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Joint density of hitting time and point to an ellipse for Brownian motion

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Chinese Science Bulletin 1997年第24期42卷 2054-2058页

作者： YIN Chuancun ZHAO Xuelei department of mathematics, Qufu Normal {2., Qufu 2.3165, china 2. Institute of mathematics, Shantou {2., Shantou 515063, china department of mathematics Qufu Normal University Qufu China Institute of mathematics Shantou University Shantou China

IT is well known that the distribution of hitting time, hitting point, last exiting time, and lastexiting point for Brownian motion to balls has been extensively studied. A similar investi-gation of rectangles or cubes has also been well done. However, analogous questions for Brow-nian motion to ellipsoid are rarely concerned. Bai and Cai obtained the distribution of

关键词： Brownian motion hitting time hitting point ellipse.

Suspended sediment flux of river:Wavelet analysis in the Panlong basin of the Upper Red River (Honghe River),china

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Chinese Science Bulletin 2007年第A2期52卷 172-179页

作者： DING WenRong~(1,2.) ZHOU Yue~(1,3) L XiXi~4 1 The Faculty of Environment Science and Engineering,kunming university of Science and Technology,kunming 650093,china 2.College of Tourism and Geography Science,yunnan Normal university,kunming 650092.china 3 yunnan university of Finance and Economics,kunming 6502.1,china 4 department of Geography,National university of Singapore 1192.0,Singapore The Faculty of Environment Science and Engineering Kunming University of Science and Technology Kunming China College of Tourism and Geography Science Yunnan Normal University Kunming China yunnan university of Finance and Economics Kunming China department of Geography National University of Singapore Singapore

这份报纸把小浪分析用于检验变化趋势，多时间规模变化，在上面的红河的 Panlong 盆的推迟的沉积流动(SSF ) 的周期、突然的变化特征，中国。结果显示 SSF 从 1951 ～ 1997 增加了，但是自从 1998，衰退了。SSF 的变化把多时间规模特征... 详细信息

这份报纸把小浪分析用于检验变化趋势，多时间规模变化，在上面的红河的 Panlong 盆的推迟的沉积流动(SSF ) 的周期、突然的变化特征，中国。结果显示 SSF 从 1951 ～ 1997 增加了，但是自从 1998，衰退了。SSF 的变化把多时间规模特征和变化在不同时间时期改变了。三周期的时间规模， 4， 7 和 2. 年，被决定。2. 年的周期的时间规模，是在三次规模之中的最明显的，通过整个研究时期延长了，而第 4-a 7 年的时间规模在某些时间时期仅仅是明显的。分别地有 2. 次越过 4 年的时间规模，越过 7 年的时间规模的 16 次和越过 2. 年的时间规模的 5 次的突然的变化。根据统计的聚会和气候数据分析，我们断定人的活动是导致了多时间规模的 SSF，而是特征的变化趋势的主要原因，周期、突然的变化被气候变化主要影响。

关键词：河流中国红河微波分析

THE PHYSICAL ENTROPY OF SINGLE CONSERVATION LAWS

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Journal of Computational mathematics 1998年第5期16卷 437-444页

作者： (department of mathematics, Peking {2., Beijing 100871, china) 北京大学数学系北京

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production

Characteristic analysis for a polynomial-like iterative equation

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Chinese Science Bulletin 1998年第3期43卷 192-196页

作者： Janusz Matkowski 1 and ZHANG Weinian 2.1. department of mathematics, Technical {2., 43_300 Bielsko_Biala, Poland 2. department of mathematics, Sichuan Union {2., Chengdu 610064, china department of mathematics Technical University Bielsko-Biala Poland department of mathematics Sichuan Union University Chengdu China

In the light of Euler’s idea for differential equations,a polynomial_like n _order iterative equation is discussed through analyzing its characteristic polynomial. An unproved result is verified rigorously for the fi... 详细信息

关键词： iterative dynamics functional equation characteristic.

A new definition of restricted Lie superalgebras

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Chinese Science Bulletin 2000年第4期45卷 316-321页

作者： WANG Ying & ZHANG Yongzheng1. department of mathematics, Harbin Institute Technology, Harbin 150001,{2. 2. department of mathematics, Northeast Normal university, Changchun 13002.,{2. department of mathematics Harbin Institute Technology Harbin China department of mathematics Northeast Normal University Changchun China

A new definition of restricted Lie superalgebras has been given; some important results on the representation theory of restricted Lie superalgebra have been obtained.

关键词： restricted Lie superalgebra p-mapping p-semilinear mapping α-representation.

Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property

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Chinese Science Bulletin 1997年第3期42卷 259-260页

作者： MAI Jiehua and GU Rongbao1.Institute of mathematics, Shantou university, Shantou 515063,{2. 2. department of mathematics, Anhui university, Hefei 2.0039,{2. Institute of mathematics Shantou University Shantou China department of mathematics Anhui University Hefei China

IN this letter we discuss the necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, every minimal set of a C^r(r≥2. flow is trivial, but it is possible for a C^0 flow to contain non-trivial minimal sets. Thus C^0 flows on closed surfaces are more complicated than C^r(r≥2. flows.

关键词： Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property

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 {2., Beijing 100875, china 2. Institute of Applied Physics and Computational mathematics, Beijing 100080, china department of mathematics Beijing Normal University Beijing China Institute of Applied Physics and Computational mathematics Beijing 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.

Nonlinear ergodic theorem for semitopological semigroups of non-Lipschitzian mappings in Banach spaces

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Chinese Science Bulletin 1997年第1期42卷 8-11页

作者： LI Gang and MA Jipu1. department of mathematics, Yangzhou Normal College, Yangzhou 2.5002.{2. 2. department of mathematics, Nanjing university, Nanjing 2.0093,{2. department of mathematics Yangzhou Normal College Yangzhou China department of mathematics Nanjing University Nanjing China

LET G be a semitopological semigroup, i. e. G is a semigroup with a Hausdorff topology such that for each s∈G the mapping s|→s·t and s|→t·s from G to G are continuous. G is called right reversible if any two closed left ideals of G have non-void intersection. In this case, (G,≤) is a directed system when the binary relation '≤' on G is defined by a≤b if and only if Let E be the uniformly convex Banach space

关键词： nonlinear semigroup ergodic theorem non-Lipschitzian mapping.

Fredholm operators in Toeplitz algebras associated with discrete abelian groups

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Chinese Science Bulletin 1998年第14期43卷 1175-1179页

作者： XU Qingxiang 1 and CHEN Xiaoman 2.1. department of mathematics, Shanghai Normal {2., Shanghai 2.02.4, china 2. Laboratory of mathematics for Nonlinear Sciences and Institute of mathematics, Fudan {2., Shanghai 2.0433, china department of mathematics Shanghai Normal University Shanghai China Laboratory of mathematics for Nonlinear Sciences and Institute of mathematics Fudan University Shanghai China

The locally finite below sets are introduced and the Fredholm operators in Toeplitz algebras associated with discrete abelian groups are studied.

关键词： discrete abelian group quasi_ordered group Toeplitz operator Fredholm operator.