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Dynamic behavior of polymer surface and the time dependence of contact angle

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Science china Chemistry 2005年第6期48卷 553-559页

作者： WANG Xinping1, CHEN Zhifang1 & SHEN Zhiquan2.1. Key Laboratory of Advanced Textile Materials and Manufacturing Technology of Education Ministry, department of Applied Chemistry, zhejiang Institute of Science and Technology, Hangzhou 310033,{2. 2. department of Polymer Science and Engineering, zhejiang university, Hangzhou 31002.,{2. 1. department of Applied Chemistry Zhejiang Institute of Science and Technology Key Laboratory of Advanced Textile Materials and Manufacturing Technology of Education Ministry 310033 Hangzhou China 2. department of Polymer Science and Engineering Zhejiang University 310027 Hangzhou China

Time-dependent contact angles were measured by depositing sessile drops of wa-ter on the polymer surfaces and monitoring the drop shape as a function of time. It was found that contact angles decreased sharply with contact time and the equilibrium contact angle was finally attained after a certain time. Values of starting (θ s) and equilibrium contact angles (θ e) obtained by the sessile drop method depend on polymer properties. The Wilhelmy plate technique was used to measure advancing and receding contact angles. The variations of starting (θ s) and equilibrium contact angles (θ e), advancing (θ a) and receding contact angles (θ r) have been studied on the oxidized surface of polymers containing polybutadiene block to explore the cause of time-dependence in contact angle measurement and the meaning of θ s and θ e. The results showed the linear relationships between starting (θ s) and advancing contact angles (θ a), the equilibrium (θ e) and receding contact angles (θ r). The similar relationship was also established between the contact angle hysteresis (θ a?θ r) and differences (θ s ?θ e) in starting contact angles and equilibrium contact angles. Therefore, time-dependence in contact angle measurement was mainly attributed to the surface reconstruction when water drops were deposited on polymer surfaces. The starting contact angle was contributed by the hydrophobic component on polymer surface and the equilibrium contact angle mainly by the hydrophilic component of polymer. These results not only demonstrated the interdependency between two contact angle measurements, the sessile drop method and the Wilhelmy plate technique, but also provided the experimental evidence to explain the cause of time-dependent contact angle. This may also provide a new method to study dynamic behavior of polymer surface.

关键词： contact angle, surface dynamic behavior, polymer surface, dynamic contact angle, time-dependence.

Stability of multiquadric quasi-interpolation to approximate high order derivatives

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Science china mathematics 2010年第4期53卷 985-992页

作者： MA LiMin 1,2.& WU ZongMin 1,1 Shanghai Key Laboratory for Contemporary Applied mathematics,School of Mathematical Sciences,Fudan university,Shanghai 2.0433,{2. 2.department of Information and Computer Science,zhejiang Gongshang university,Hangzhou 310018,{2. 1. Shanghai Key Laboratory for Contemporary Applied mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China2. Department of Information and Computer Science Zhejiang Gongshang University Hangzhou 310018 China

Numerical simulation of the high order derivatives based on the sampling data is an important and basic problem in numerical approximation,especially for solving the differential equations *** classical method is the divided difference ***,it has been shown strongly unstable in ***,it can only be used to simulate the lower order derivatives in *** simulate the high order derivatives,this paper suggests a new method using multiquadric *** stability of the multiquadric quasi-interpolation method is compared with the classical divided difference ***,some numerical examples are presented to confirm the theoretical *** theoretical results and numerical examples show that the multiquadric quasi-interpolation method is much stabler than the divided difference *** property shows that multiquadric quasi-interpolation method is an efficient tool to construct an approximation of high order derivatives based on scattered sampling data even with noise.

关键词： numerical differential radial basis functions (RBFs) Hardy’s multiquadric (MQ) quasiinterpolation divided difference method white noise expectation variance

Minimal systems of generators for central division algebra and semi-simple algebra

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Chinese Science Bulletin 1998年第21期43卷 1777-1780页

作者： QIU Qizhang 1 and SUN Ling 2.1. department of mathematics, Wuhan {2., Wuhan 430072. china 2. department of Information science, Wuhan {2., Wuhan 430072. china. department of mathematics Wuhan University Wuhan China department of Information science Wuhan University Wuhan China

Suppose that F is a field of characteristic zero and (ⅰ) D is a finite-dimensional central division algabra over F; (ⅱ) A is a finite-dimensional semi-simple algabra over F. It is proved that as F-algebras, D and A ... 详细信息

关键词： central division algebra semi-simple algebra generator minimal system of generators.

A new definition of restricted Lie superalgebras

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Chinese Science Bulletin 2000年第4期45卷 316-321页

作者： WANG Ying & ZHANG Yongzheng1. department of mathematics, Harbin Institute Technology, Harbin 150001,{2. 2. department of mathematics, Northeast Normal university, Changchun 13002.,{2. department of mathematics Harbin Institute Technology Harbin China department of mathematics Northeast Normal University Changchun China

A new definition of restricted Lie superalgebras has been given; some important results on the representation theory of restricted Lie superalgebra have been obtained.

关键词： restricted Lie superalgebra p-mapping p-semilinear mapping α-representation.

Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property

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Chinese Science Bulletin 1997年第3期42卷 259-260页

作者： MAI Jiehua and GU Rongbao1.Institute of mathematics, Shantou university, Shantou 515063,{2. 2. department of mathematics, Anhui university, Hefei 2.0039,{2. Institute of mathematics Shantou University Shantou China department of mathematics Anhui University Hefei China

IN this letter we discuss the necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, every minimal set of a C^r(r≥2. flow is trivial, but it is possible for a C^0 flow to contain non-trivial minimal sets. Thus C^0 flows on closed surfaces are more complicated than C^r(r≥2. flows.

关键词： Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property

NONOSCILLATION RESULTS FOR A CLASS OF THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS

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Applied mathematics and Mechanics(English Edition) 2002年第10期23卷 1170-1175页

作者： Pakize Temtek 1, Aydn Tiryaki 2.(1 department of mathematics, Faculty of Arts and Science, Erciyes {2., 38039, Kayseri, Turkey 2.department of mathematics, Faculty of Arts and Science, Gazi {2., Teknikokullar 06500 Ankara, Turke department of mathematics Faculty of Arts and Science Erciyes University 38039 Kayseri Turkey department of mathematics Faculty of Arts and Science Gazi University Teknikokullar 06500 Ankara Turkey

Sufficient conditions for the nonoscillatory solutions of a class of third order nonlinear differential equations are presented. The results obtained generalize some criteria given by Parhi. In some special cases, som... 详细信息

关键词： differential equation nonlinear nonoscillatory solution Parhi criteria

Parabolic equation of the m-Laplacian with nonlinear boundary condition

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Chinese Science Bulletin 1998年第11期43卷 905-908页

作者： WANG Shu+ 1, 2. WANG Mingxin 3, XIE Chunhong 1 1. department of mathematics, Nanjing {2., Nanjing 2.0093, china 2. department of mathematics, Henan {2., Kaifeng 475001, china 3. department of Applied mathematics, Southeast {2., department of Mathernntics Nanjing University Nanjing China department of mathematics Henan University Kaifeng China department of Applied mathematics Southeast University Nanjing China

The existence and nonexistence of global positive weak solutions of parabolic equation of the m-Laplician with nonlinear boundary condition are dealt with. The necessary and sufficient conditions on the existence of a... 详细信息

关键词： nonlinear boundary condition parabolic equation of m-Laplacian global solution blow-up.

New Exact Solutions to (2.1)-Dimensional Variable Coefficients Broer-Kaup Equations

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Communications in Theoretical Physics 2006年第9期46卷 393-396页

作者： ZHU Jia-Min~(1,2.+) MA Zheng-Yi~(1,2. ~1 department of Physics, zhejiang Lishui {2., Lishui 32.000, china ~2.Shanghai Institute of Applied mathematics and Mechanics, Shanghai 2.0072. china department of Physics Zhejiang Lishui University Shanghai Institute of Applied mathematics and Mechanics

In this paper, using the variable coefficient generalized projected Ricatti equation expansion method, we present explicit solutions of the (2.1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.

关键词： variable coefficient generalized projected Ricatti equation method (2.1)-dimensional variable coefficients Broer Kaup equations Weierstrass function solution solitary wave solution trigonometric function solution

On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengrong 2.and YU Yuanhong 3 1. department of Applied mathematics, Beijing Institute of Technology, Beijing 100081,{2. 2. department of mathematics, Yunnan university, Kunming 650091,{2. 3. Institute of Applied mathematics, C department of Applied mathematics Beijing Institute of Technology Beijing China department of mathematics Yunnan University Kunming China Institute of Applied mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.