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Weierstrass Representation for Surfaces in the Three-Dimensional Heisenberg Group

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Chinese Annals of Mathematics,Series B 2010年第1期31卷 119-132页

作者： Qun CHEN Hongbing QIU school of Mathematics and Statistics Wuhan University Wuhan 430072 China Corresponding author. school of mathematical sciences Fudan University Shanghai 200433 China

The authors define the Gauss map of surfaces in the three-dimensional Heisenberg group and give a representation formula for surfaces of prescribed mean ***,a second order partial differential equation for the Gauss m... 详细信息

关键词： Heisenberg group Mean curvature Weierstrass representation

ON INTERACTION OF SHOCK AND SOUND WAVE (Ⅰ)

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Chinese Annals of Mathematics,Series B 1996年第4期17卷 35-42页

作者： CHEN SHUXING(Institute of Mathematics, fudan university shanghai 2.0433, china.) 复旦大学数学系上海

This paper studies the ioteraction of shock and gradient wave (sound wave) of solutions to the system of inviscid isentropic gas dynamics as a model for the corresponding problems for nonlinear hyperbolic systems. The problem can be reduced to a boundary value problem in a wedged domain. By using the method of constructing asymptotic solutions and Newton’s iteration process it is proved that if a weak shock hits a gradient wave, then the grandient wave will split into two gradient waves, while the shock continuses propagating. In this paper the author reduces the problem to a standard form and constructs asymptotic solution of the problem. The existence of the genuine solution will be given in the following paper.

关键词： Shock wave Sound wave Nonliner hyperbolic system Asymptotic solution

A new scheme of digital communication using chaotic signals in MIMO channels

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Science china.Information sciences) 2012年第10期55卷 2183-2193页

作者： MA HuanFei 1 & KAN HaiBin 2 1 school of mathematical sciences,Soochow university,Suzhou 215006,china.2 school of Computer Science,fudan university,shanghai 2.0433,china school of mathematical sciences Soochow University Suzhou China school of Computer Science Fudan University Shanghai China

This paper proposes a new digital communication scheme,which uses chaotic signals based on the adaptive synchronization and parameter identification technique of chaotic systems reported *** to the multi signal character,this scheme combines the chaotic signal transmission with the MIMO channel technique in a wireless environment,which is different from the traditional chaotic communication *** a practical perspective,an outline of modulation,channel model,demodulation and non-coherent detection is ***,system performance is evaluated by simulations,and improvements on this scheme are also discussed.

关键词： chaotic modulation chaotic digital communication mapping parameters MIMO channel

SIMULATION OF FLUID-SOLID INTERACTION ON WATER DITCHING OF AN AIRPLANE BY ALE METHOD

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Journal of Hydrodynamics 2011年第5期23卷 637-642页

作者： HUA Cheng FANG Chao CHENG Jin Department of Mechanics and Engineering Science Fudan University Shanghai 200433 China school of mathematical sciences Fudan University Shanghai 200433 China

Ditching is considered as one of the important aspects of safety performances of airplanes. It is related primarily with the fluid-solid interaction, whose studies mainly depend on experiments at the present time. Numerical and analytical methods for fluid-solid interaction by using 3-D full scale airplane＇s model will reduce the dependence on the expensive model tests. Numerical studies can be used to estimate the safety of ditching and provide a reference for the crashworthiness design. This article proposes a 3-D dynamical structural model after the real shape of an airplane and an Arbitrary Lagrange-Euler （ALE） fluid-field model, to simulate the fluid-solid interactions caused by low speed ditching. The simulation is based on interaction computational methods, within LS-DYNA nonlinear finite-element code. The results of pressure distributions and accelerating time histories of the airplane＇s subfloor are discussed in the context of the safety of ditching, and the simulation results and the analytical methods are verified.

关键词： ditching fluid structure interaction Arbitrary Lagrange-Euler (ALE) finite element method

Global Bifurcation of a Perturbed Double-Homoclinic Loop

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Chinese Annals of Mathematics,Series B 2006年第4期27卷 425-436页

作者： Desheng SHANG Maoan HAN school of Mathematics and Information Science Shandong University of Technology Zibo 255049 Shandong China. school of mathematical sciences Shanghai Normal University Shanghai 200234 China.

This paper deals with a kind of fourth degree systems with perturbations. By using the method of multi-parameter perturbation theory and qualitative analysis, it is proved that the system can have six limit cycles.

关键词： Perturbation Bifurcation Cubic system Limit cycle Hamiltonian system Homoclinic loop

Determination of Unknown Boundary in the Composite Materials with Stefan-Boltzmann Conditions

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Chinese Annals of Mathematics,Series B 2010年第2期31卷 145-162页

作者： Xiaoyi HU Wenbin CHEN school of mathematical sciences Fudan University Shanghai 200433 China.

Abstract The authors consider one specific kind of heat transfer problems in a threedimensional layered domain, with nonlinear Stefan-Boltzmann conditions on the boundaries as well as on the interfaces. To determine the unknown part of the boundary （or corrosion） by the Cauchy data on the reachable part is an important inverse problem in engineering. The mathematical model of this problem is introduced, the well-posedness of the forward problems and the uniqueness of the inverse problems are obtained.

关键词： Inverse heat problem Stefan-Boltzmann conditions Uniqueness

Koszul Differential Graded Algebras and BGG Correspondence II

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Chinese Annals of Mathematics,Series B 2010年第1期31卷 133-144页

作者： Jiwei HE Quanshui WU Department of Mathematics Shaoxing College of Arts and Sciences Shaoxing 312000 Zhejiang China school of mathematical sciences Fudan University Shanghai 200433 China

The concept of Koszul differential graded (DG for short) algebra is introduced in [8].Let A be a Koszul DG *** the Ext-algebra of A is finite-dimensional,i.e.,the trivial module A k is a compact object in the derived category of DG A-modules,then it is shown in [8] that A has many nice ***,if the Ext-algebra is infinitedimensional,little is known about *** shown in [15] (see also Proposition 2.2),A k is not compact if H(A) is *** this paper,it is proved that the Koszul duality theorem also holds when H(A) is finite-dimensional by using Foxby duality.A DG version of the BGG correspondence is deduced from the Koszul duality theorem.

关键词： Koszul differential graded algebra Koszul duality BGG correspondence

ON TAYLOR'S CONJECTURE ABOUT THE PACKING MEASURES OF CARTESIAN PRODUCT SETS

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Chinese Annals of Mathematics,Series B 1996年第1期17卷 121-126页

作者： XU YOU REN FUYAO(Institute of Mathematics, fudan university, shanghai 2.0433, china.) 复旦大学数学所上海

It is proved that if E R, F Rn, then P(E x F,12) ≤c. P(E, 1)P(E, 2), where P(, ) denotes the -packing measure, belongs to a class of Hausdorff functions, the positive constat c deponds only on 1,2 and n.

关键词： Packing measure Hausdorff measure Cartesian product set

COMPLETE EXTREMAL SURFACES OF MIXED TYPE IN 3-DIMENSIONAL MINKOWSKI SPACE

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Chinese Annals of Mathematics,Series B 1994年第4期15卷 385-400页

作者： GU CHAOHAO (Institute of Mathematics, fudan university,shanghai 2.0433, china.) fudan UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

Many complete extremal surfaces of mixed type are constructed with explicit expressions. Itis proved that there exist complete extremal surfaces of mixed type which have a given numberof time-like spans and a given nu... 详细信息

关键词： Extremal surface Mixed type Minkowski space.