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厄尔尼诺大气物理机理的周期解

物理学报 2008年第9期57卷 5366-5368页

作者：李晓静江苏技术师范学院数理学院

运用重合度理论探讨了一类非线性问题的周期解.然后将其应用于一个厄尔尼诺大气物理机理振荡,简捷地得到了该模型的周期解.

关键词：非线性厄尔尼诺现象周期解

CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES

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Chinese Annals of mathematics,Series B 1996年第2期17卷 227-236页

作者： HAN DEGUANG department of mathematics, Qufa normal university, Qufu 273165, Shandong, china. QUFA normal UNIV DEPT MATHQUFU 273165SHANDONGPEOPLES R CHINA

This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0+ (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional.

关键词： Nest algebra Derivation Continuity Linearity Banach space

Estimates for eigenvalues of Laplacian operator with any order

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Science china mathematics 2007年第8期50卷 1078-1086页

作者： Fa-en WU~(1+) Lin-fen CAO~2 1 department of mathematics,Beijing Jiaotong university,Beijing 100044,china 2.department of mathematics,Henan normal university,Xinxiang 453007,china department of mathematics Beijing Jiaotong University Beijing 100044 China department of mathematics Henan Normal University Xinxiang 453007 China

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2 \leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Laplacian operator with any order l: $$\left\{ \begin{gathered} ( - \vartriangle )^l u = \lambda u, in D \hfill \\ u = \frac{{\partial u}}{{\partial \vec n}} = \cdots = \frac{{\partial ^{l - 1} u}}{{\partial \vec n^{l - 1} }} = 0, on \partial D \hfill \\ \end{gathered} \right.$$ . Then we obtain an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues. $$\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )} \leqslant \frac{1}{n}[4l(n + 2l - 2)]^{\tfrac{1}{2}} \left\{ {\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{{l - 1}}{l}} \sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{1}{l}} } } } \right\}^{\tfrac{1}{2}} $$ . This ineguality is independent of the domain D. Furthermore, for any l ? 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.

关键词： Dirichlet problem eigenvalue estimate Laplacian operator 35P15 58G25

Moment bounds for IID sequences under sublinear expectations

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Science china mathematics 2011年第10期54卷 2155-2160页

作者： HU Feng1,2 1department of mathematics,Qufu normal university,Qufu 273165,china 2School of mathematics,Shandong university,Jinan 250100,china 1. department of mathematics Qufu Normal University Qufu 273165 China2. School of Mathematics Shandong University Jinan 250100 China

With the notion of independent identically distributed(IID) random variables under sublinear expectations introduced by Peng,we investigate moment bounds for IID sequences under sublinear expectations. We obtain a moment inequality for a sequence of IID random variables under sublinear expectations. As an application of this inequality,we get the following result:For any continuous functionsatisfying the growth condition |(x) | C(1 + |x|p) for some C > 0,p 1 depending on ,the central limit theorem under sublinear expectations obtained by Peng still holds.

关键词： moment bound sublinear expectation IID random variables G-normal distribution central limit theorem

Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems

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Science china mathematics 2006年第12期49卷 1864-1866页

作者： CHEN Jing & BAI Yuzhen department of mathematics, Nanjing university, Nanjing 210093, china department of mathematics, Qufu normal university, Qufu 273165, china 1. department of mathematics Nanjing University Nanjing 210093 China 2. department of mathematics Qufu Normal University Qufu 273165 China

Mane conjectured that every minimal measure in the generic Lagrangian systems is uniquely ergodic. In this paper, we will show that the answer to the Mane's conjecture is negative by analyzing the structure of the sup... 详细信息

关键词： minimal probability measure,uniquely ergodic,Mather theory,Lagrangian systems.

Decomposition of integrable holomorphic quadratic differential on Riemann surface of infinite type

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Science china mathematics 2010年第8期53卷 2039-2044页

作者： CHENG Tao department of mathematics,East china normal university,Shanghai 200241,china 1. department of mathematics East China Normal University Shanghai 200241 China

In this paper,decomposition of the integrable holomorphic quadratic differential on Riemann surface of infinite type is ***,Schleicher and Shishikura gave a thick-thin decomposition on Riemann surface of finite type with an integrable holomorphic quadratic differential and they thought their result might be generalized to arbitrary hyperbolic Riemann surface of infinite *** confirm what they thought is right and give a proposition(Proposition 2.2) of its own interest.

关键词： holomorphic quadratic differential decomposition collar

Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

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Science china mathematics 2007年第9期50卷 1251-1266页

作者： Ling-hua KONG~(1+) Ming-xin WANG~(2,3) 1 department of Applied mathematics,Dalian university of Technology,Dalian 116024,china 2.department of mathematics,Southeast university,Nanjing 210018,china 3 department of mathematics,Xuzhou normal university,Xuzhou 221116,china 1. department of Applied mathematics Dalian University of Technology Dalian 116024 China 2. department of mathematics Southeast University Nanjing 210018 China 3. department of mathematics Xuzhou Normal University Xuzhou 221116 China

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and ν blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.

关键词： parabolic system nonlocal sources nonlocal boundary conditions blow-up set simultaneous blow-up uniform blow-up profile 35K15 35K65

The pointwise dimension of self-similar measures

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Chinese Science Bulletin 1999年第23期44卷 2136-2140页

作者： CHEN Ercai and XIONG Jincheng department of mathematics , Nanjing normal university , Nanjing 210097, china department of mathematics , South china normal university, Guangzhou 510631 , china department of mathematics Nanjing Normal University Nanjing China department of mathematics South China Normal University Guangzhou China

The problem about the existence of pointwise dimension of self-similar measure has been discussed. The Hausdorff dimension of the set of those points for which the pointwise dimension does not exist equals the dimenti... 详细信息

关键词： self-similar measure point wise dimension Hausdorff dimension multifractal symbolic space.

Cartesian closedness of categories of completely distributive lattices

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Chinese Science Bulletin 1998年第24期43卷 2059-2063页

作者： ZHANG Dexue 1 and YANG Zhongqiang 2 1. department of mathematics, Sichuan university, Chengdu 610064, china 2. department of mathematics, Shaanxi normal university, Xi’an 710062, china department of mathematics Sichuan University Chengdu China department of mathematics Shaanxi Normal University Xi’an China

The category of completely distributive lattices with Scott continuous functions is cartesian closed. Neither the category of completely distributive lattices with arbitrary union preserving mappings nor the category ... 详细信息

关键词： completely distributive lattice continuous lattice cartesian closedness.