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Strong uniqueness of best approximations in spaces of bounded linear operators

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Science china mathematics 2004年第3期47卷 339-351页

作者： LI Chong HE Jinsu department of mathematics, Zhejiang university Hangzhou 310027, china department of mathematics, Zhejiang normal university Jinhua 321004, china 1. department of mathematics Zhejiang University 310027 Hangzhou China 2. department of mathematics Zhejiang Normal University 321004 Jinhua China

The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator *** results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's *** recent results due to Lewicki and others are extended and improved.

关键词： best approximation operator, RS-set, sun, strong uniqueness, uniqueness element.

The generalized Roper-Suffridge extension operator in Banach spaces (Ⅲ)

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Science china mathematics 2009年第11期52卷 2432-2446页

作者： ZHU YuCan1 & LIU MingSheng2 1 department of mathematics,Fuzhou university,Fuzhou 350002,china 2 department of mathematics,South china normal university,Guangzhou 510631,china 1. department of mathematics Fuzhou University Fuzhou 350002 China 2. department of mathematics South China Normal University Guangzhou 510631 China

Suppose that X is a complex Banach space with the norm ||·|| and n is a positive integer with dim X ≥n≥ 2. In this paper,we consider the generalized Roper-Suffridge extension operator Φn,β2,γ2,...,βn+1,γn+1(f)... 详细信息

关键词： Roper-Suffridge extension operator biholomorphic starlike mapping almost spirallike mapping of type β and order α spirallike mapping of type β and order α

Steady-state responses of axially accelerating viscoelastic beams: Approximate analysis and numerical confirmation

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Science china(Physics,Mechanics & Astronomy) 2008年第11期51卷 1707-1721页

作者： CHEN LiQun1,2 & DING Hu2 1 department of Mechanics, shanghai university, shanghai 200444, china 2 shanghai Institute of Applied mathematics and Mechanics, shanghai 200070, china department of Mechanics Shanghai University Shanghai 200444 China shanghai Institute of Applied mathematics and Mechanics Shanghai 200070 China

Nonlinear parametric vibration of axially accelerating viscoelastic beams is inves-tigated via an approximate analytical method with numerical confirmations. Based on nonlinear models of a finite-small-stretching slender beam moving at a speed with a periodic fluctuation, a solvability condition is established via the method of multiple scales for subharmonic resonance. Therefore, the amplitudes of steady-state periodic responses and their existence conditions are derived. The amplitudes of stable steady-state responses increase with the amplitude of the axial speed fluctuation, and decrease with the viscosity coefficient and the nonlinear coefficient. The minimum of the detuning parameter which causes the existence of a stable steady-state periodic response decreases with the amplitude of the axial speed fluctuation, and increases with the viscosity coefficient. Nu-merical solutions are sought via the finite difference scheme for a nonlinear par-tial-differential equation and a nonlinear integro-partial-differential equation. The calculation results qualitatively confirm the effects of the related parameters pre-dicted by the approximate analysis on the amplitude and the existence condition of the stable steady-state periodic responses. Quantitative comparisons demonstrate that the approximate analysis results have rather high precision.

关键词： nonlinearity parametric vibration axially accelerating beam method of multiple scales numerical confir-mation

Completely regular paracompact reflection of locales

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Science china mathematics 2006年第6期49卷 820-826页

作者： HE Wei & LUO Maokang department of mathematics, Nanjing normal university, Nanjing 210097, china department of mathematics, Sichuan university, Chengdu 610064, china department of mathematics Nanjing Normal University Nanjing 210097 China department of mathematics Sichuan University Chengdu 610064 China

We give an explicit construction of the completely regular paracompact reflection pL of a completely regular locale L described as a sublocale of the Stone-tech compactification βL of L.

关键词： completely regular paracompact locale, nucleus.

Preparation of PFSA/PSf hollow fiber composite membranes with recovered PFSA for the pervaporation separation of EtOH/H_2O

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Science china Chemistry 2010年第1期53卷 273-280页

作者： LANG WanZhong1,2,TONG Wei2,XU ZhenLiang2 & GUO YaJun1 1department of Chemistry,shanghai normal university,shanghai 200234,china 2Chemical Engineering Research Center,east china university of Science and Technology,shanghai 200237,china 1. department of Chemistry Shanghai Normal University Shanghai 200234 China2. Chemical Engineering Research Center East China University of Science and Technology Shanghai 200237 China

Perfluorosulfonic acid/Polysulfone(PFSA/PSf) hollow fiber composite membranes have been prepared by dip-coating method using PSf ultrafiltration(UF) membrane as substrate with recovered *** composite membranes were applied to the pervaporation separation of 95% ethanol(EtOH)/H2O *** images show that the thickness of the PFSA skin layer of the composite membranes is about 2 μm,much thinner than those of other PFSA composite membranes revealed in the *** of annealing temperature,coating solution concentration and counter-ions of PFSA on the pervaporation performances of the composite membranes were *** total flux decreases and separation factor increases with the increase of annealing *** highest permeation flux of 3230 g m-2 h-1 and a separation factor of 5.4 is obtained for the composite membrane annealed at 80°*** lowest permeation flux of 396 g m-2 h-1 and a separation factor of 27.7 is obtained for the composite membrane annealed at 160°*** permeation performances of the PFSA/PSf composite membrane are evidently influenced by the counter-ions of *** flux sequence of the PFSA/PSf composite membranes with different counter-ions is H+>Li+>Ca2+>Mg2+>Na+>K+>Ba2+>Fe3+>Al3+,and the separation factor sequence is H+2+2+2+Na+>K+.There are very little variations of △Eapp values between the composite membranes with three divalent counterions(Mg2+,Ca2+ and Ba2+),and the △Eapp values of the composite membranes with two trivalent counterions(Fe3+ and Al3+) are relatively high.

关键词： pervaporation hollow fiber composite membrane perfluorslulfonic acid(PFSA) ethanol(EtOH)/H2O mixture

Problems in Homoclinic Bifurcation with Higher Dimensions

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Acta Mathematica Sinica,English Series 1998年第3期14卷 341-352页

作者： Zhu Deming department of mathematics, east china normal university. shanghai 200062. china department of mathematics East China Normal University 200062 Shanghai China

In this paper, a suitable local coordinate system is constructed by using exponential dichotomies and generalizing the Floquet method from periodic systems to nonperiodic systems. Then the Poincare map is established to solve various problems in homoclinic bifurcations with codimension one or two. Bifurcation diagrams and bifurcation curves are given.

关键词： Exponential dichotomy Local coordinates Homoclinic bifurcation Periodic orbit

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

SINGLE BIRTH PROCESSES

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Chinese Annals of mathematics,Series B 1999年第1期20卷 77-82页

作者： CHEN MUFA(department of mathematics,Beijing normal university,Beijing 100875,china) Beijing normal Univ Dept Math Beijing 100875 Peoples R China

The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2 (this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied

关键词： Markov chains Single birth process Uniqueness criterion

Uniform blow-up profiles and boundary layer for a parabolic system with localized nonlinear reaction terms

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Science china mathematics 2005年第2期48卷 185-197页

作者： LI Huiling & WANG Mingxin department of mathematics, Southeast university, Nanjing 210018, china department of mathematics, Xuzhou normal university, Xuzhou 221116, china 1. department of mathematics Southeast University 210018 Nanjing China 2. department of mathematics Xuzhou Normal University 221116 Xuzhou China

This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the classical solution blows up in the finite time, secondly give necessary conditions and a sufficient condition for that two components blow up simultaneously, and then obtain the uniform blow-up profiles in the interior. Finally we describe the asymptotic behavior of the blow-up solution in the boundary layer.

关键词： parabolic system, localized nonlinear reaction terms, blow-up profiles, boundary layer size.