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PRIMITIVITY OF SMASH PRODUCT C_q#B_q

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Chinese Annals of Mathematics,Series B 1994年第4期15卷 443-452页

作者： LU DIMING(institute of Mathematics,fudan university,shanghai 200433, china.) fudan UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

It is proved that the Smash product is a primitive algebra,where Bq is the Hopfalgebra corresponding to the compact quantum group SqU(2) and Cq is a Hopf-subalgebra of the topological dual.

关键词： q-binomal coefficient Smash product Quantum group.

A Modified Binomial Tree Method for Currency Lookback Options

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Acta Mathematica Sinica,English Series 2000年第3期16卷 445-454页

作者： Min Dai institute of Mathematics,fudan university,shanghai 200433,P.R.china institute of Mathematics Fudan University Shanghai 200433 P. R. China

The binomial tree method is the most popular numerical approach to pricing options. However,for currency lookback options,this method is not consistent with the corresponding continuous models,which leads to slow speed of *** the basis of the PDE approach,we develop a consistent numerical scheme called the modified binomial tree *** possesses one order of accuracy and its efficiency is demonstrated by numerical *** convergence proofs are also produced in terms of numerical analysis and the notion of viscosity solution.

关键词： Modified binomial tree method Currency lookback options Convergence

THE GAUSS MAP OF TIMELIKE SURFACES IN R1^n

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Chinese Annals of Mathematics,Series B 1995年第3期16卷 361-370页

作者： HONG JIANQIAO(institute of Mathematics, fudan university, shanghai 200433, china.) fudan UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

Gauss maps of oriented timelike 2-surfaces in are characterized, and it is shown that Gallss maps can determine surfaces locally as they do in case. Moreover, some essential differences are discovered between the properties of the Gauss maps of surfaces in Rn and those of the Gauss maps of timelike surfaces in. In particular, a counterexample shows that a nonminimal timelike surface in cannot be essentially determined by its Gauss map.

关键词： Timelike surface Gauss map External surface.

FORMATION OF SINGULARITIES FOR A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEM

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Chinese Annals of Mathematics,Series B 2002年第4期23卷 439-454页

作者： WANG LIBINinstitute of Mathematics, fudan university, shanghai 200433, china. institute of Mathematics Fudan University Shanghai 200433 China

The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.

关键词： Formation of singularity Quasilinear non-strictly hyperbolic system Weak linear degeneracy

Sharpness on the Lower Bound of the Lifespan of Solutions to Nonlinear Wave Equations

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Chinese Annals of Mathematics,Series B 2011年第4期32卷 521-526页

作者： Yi ZHOU 1 Wei HAN 2 1 Nonlinear mathematical Modeling and Methods Laboratory shanghai Key Laboratory for Contem- porary Applied Mathematics School of mathematical Sciences, fudan university, shanghai 200433, china. 2 School of mathematical Sciences, fudan university, shanghai 200433, china Department of Mathematics, North university of china, Taiyuan 030051, china. Nonlinear mathematical Modeling and Methods Laboratory shanghai Key Laboratory for Contemporary Applied Mathematics School of mathematical Sciences Fudan University Shanghai China School of mathematical Sciences Fudan University Shanghai China Department of Mathematics North University of China Taiyuan China

This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2 and cubic nonlinearity （see the results of T. T. Li and Y. M. Chen in 1992）. For this purpose, the authors consider the following Cauchy problem： { where □=δt^2-∑i=1n δx^^2 is the wave operator, g（x）（≡/） 0 is a smooth non-negative function with compact support, and ε 〉 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T（ε） of solutions has an upper bound T（ε） ≤ exp（Aε-2） with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.

关键词： Nonlinear wave equation Cauchy problem Lifespan

TOEPLITZ C-ALGEBRA OVER THE L-SHAPED DOMAIN IN C^m

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Chinese Annals of Mathematics,Series B 1996年第3期17卷 325-334页

作者： XU SHENGZHI CHEN XIAOMAN YAN SHAOZONG(institute of Mathematics, fudan university, shanghai 200433, china) institute of Mathematics Fudan University Shanghai 200433 China

The authors investigate the Toeplitz C-algebra over the L-shaped domain in Cn by thegroupoid approach, and successfully parameterise the unit space of the groupoid associated tothe Toeplitz C-algebra.

关键词： L-shaped domain Toeplitz C-algebra Parameterization

On the Neighborhood in Stabilizing Period-T Orbits for Chaotic m Degree Polynomial Dynamical System

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 242-247页

作者： Enguo GU Jiong RUAN and Zhenxun HUANG (institute of Mathematics, fudan university, shanghai 200433,china) institute of Mathematics Fudan University Shanghai 200433 China

In this paper, a problem of stabilizing a period-T orbit in discrete Chaotic m degree polynomial dynamical systems is studied. The aim is to present a new method for determining the neighborhood of a period-T point in which the system remains stable when subjected to a linear feedback control. A theorem on the existence of neighborhood is rigorously proved using idea from functional analysis and polar coordinate *** ways of implementing the obtained theorem in the Henon map are proposed. Thevalidity of this method is shown by numerical simulation.

关键词： neighborhood of period-T orbit controlling chaotic discrete system gain matrix

Optimal Control of Semilinear Elliptic Variational Bilateral Problem

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Acta Mathematica Sinica,English Series 2000年第1期16卷 123-140页

作者： Qihong Chen institute of Mathematics,fudan university,shanghai 200433,P.R.china shanghai Normal university,shanghai 200023,P.R.china institute of Mathematics Fudan University Shanghai 200433 P.R. China shanghai Normal university Shanghai 200023 P.R. China

This paper is concerned with an optimal control problem for semilinear elliptic variational inequalities associated with bilateral *** and optimality conditions of the optimal pair are established.

关键词： Elliptic bilateral variational inequality Optimal control Existence Optimality condition

ON SOME CONSTANTS OF QUASICONFORMAL DEFORMATION AND ZYGMUND CLASS

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Chinese Annals of Mathematics,Series B 1995年第3期16卷 325-330页

作者： CHEN JIXIU WEI HANBAI(institute of Mathematics, fudan university, shanghai 200433, china.) 复旦大学数学所上海

A real-valued function f(x)on belongs to Zygmund class if its Zygmund norm It is proved that when f ∈, there exists an extension F(z)of f to H = {Imz > 0} such that It is also proved that if f(0)=f(1)= 0,then

关键词： Quasiconformal deformation Zygmund class Beurling-Ahlfors extension.