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Resolution of Internal Total ReflectionScanning Near-field Optical Microscopy

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Chinese Journal of Lasers 2002年第2期11卷 33-38页

作者： GE Huayong GUO Qizhi TAN Weihan (department of Physics, shanghai university, shanghai 200436, china ) department of Physics Shanghai Universit 上海 200436

In this paper, the probe-sample interaction equation based on Mie’s scattering theory is derived, and the resolution of scanning near field optical microscopy is calculated numerically. The results show that the offset of far-field component to near-field component in total field plays an important role in the resolution and the size of samples also has influence on resolution.

关键词： scanning near field optical microscopy (SNOM) resolution offset of far-field component to near-field component

Modern thermodynamics-New concepts based on the second law of thermodynamics

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Progress in Natural Science:Materials International 2009年第1期19卷 125-135页

作者： Jitao Wang department of Microelectronics,Fudan university,shanghai 200433,china [a]department of Microelectronics Fudan University Shanghai 200433 China

Thermodynamics is a core part of *** all scientists should have a basic knowledge of *** is a science of development,and is a viewpoint of scientific development in natural *** of thermodynamics has influence not only on natural sciences,but also on social sciences and *** concepts and definitions are very important for any discipline of science,so what is classical thermodynamics and what is modern thermodynamics have become the key points of puzzledom in *** this paper,after clarification of fundamental concept in thermodynamics,a complete basic modern classification of thermodynamics is naturally *** is suggested that extended Carnot theorem and dissipation decrease theorem,together with the laws of thermodynamics,are the most fundamental theorems in thermodynamics *** thermodynamics is a new field besides equilibrium thermodynamics belonging to the equal part of the second law of thermodynamics.

关键词： Modern thermodynamics Second law of thermodynamics Thermodynamic coupling Spiral reactions Chemical oscillation Low-pressure diamond growth

MORPHOLOGY OF MELT SPINNING SUPERSATURATED B2 NiAl

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Acta Metallurgica Sinica(English Letters) 1996年第2期9卷 89-93页

作者： SUN Baode CHE Xiaozhou LIN Dongliang ZHOU Yaohe(department of Materials Engineering,shanghai Jiaotong university,shanghai 20030,china)(department of Materials Science,shanghai Jiaotong university,shanghai 200030,china) shanghai Jiaotong Univ Shanghai China

The morphology and structure of melt spinning Ni-33.6at% Al doped with B and RE were *** results show that the alloy consists of L10 martensitic grains and L12 Ni3Al at the grain boundaries when it contains no B and *** addition of 0.11-0.31wt% B can suppress the martensitic transformation and Ni3Al separation at the boundaries,and a supersaturated B2 single phase NiAl is *** addition of 0.05wt% RE can eliminate Ni3Al precipitated at the boundaries and get complete martensite,but 0.2-0.8wt% RE addition can suppress the martensitic transformation, and supersaturated B2 single phase NiAl is *** formation mechanism of supersaturated B2 single phase NiAl has been analyzed.

关键词： NiAl supersaturate morphologl melt spinning

ON THE EXISTENCE OF FIXED POINTS FOR LIPSCHITZIAN SEMIGROUPS IN BANACH SPACES

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Chinese Annals of Mathematics,Series B 2001年第3期22卷 397-404页

作者： ZENG LUCHUAN, YANG YALI department of Matematics, shanghai Normal university, shanghai 200234, china. department of Mathematics Shanghai Normal Univeristy Shanghai 200234 China

Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| < Np, where Np is n→ t s the normal structure coefficient of X. ... 详细信息

Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| 2)T is asymptotically regular on E. The authors prove that there exists a z E such that T(s)z = z for all s S. Fruther, under the similar condition, the existence of fixed points of Lipschitzian semigroups in a uniformly convex Banach space is discussed.

关键词： Fixed points Lipschitzian semigroups Asymptotic regularity Normal structure coefficient Asymptotic center

The geodetic numbers of graphs and digraphs

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Science china Mathematics 2007年第8期50卷 1163-1172页

作者： Chang-hong LU~(1,2) 1 department of Mathematics,East china Normal university,shanghai 200062,china 2 Institute of Theoretical Computing,East china Narnal university,shanghai 200062,china 1. department of Mathematics East China Normal University Shanghai 200062 China 2. Institute of Theoretical Computing East China Narnal University Shanghai 200062 China

For every two vertices u and v in a graph G, a u-v geodesic is a shortest path between u and v. Let I(u, v) denote the set of all vertices lying on a u-v geodesic. For a vertex subset S, let I(S) denote the union of all I(u, v) for u, v ∈ S. The geodetic number g(G) of a graph G is the minimum cardinality of a set S with I(S) = V (G). For a digraph D, there is analogous terminology for the geodetic number g(D). The geodetic spectrum of a graph G, denoted by S(G), is the set of geodetic numbers of all orientations of graph G. The lower geodetic number is g ?(G) = minS(G) and the upper geodetic number is g +(G) = maxS(G). The main purpose of this paper is to study the relations among g(G), g ?(G) and g +(G) for connected graphs G. In addition, a sufficient and necessary condition for the equality of g(G) and g(G × K 2) is presented, which improves a result of Chartrand, Harary and Zhang.

关键词： convex set digraph distance geodesic geodetic number 05C12 05C20

Beam Polarization Dependence of Diffraction Efficiency in Photorefractive LiNbO3 Crystal

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Chinese Journal of Lasers 2000年第5期9卷 62-68页

作者： YAN Xiaona 1 YAN Jinkui 1 YU Bingkun 1 LIU Liren 2 ( 1 department of Physics, shanghai university, No.99 of Qixiang Road, shanghai 200436, china 2 Information Optics Laboratory, shanghai Institute of Optics and Fine mechanics, The 上海大学上海中科院上海光学精密机械所信息光学开放实验室上海

In weak doped photorefractive LiNbO 3 crystal, the diffraction efficiency is highly relevant to the writing and reading beam polarizations. In this paper, based on dynamic coupled wave equations, we theoretically discuss the diffraction efficiency under four writing and reading polarization conditions, then reach the proven conclusion that with o polarized beams to write and with e polarized beam to readout, the diffraction is the largest.

关键词： defraction efficiency beam polarization refractive index

A NONLOCAL NONLINEAR BOUNDARYVALUE PROBLEM FOR THE HEAT EQUATIONS

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Chinese Annals of Mathematics,Series B 1996年第3期17卷 365-374页

作者： YAN JINHAI(department of Mathematics, Fudan university, shanghai 200433, china) FUDAN UNIV DEPT MATHSHANGHAI 200433PEOPLES R CHINA

The existence and limit behaviour of the solution for a kind of nonlocal nonlinear boundaryvalue condition on a part of the boundary is studied for the heat equation, which physicallymeans that the potential is the function of the total flux. When this part of boundary shrinksto a point in a certain wayt this condition either results in a Dirac measure or simply disappearsin the corresponding problem.

关键词： Heat equation Nonlinear boundary problem Potential Limit behavior

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

VISCOSITY EFFECTS ON THE BEHAVIOR OF A RISING BUBBLE

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Journal of Hydrodynamics 2010年第1期22卷 81-89页

作者： WANG Han ZHANG Zhen-yu YANG Yong-ming ZHANG Hui-sheng department of mechanics and Engineering Science Fudan University Shanghai 200433 China department of Mathematics Shanghai University of Finance and Economics Shanghai 200433 China

In the incompressible fluid flow regime, without taking consideration of surface tension effects, the viscosity effects on the behavior of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by the Volume Of Fluid （VOF） method. The ratio of the gas density to the liquid density is taken as 0.001, and the gas viscosity to the liquid viscosity is 0.01, which is close to the case of an air bubble rising in water. It is found by numerical experiments that there exist two critical Reynolds numbers Re1 and Re2 , which are in between 30 and 50 and in between 10 and 20, respectively. As Re 〉 Re1 the bubble will have the transition to toroidal form, and the toroidal bubble will break down into two toroidal bubbles. In this case viscosity will damp the development of the liquid jet and delay the formation of the toroidal bubble. As Re〈Re1 the transition will not happen. As Re2 〈 Re 〈 Re1, the bubble will split from its rim into a toroidal bubble and a spherical cap-like bubble, and as Re〈Re2 the splitting will not occur and the bubble can finally reach a stationary shape. With the decrease of the Reynolds number, the stationary shape changes from spherical-cap bubble with skirt to dimpled peach-like bubble. Before the bubble reaches its stationary shape the vortex structure in the flow field varies with time. The vortex structure corresponding to bubble stationary shape varies with the Reynolds number. It is also found that there exists another critical Reynolds number Re^＊ which is in between Re1 and Re2 , and as Re 〈 Re^＊, after the bubble rises in an accelerating manner for a moment, it will rise with an almost constant speed, and the speed increases with increasing Reynolds number. As Re 〉 Re^＊, it will not rise with a constant speed. The mechanism of the above phenomena has been analyzed theoretically and numerically.

关键词： rising bubble viscosity effects buoyancy force Volume Of Fluid (VOF) method