojun1,3 1. institute of mathematics, Shaanxi Normal {2., Xi’an 710062. china 2. School of Sciences, lanzhou {2. of Technology, lanzhou 730050, china 3. Research Center for Science, Xi’an jiaotong {2., Xi’an 710049, china 1. institute of mathematics Shaanxi Normal University Xi’an 710062 China 2. School of Sciences Lanzhou University of Technology Lanzhou 730050 China 3. Research Center for Science Xi’an Jiaotong University Xi’an 710049 China

By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized Lu- kasiewicz propositional logic system Ln^＊ is introduced in the present paper. It is proved that the set consisting of truth degrees of all formulas is dense in [0,1], and a general expres- sion of truth degrees of formulas as well as a deduction rule of truth degrees is then obtained. Moreover, similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in n-valued generalized Lukasiewicz propositional logic is established.

关键词： truth degree similarity degree approximate reasoning.

An improvement in stability of delay difference systems

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Chinese Science Bulletin 1998年第7期43卷 544-547页

作者： ZHANG Shunian Department of applied mathematics, Shanghai {2. university, Shanghai 2.02.0, china Department of applied mathematics Shanghai Jiaotong University Shanghai China

A new result on the stability of delay difference equations is established, in which a kind of weighted norm for x is adopted in order to estimate the upper bound of Liapunov functional.

关键词： delay difference systems uniform asymptotic stability in terms of two measures Liapunov functionals.

Two-dimensional Riemann problems of simplified Euler equation

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Chinese Science Bulletin 1998年第6期43卷 441-444页

作者： YANG Xiaozhou 1,2.and HUANG Feimin+1 1. institute of applied mathematics, Chinese Academy of Sciences, Beijing 100080, china 2. Department of {2., Shantou university, Guangdong 515063, china institute of applied mathematics Chinese Academy of Sciences Beijing China Department of mathematics Shantou University Guangdong China

The two-dimensional Riemann problem of simplifed Euler equation is discussed, in which initial value contains two different constant states that are separated by a smooth curve. This problem is a natural description of realistic phenomena, but it is hard to study by conventional idea. So a new approach is proposed. Some new properties about two-dimensional rarefaction wave, shock wave and intermediate state of solutions are disclosed.

关键词： D Riemann problem implicit functions cylindrical surface pencil of cylindrical surface.

Normality and shared values concerning differential polynomials

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Science china mathematics 2010年第3期53卷 749-754页

作者： LEI ChunLin 1 & FANG MingLiang 2. 1 Department of applied mathematics, South{2. Agricultural university, Guangzhou 510642.{2. 2.institute of applied mathematics, South{2. Agricultural university, Guangzhou 510642.{2. 1. Department of applied mathematics South China Agricultural University Guangzhou 510642 China2. Institute of Applied Mathematics South China Agricultural University Guangzhou 510642 China

Let F be a family of functions meromorphic in a domain D, let P be a polynomial with either deg P≥3 or deg P = 2.and P having only one distinct zero, and let b be a finite nonzero complex number. If, each pair of fun... 详细信息

关键词： meromorphic function normality shared value