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THE INDUCED REPRESENTATION OF C^＊-GROUPOID DYNAMIC SYSTEMS

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Chinese Annals of mathematics,Series B 1996年第1期17卷 103-114页

作者： FANG XIAOCHUN(department of mathematics, tongji university, shanghai 200029, china.) department of mathematics Tongji University Shanghai 200029 China

Let G be a second countable locally compact groupoid with Haar system {λu}, H be a closed subgroupoid containing Go with Haar system {λuH}. *** introduced the C*-Groupoid dynamic system (G, A, α) and its reduced crossed product Cr.d(G, A) in [2], where A is a C*-algebra, α is the homomorphism G→Aut(A). In this paper the author introduces the C*-groupoid dynamic systems (H, A, α|H) and (H\G2, A, α) induced by (G, A, α) and proves that C~*red(H, A) and C~*red(H\G2, A) are strongly Morita equivalent. Moreover the induced representation from C~*red(H, A) to C~*red(G, A) is got.

关键词： C~*-groupoid dynamic system Induced representation Haar system

STABILITY OF IMPULSIVE LINEAR HYBRID SYSTEMS WITH TIME DELAY

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Journal of Systems Science & Complexity 2010年第4期23卷 738-747页

作者： Yu ZHANG·Jitao SUN department of mathematics,tongji university,shanghai 2.0092.china. department of mathematics Tongji University Shanghai China

This paper investigates the stability of impulsive linear hybrid systems with time *** a number of delay-independent/delay-dependent stability criteria are obtained by using Lyapunovfunctions or Lyapunov *** examples ... 详细信息

关键词： Impulsive linear hybrid system Lyapunov function Lyapunov functional time delay.

Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc

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Science china mathematics 2010年第4期53卷 1017-1024页

作者： LIU Yang 1,& CHEN ZhiHua 2 1 department of mathematics,Zhejiang Normal university,Jinhua 321004,china 2.department of mathematics,tongji university,shanghai 2.0092.china department of mathematics Zhejiang Normal University Jinhua China department of mathematics Tongji University Shanghai China

We give higher order derivatives Schwarz-Pick estimates for all positive real part holomorphic functions on Bn and D n,and generalize early work on Schwarz-Pick estimate of higher order derivatives for holomorphic fun... 详细信息

关键词： Schwarz-Pick estimate holomorphic function Taylor expansion

p-th moment exponential stability of stochastic differential equations with impulse effect

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Science china(Information Sciences) 2011年第8期54卷 1702-1711页

作者： SHEN LiJuan 1,2 & SUN JiTao 11 department of mathematics, tongji university,shanghai 2.0092.china 2.department of mathematics,Luoyang Normal university, Luoyang 471022,china department of mathematics Tongji University Shanghai China department of mathematics Luoyang Normal University Luoyang China

The p-th moment exponential stability of stochastic differential equations with impulse effect is *** employing the method of vector Lyapunov functions,some sufficient conditions for the p-th moment exponential stability are *** addition,the usual restriction of the growth rate of Lyapunov function is replaced by the condition of the drift and diffusion coefficients to study the p-th moment exponential *** examples are also discussed to illustrate the effectiremess of the results obtained.

关键词： stochastic differential equations impulse p-th moment exponential stability vector Lyapunov functions

A NUMERICAL METHOD FOR DETERMINING THE OPTIMAL EXERCISE PRICE TO AMERICAN OPTIONS

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Journal of Computational mathematics 2003年第3期21卷 305-310页

作者： Xiong-hua Wu Xiu-juan Feng (department of Applied mathematics, tongji university, shanghai 2.0092, china ) department of Applied mathematics Tongji University 上海 800092

American options can be exercised prior to the date of expiration, the valuation of American options then constitutes a free boundary value problem. How to determine the free boundary, i.e. the optimal exercise price, is a key problem. In this paper, a nonlinear equation is given. The free boundary can be obtained by solving the nonlinear equation and the numerical results are better.

关键词： American options Free boundary Optimal exercise price Nonlinear equation.

On the generalized Busemann-Petty problem

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Science china mathematics 2007年第8期50卷 1103-1116页

作者： Song-jun L~(1,2+) Gang-song LENG~1 1.College of mathematics and Computer Science,Chongqing Normal university,Chongqin 400047,china 2.department of mathematics,shanghai university,shanghai 200444,china College of mathematics and Computer Science Chongqing Normal University Chongqin China department of mathematics Shanghai University Shanghai China

The generalized Busemann-Petty problem asks whether the origin-symmetric convex bodies in ? n with a larger volume of all i-dimensional sections necessarily have a larger volume. As proved by Bourgain and Zhang, the answer to this question is negative if i > 3. The problem is still open for i = 2, 3. In this article we prove two specific affirmative answers to the generalized Busemann-Petty problem if the body with a smaller i-dimensional volume belongs to given classes. Our results generalize Zhang’s specific affirmative answer to the generalized Busemann-Petty problem.

关键词： star body cross i-section dual mixed volume Radon transform 52A30 52A40

GLOBALLY CONVERGENT INEXACT GENERALIZED NEWTON METHODS WITH DECREASING NORM OF THE GRADIENT

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Journal of Computational mathematics 2002年第3期20卷 289-300页

作者： Ding-guo Pu (department of mathematics, tongji university, shanghai 200331, china) department of mathematics Tongji University 上海 200331

Presents information on a study which proposed a type of globally convergent inexact generalized Newton methods to solve unconstrained optimization problems. Theorems on inexact generalized Newton algorithm with decre... 详细信息

关键词： nonsmooth optimization inexact Newton method generalized Newton method global convergence superlinear rate

A MULTI-GRID ALGORITHM FOR STOKES PROBLEM

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Journal of Computational mathematics 1995年第4期13卷 291-305页

作者： Z. Huang(department of Applied mathematics, tongji university, shanghai, china) 同济大学应用数学系上海

In this paper we describe a multi-grid algorithm for the penalty procedure of Stokes problem. It is proved that the convergence rate df the algorithm is bounded away from 1 independently of the meshsize. For convenien... 详细信息

关键词： Math Grid ED EH Bank

Immortal solution of the Ricci flow

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Science china mathematics 2005年第Z1期48卷 217-224页

作者： RUAN Qihua & CHEN Zhihua department of Applied mathematics, tongji university, shanghai 2.0092, china department of mathematics, Putian College, Putian 351100, china department of Applied mathematics Tongji University Shanghai China department of mathematics Putian College Putian China

For any complete noncompact Kahler manifold with nonnegative and bounded holomorphic bisectional curvature, we provide the necessary and sufficient condition for the immortal solution to the Ricci flow.

关键词： Ricci flow, immortal solution, holomorphic bisectional curvature.