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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 university, Beijing 100871, China) Beijing Univ Dept Math Beijing 100871 Peoples R China

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

Shape blending of artistic brushstroke represented by disk B-spline curves

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Progress in Natural Science:Materials International 2007年第12期17卷 1501-1507页

作者： Cheng Min1,2 and Wang Guojin1(1. department of mathematics, Zhejiang university, Hangzhou 310027, China 2. department of mathematics, Zhejiang university of Technology, Hangzhou 310032, China) department of mathematics Zhejiang University Hangzhou 310027 China 2. department of mathematics Zhejiang University of Technology Hangzhou 310032 China

This paper presents an algorithm for automatically generating in-between frames of two artistic brushstrokes. The basic idea of the algorithm is to represent the two key frames of artistic brushstrokes in disk B-spline curves, and then make blending of their geometric intrinsic variables. Given two key frames of artistic brushstrokes, the skeleton curves can be obtained by certain skeleton-based techniques. After disk B-spline representation of the key frames is generated, interpolation of the intrinsic variables of the initial and the target disk B-spline curves is carried out. Examples show that this method can efficiently create in-between frames of artistic brushstrokes.

关键词： computer aided calligraphy shape blending brushstroke disk B-spline curve skeleton.

Bifurcations of travelling wave solutions for two generalized Boussinesq systems

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Science China mathematics 2008年第9期51卷 1577-1592页

作者： LI JiBin1,2 1 department of mathematics, Zhejiang Normal university, Jinhua 321004, China 2.department of mathematics, Kunming university of Science and Technology, Kunming 650093, China department of mathematics Zhejiang Normal University Jinhua 321004 China department of mathematics Kunming University of Science and Technology Kunming 650093 China

Using the methods of dynamical systems for two generalized Boussinesq systems, the existence of all possible solitary wave solutions and many uncountably infinite periodic wave solutions is obtained. Exact explicit parametric representations of the travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

关键词： nonlinear wave bifurcation solitary wave exact explicit solution generalized Boussinesq system 34C37 34C23 74J30 58Z05

Congruences on ideal nil-extension of completely regular semigroups

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Chinese Science Bulletin 1998年第5期43卷 379-381页

作者： REN Xueming 1, 2 GUO Yuqi 2 and CEN Jiaping (Shum Kar-ping) 31. department of mathematics, Xi’an university of Architecture & Technology, Xi’an 710055, China 2. department of mathematics, Yunnan university, Kunming 650091, China 3. department of department of mathematics Xi’an University of Architecture & Technology Xi’an China department of mathematics Yunnan University Kunming China department of mathematics Chinese University of Hong Kong Hong Kong

Let S be an ideal nil-extension of a completely regular semigroup K by a nil semigroup Q with zero. A concept of admissible congruence pairs (δ,ω) of S is introduced, where δ and ω are a congruence on Q and a congruence on K respectively. It is proved that every congruence on S can be uniquely respresented by an admissible congruence pair (δ,ω) of S. Suppose that ρ K denotes the Rees congruence induced by the ideal K of S. Then it is shown that for any congruence σ on S,a mapping Γ:σ|→(σ Q,σ K) is an order-preserving bijection from the set of all congruences on S onto the set of all admissible congruence pairs of S,where σ K is the restriction of σ to K and σ Q=(σ∨ρ K)/ρ K. Moreover,the lattice of congruences of S is also discussed. As a special case,every congruence on completely Archimedean semigroups S is described by an admissible quarterple of S. The following question is asked: Is the lattice of congruences of the completely Archimedean semigroup a semimodular lattice?

关键词： completely regular semigroups ideal nil-extension congruences.

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

A NONMONOTONE TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION SUBJECT TO GENERAL CONSTRAINTS

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Journal of Computational mathematics 2003年第2期21卷 237-246页

作者： Hongchao Zhang+ (department of mathematics, university of Florida, Gainesville, FL, usa 32611 ) department of mathematics University of Florida 美国 Gainesville

In this paper we present a nonmonotone trust region algorithm for general nonlinear constrained optimization problems. The main idea of this paper is to combine Yuan's technique[1] with a nonmonotone method similar to Ke and Han [2]. This new algorithm may not only keep the robust properties of the algorithm given by Yuan, but also have some advantages led by the nonmonotone technique. Under very mild conditions, global convergence for the algorithm is given. Numerical experiments demonstrate the efficiency of the algorithm.

关键词： Nonlinear optimization Nonmonotone algorithm Trust region General con-straintss

On the Birch-Swinnerton-Dyer Conjecture of Elliptic Curves E_D:y^2=x^3-D^2x

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Acta Mathematica Sinica,English Series 2000年第2期16卷 229-236页

作者： Delang Li department of mathematics,Sichuan Union university,Chengdu 610064,P.R.China Ye Tian department of mathematics,Columbia university,New York,NY 10027,usa department of mathematics Sichuan Union University Chengdu 610064 P. R. China department of mathematics Columbia University New York NY 10027 USA

We prove in this paper that the BSD conjecture holds for a certain kind of elliptic curves.

关键词： Elliptic curve BSD conjecture Graph 2-component

L^p-Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernels

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Acta Mathematica Sinica,English Series 2000年第4期16卷 593-600页

作者： Yong Ding department of mathematics, Beijing Normal university, Beijing 100875, P. R. China Dashan Fan department of mathematics, Anhui university and university of Wisconsin-Milwaukee. MW 53201 usa Yibiao Pan department of mathematics, university of Pittsburgh. Pittsburgh. Pennsylvania 15260. usa department of mathematics Beijing Normal University Beijing 100875 P. R. China department of mathematics Anhui University and University of Wisconsin-Milwaukee Wisconsin MW 53201 USA department of mathematics University of Pittsburgh Pittsburgh USA

We give the Lp-boundedness for a class of Marcinkiewicz integral operators μΩ, μΩ.λ and μΩ.S related to the Littlewood-Paley g-function, gλ-function and the area integral S, respectively. These operators have the kernel functions Ω∈H1(Sn-1), the Hardy space on Sn-1. The results in this paper substantially improve and extend the known results.

关键词： Marcinkiewicz integral g-function g_λ~*-function Area integral H^1 space Rough kernel

Rate of convergence for the Legendre pseudospectral optimal control of feedback linearizable systems

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控制理论与应用（英文版） 2010年第4期8卷 391-405页

作者： Wei KANG (department of Applied mathematics,Naval Postgraduate School,Monterey ca 93943,usa) department of Applied mathematics Naval Postgraduate School Monterey USA

Pseudospectral （PS） computational methods for nonlinear constrained optimal control have been applied to many industrial-strength problems,notably,the recent zero-propellant-maneuvering of the international space station performed by *** this paper,we prove a theorem on the rate of convergence for the optimal cost computed using a Legendre PS *** addition to the high-order convergence rate,two theorems are proved for the existence and convergence of the approximate *** to existing work on PS optimal control as well as some other direct computational methods,the proofs do not use necessary conditions of optimal ***,we do not make coercivity type of *** a result,the theory does not require the local uniqueness of optimal *** addition,a restrictive assumption on the cluster points of discrete solutions made in existing convergence theorems is removed.

关键词： Computational optimal control Pseudospectral method Convergence