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DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (department of mathematics, Shanghai Normal university, Shanghai 2.02.4, China) department of mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.

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 China Agricultural {2., Guangzhou 510642. China 2.Institute of Applied mathematics, South China Agricultural {2., Guangzhou 510642. China 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

THE INDUCED REPRESENTATION OF C^＊-GROUPOID DYNAMIC SYSTEMS

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Chinese Annals of mathematics,Series B 1996年第1期17卷 103-114页

作者： FANG XIAOCHUN(department of mathematics, Tongji university, Shanghai 2.002., China.) TONGJI UNIV DEPT MATHSHANGHAI 200029PEOPLES R CHINA

Let G be a second countable locally compact groupoid with Haar system {λu}, H be a closed subgroupoid containing Go with Haar system {λuH}. *** introduced the C*-Groupoid dynamic system (G, A, α) and its reduced crossed product Cr.d(G, A) in [2., where A is a C*-algebra, α is the homomorphism G→Aut(A). In this paper the author introduces the C*-groupoid dynamic systems (H, A, α|H) and (H\G2. A, α) induced by (G, A, α) and proves that C~*red(H, A) and C~*red(H\G2. A) are strongly Morita equivalent. Moreover the induced representation from C~*red(H, A) to C~*red(G, A) is got.

关键词： C~*-groupoid dynamic system Induced representation Haar system

Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics

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Science China(Physics,Mechanics & Astronomy) 2006年第3期49卷 257-272页

作者： XU Mingyu1 & TAN Wenchang2.1. Institute of Applied mathematics, School of Math & System Science, Shandong university, Jinan 2.0100, China 2. State Key Laboratory of Turbulence and Complex Systems & {2. of Mechanics and Engineering Science, Peking university, Beijing 100871, China 1. Institute of Applied mathematics School of Math & System Science Shandong University Jinan 250100 China 2. State Key Laboratory of Turbulence and Complex Systems & department of Mechanics and Engineering Science Peking University Beijing 100871 China

From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equa- tions) used for describing intermediate processes and critical phenomena in physics and mechanics, their progress in theory and methods and their applications to modern me- chanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.

关键词： fractional operators,intermediate processes,critical phenomena,modern mechanics

Oscillatory and Asymptotic Behaviour of Fourth Order Nonlinear Difference Equations

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Acta Mathematica Sinica,English Series 1997年第1期13卷 105-115页

作者： Yan Jurang (department of mathematics,shanxi {2.,Taiyuan,030006,China)Liu Bin (department of mathematics,Hubei Normal {2.,Huangshi,435002.China) department of mathematics Shanxi University 030006 Taiyuan China

This paper considers a class of fourth order nonlinear difference equations Δ2.rnΔ2.n）+ f（n,yn）=0,n∈N（n0）,where f（n,y）may be classified as superlinear,sublinear,strongly super- linear and strongly *** super... 详细信息

This paper considers a class of fourth order nonlinear difference equations Δ2./sup>（rnΔ2./sup>yn）+ f（n,yn）=0,n∈N（n0）,where f（n,y）may be classified as superlinear,sublinear,strongly super- linear and strongly *** superlinear and sublinear cases,necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic *** strongly superlinear and strongly sublinear cases,sufficient conditions are given for all solutions to be oscillatory.

关键词： Nonlinear difference equation Oscillation Asymptotic behaviour.

(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 2.0093,China) Nanjing Univ Dept Math Nanjing 210093 Peoples R 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

A Series of Soliton-like and Double-like Periodic Solutions of a (2.1)-Dimensional Asymmetric Nizhnik-Novikov-Vesselov Equation

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Communications in Theoretical Physics 2004年第11期42卷 655-660页

作者： CHEN Yong,~(1,3,4, WANG Qi~(2.4) LI Biao~(2.4) ~1department of mathematics,Ningbo university,Ningbo 3152.1,China ~2.2. of Applied mathematics,Dalian university of Technology,Dalian 11602.,China ~3{2. of Physics,Shanghai Jiao Tong university,Shanghai 2.0030,China ~4Key Laboratory of mathematics Mechanization~ the Chinese Academy of Sciences,Beijing 100080,China Key Laboratory of mathematics Mechanization the Chinese Academy of Sciences Beijing 100080 China

We generalize the algebraic method presented by Fan [***.A:***.36 (2.03) 7009)] to uniformlyconstruct a series of soliton-like solutions and double-llke periodic solutions for nonlinear partial differential equations(NPDE),As an application of the method,we choose a (2.1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equa-tion and successfully construct new and more general solutions including a series of nontraveling wave and coefficientfunctions’ soliton-like solutions,double-like periodic and trigonometric-like function solutions.

关键词： symbolic computation soliton-like solution Weierstrass and Jacobi elliptic functions periodic solution

ON CLASSIFICATION OF PROJECTIVE VARIETIES WITH NON-INTEGRAL NEF VALUES

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Chinese Annals of mathematics,Series B 2001年第2期22卷 255-262页

作者： ZHAO YICAI department of mathematics, Jinan university, GuangZhou 510632. China. department of mathematics Jinan University Guangzhou 510632 China

Let M be an n-dimensional normal projective variety with only Gorenstein, terminal, Qfactorial singularities. Let L be an ample line bundle on M. Let r denote the nef value of (M, L). The classification of (M, L) via ... 详细信息

关键词： Nef value morphism Ample line bundle Projective variety

Correlation of zeros of automorphic L-functions

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Science China mathematics 2008年第7期51卷 1147-1166页

作者： LIU JianYa1 & YE YangBo1,2.1 School of mathematics,Shandong university,Jinan 2.0100, China 2.2.,The university of Iowa,Iowa City,IA 52.42.1419,USA 1. School of mathematics Shandong University Jinan 250100 China 2. department of mathematics The University of Iowa Iowa City IA 52242-1419 USA

We compute the n-level correlation of normalized nontrivial zeros of a product of Lfunctions: L(s, π1) … L(s, π k ), where πj, j = 1, …, k, are automorphic cuspidal representations of GL mj (?A). Here the sizes of the groups GL mj (?A) are not necessarily the same. When these L(s, π j ) are distinct, we prove that their nontrivial zeros are uncorrelated, as predicted by random matrix theory and verified numerically. When L(s, π j ) are not necessarily distinct, our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble (GUE) models of individual L-functions and products of lower rank GUEs. The results are unconditional when m 1, …, m k ? 4, but are under Hypothesis H in other cases.

关键词： automorphic L-function zero correlation Selberg’s orthogonality conjecture 11F70 11M2. 11M41