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Some new results on planar harmonic mappings

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Science china mathematics 2010年第3期53卷 597-604页

作者： CHEN HuaiHui department of mathematics, Nanjing normal university, Nanjing 210097, china 1. department of mathematics Nanjing Normal University Nanjing 210097 China

This survey paper contains some new results on the Landau theorem, Bloch theorem and Schwarz-Pick lemma for planar harmonic mappings.

关键词： harmonic mapping Landau theorem Bloch constant Schwarz-Pick lemma quasi-regularity

Multi-parameter infinite-dimensional(r,δ)-OU process

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Chinese Science Bulletin 1999年第5期44卷 418-423页

作者： WANG ZikunInstitute of mathematics, Shantou university, Shantou 515063, china department of mathematics, Beijing normal university, Beijing 100875, china Institute of mathematics Shantou University Shantou China department of mathematics Beijing Normal University Beijing China

The definition of n-parameter infinite-dimensional (r, δ) -Ornstein-Uhlenbeck process {X_t (·)}((r,δ)-OUP_n~∞ for short) is given. The absolute continuity of distribution μ_t of X_t(·) and the limit of X_t(·) w... 详细信息

关键词： multi-parameter (r δ)-OUPn∞ absolute continuity in hierarchy.

Differential operators and automorphism schemes

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Science china mathematics 2010年第9期53卷 2363-2380页

作者： LI KeZheng department of mathematics,Capital normal university,Beijing 100048,china 1. department of mathematics Capital Normal University Beijing 100048 China

The ring of global differential operators of a variety is in closed and deep relation with its automorphism *** relation can be applied to the study of homogeneous schemes,giving some criteria of homogeneity,a general... 详细信息

关键词： differential operator deformative automorphism automorphism scheme homogeneous scheme abelian variety

On the Cayley-Bacharach property and the construction of vector bundles

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Science china mathematics 2011年第9期54卷 1891-1898页

作者： SUN Hao 1,2 1 department of mathematics and Statistics,Huazhong normal university,Wuhan 430079,china 2 department of mathematics,East china normal university,Shanghai 200241,china 1. department of mathematics and Statistics Huazhong Normal University Wuhan 430079 China2. Department of Mathematics East China Normal University Shanghai 200241 China

We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2 for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bund... 详细信息

关键词： Cayley-Bacharach property vector bundle reflexive sheaf k-very ample

Bergman kernel function on Hua construction of the fourth type

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Progress in Natural Science:Materials International 2007年第8期17卷 893-899页

作者： Yin Weiping~(**) Lin Ping (department of mathematics,Capital normal university,Beijing 100037,china) [a]department of mathematics Capital Normal University Beijing China

This paper introduces the Hua construction and presents the holomorphic automorphism group of the Hua construction of the fourth *** the Bergman kernel function,under the condition of holomorphie automorphism and the standard complete or- thonormal system of the semi-Reinhardt domain,the infinite series form of the Bergman kernel function is *** applying the prop- erties of polynomial andΓfunctions,various identification relations of the aforementioned form are developed and the explicit formula of the Bergman kernel function for the Hua construction of the fourth type is obtained,which suggest that many of the previously-reported results are only the special cases of our findings.

关键词： Hua construction Bergman kernel function holomorphic automorphism group

EXISTENCE OF LIMIT CYCLES IN A MULTIPLY-CONNECTED REGION

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Chinese Annals of mathematics,Series B 1999年第2期20卷 169-172页

作者： ZHANG XIANG(department of mathematics, Naming normal university, Naming 210097, china.) Nanjing normal Univ Dept Math Nanjing 210097 Peoples R China

In this paper,a conjecture about the existence of limit cycles in a multiply-connected regionproposed by Ye Yanqian is proved.

关键词： Multiply-connected region Annulus theorem Limit cycle

ON THE RANGE OF RANDOM WALKS IN RANDOM ENVIRONMENT　

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Chinese Annals of mathematics,Series B 1995年第1期16卷 131-138页

作者： ZHOU XIANYIN(department of mathematics, Beijing normal university, Beijing 100875, china.) BEIJING normal UNIV DEPT MATHBEIJING 100875PEOPLES R CHINA

The range of random walk on Z￣d in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk on Zdin some random environments holds if d... 详细信息

关键词： Law of large numbers Ergodic theorem Range of random walk Random environment Effective resistance.

The　θ－Methods　in　Numerical　Solution　of　Systems　of　Differential　Equations　with　Two　Delay　Terms

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Journal of Systems Engineering and Electronics 1994年第3期5卷 32-40页

作者： Tian Hongjiong & Kuang Jiaoxun (department of mathematics, Shanghai normal university, Shanghai 200234, china) department of mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤*** aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.

关键词： Delay differential equations Numerical solution θ-methods Asymptotic stability Schur polynomial.

Pairing problem of generators in Kac-Moody algebras

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Chinese Science Bulletin 1998年第22期43卷 1872-1879页

作者： LU Caihui department of mathematics, Capital normal university, Beijing 100037, china department of mathematics Capital Normal University Beijing China

The following result is proved: in any Kac Moody algebra g(A) , (ⅰ) given any non central element h in the Cartan subalgebra  , or (ⅱ) given any real root vector x β, β∈Δ re . There exists y∈g(A) such that th... 详细信息

关键词： generator root system real root vector.