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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, {2. normal University, {2. 2.02.4, china 2. Laboratory of mathematics for Nonlinear Sciences and Institute of mathematics, Fudan University, {2. 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.

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,{2. 2.department of mathematics,shanghai University,shanghai 2.0444,{2. 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 52.30 52.40

Note on families of semistable curves over P^1 with 4 singular fibers whose Jacobian are non-compact

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Science china mathematics 2010年第7期53卷 1710-1713页

作者： YU Fei 1, 2.1 Academy of mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, china {2., east china normal University, shanghai 2.0062. china Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing China department of mathematics East China Normal University Shanghai China

Let f : S → P 1 be a semistable family of curves of genus g 2. We prove that if f admits exactly 5 singular fibers and 4 of them have non-compact Jacobian, then g = 2.

关键词： singular fiber adjoint linear system non-compact Jacobian

FLOATING QUANTIZATION EFFECTS ON MULTIRATE SAMPLED-DATA NONLINEAR CONTROL SYSTEMS

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Acta Mathematica Scientia 2007年第3期27卷 635-644页

作者：余宏旺汪志鸣 department of mathematics East China Normal University

In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.

关键词： Multirate sampled-data control systems quantization Schur stable uniformly ultimately bounded

K-uniformly rotund spaces and k-uniformly smooth spaces

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Chinese Science Bulletin 1998年第2期43卷 92-95页

作者： Suyalatu 1 and WU Congxin 2.1. department of mathematics,Inner Mongolia {2. University, Huhhot 01002., china 2. department of mathematics, Harbin Institute of Technology, Harbin 150006, china department of mathematics Inner Mongolia Normal University Huhhot China department of mathematics Harbin Institute of Technology Harbin China

The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1)US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.

关键词： K_uniform smoothness K_uniform convexity.

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural Science:Materials International 2004年第1期14卷 16-21页

作者： LI Hongxing 1*, YOU Fei 1 and PENG Jiayin 2.1. department of mathematics, Beijing {2. University, Beijing 100875, china 2. department of mathematics, Neijiang Teacher's College, Neijiang 641112. china) Beijing normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 2. fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational mathematics 2001年第3期19卷 241-258页

作者： De-tong Zhu (department of mathematics, {2. normal University, {2. 2.02.4, china) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

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 {2. University,Jinhua 32.004,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,{2. 2.0092.china 2.department of mathematics,Luoyang normal University, Luoyang 47102.,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