Some generalizations of generalized bi-quasivariational inequalities

The purpose of this paper is to introduce and study the existenee problems of solutions for a class of new bi-quasi-variational inequalities. The resuhs presented in this paper unify, sharpen and extend many recent results.     

SOME FURTHER GENERALIZATIONS OF KY FAN’S MINIMAX INEQUALITY AND ITS APPLICATIONS TO VARIATIONAL INEQUALITIES

The purpose of this paper is to introduce the concept of generalized KKM mapping andto obtain some general version of the famous KKM theorem and Ky Fan’s minimaxinequality.As applications,we utilize the results presented in this paper to study the saddlepoint problem and the existence problem of solutions for a class of quasi-variationalinequalities.The results obtained in this paper extend and improve some recent results of[1-6].     

A note on novel generalizations of the Maxwell fluid model

In this note we generalize the classical viscoelastic fluid model due to Maxwell to allow the relaxation time and the viscosity to depend on the stress. Such models are very useful in describing the response of geological and many other polymeric fluids. The procedure that is adopted to carry out the generalization allows one to have the springs and dashpots and their three dimensional generalizations, to be described by implicit constitutive theories thereby greatly enlarging the class of constitutive models that can be put into place to describe the response of complex viscoelastic fluids.     

APPLICATIONS OF STAIR MATRICES AND THEIR GENERALIZATIONS TO ITERATIVE METHODS

Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method (GAOR) is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.     

On K-BKZ and other viscoelastic models as continuum generalizations of the classical spring-dashpot models

An alternate constitutive formulation for visco-elastic materials, with particular emphasis on macromolecular viscoelastic fluids, is presented by generalizing Maxwell's idealized separation of elastic and relaxation mechanisms. The notion ofrelative rate of change of elastic stress is identified, abstracted, and formulated with the help of the established theory of finitely elastic isotropic materials. This given a local rate-type constitutive relation for an elastic mechanism in a simple material.For the simplest class of viscoelastic polymer melts, the notion of rate of change of elastic stress and its damped accumulation is identified and formulated. Under conditions of moderate strain rates, this scheme implies the reliable K-BKZ model for a class of polymer melts. An obvious extension generalizes the remaining classical spring-dashpot models. I Set of second-order tensors.A I is identified with a 3 × 3 matrix in a Cartesian co-ordinate system - I ^sym Set of symmetric second order tensors - Q Orthogonal tensor, i.e.Q ^T=Q ^–1. - Symbol for the value of the functional H:X I ^sym, whereX is the set of piecewise continuous and differentiable strain historiesF _to : [t ₀,t] I Other functionals, unless otherwise specified, should be interpreted in a similar manner.     

SOME CONVERGENCE PROBLEM OF ITERATIVE SEQUENCESFOR ACCRETIVE AND PSEUDO-CONTRACTIVETYPE MAPPING IN BANACH SPACES

1　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＴｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒ,ｗｅａｓｓｕｍｅｔｈａｔＥｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅ ,Ｅ ｉｓｔｈｅｔｏｐｏｌｏｇｉｃａｌｄｕａｌｓｐａｃｅｏｆＥ ;〈· ,·〉ｉｓｔｈｅｄｕａｌｐａｉｒｂｅｔｗｅｅｎＥａｎｄＥ ,Ｄ(Ｔ) ,Ｒ(Ｔ) ,Ｎ(Ｔ) ,Ｆ(Ｔ)ｄｅｎｏｔｅｔｈｅｄｏｍａｉｎｏｆＴ ,ｒａｎｇｅｏｆＴ ,ｔｈｅｓｅｔｏｆａｌｌｚｅｒｏｐｏｉｎｔｓｏｆＴａｎｄｔｈｅｓｅｔｏｆａｌｌｆｉｘｅｄｐｏｉｎｔｓｏｆＴｒｅｓｐｅｃｔｉｖｅｌｙ…     

Geometric calculus for second-order differential equations and generalizations of the inverse problem of Lagrangian mechanics

We review the main features of the geometric calculus which has been introduced over the past 15 years in the study of second-order ordinary differential equations and then explain how a recently introduced generalization of the inverse problem of Lagrangian mechanics can be very concisely dealt with by this calculus in an intrinsic way. This paper is an account of the lecture with the same title presented at the ICDVC-2010 Conference in Hangzhou, May 12–14 (2010).     

斯托克斯阻力公式的简单推导

斯托克斯阻力公式的传统推导有些复杂.本文根据线性齐次微分方程所满足的叠加原理提出了一个简单的推导.由于斯托克斯方程是一个二阶线性偏微分方程,根据球表面的两个速度分量条件,方程应该有两个线性独立的和完备的解,这两个解应该构成方程的基本解组,它们的线性组合应该就是方程的通解.使用拉普拉斯方程的解以及量纲分析,找到了这两个解.这两个解的线性组合就是斯托克斯问题的解.     

A simple derivation of the Stokes formula of the drag

斯托克斯阻力公式的传统推导有些复杂.本文根据线性齐次微分方程所满足的叠加原理提出了一个简单的推导.由于斯托克斯方程是一个二阶线性偏微分方程,根据球表面的两个速度分量条件,方程应该有两个线性独立的和完备的解,这两个解应该构成方程的基本解组,它们的线性组合应该就是方程的通解.使用拉普拉斯方程的解以及量纲分析,找到了这两个解.这两个解的线性组合就是斯托克斯问题的解.     

An interpolation formula of the derivatives of higher order

ＡＮＩＮＴＥＲＰＯＬＡＴＩＯＮＦＯＲＭＵＬＡＯＦＴＨＥＤＥＲＩＶＡＴＩＶＥＳＯＦＨＩＧＨＥＲＯＲＤＥＲＧｕｉＺｕ－ｈｕａ（桂祖华）（ＴｈｅＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ＳｈａｎｇｈａｉＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔ...     

Flow mapping of the mercury flow

 An ultrasonic velocity profile (UVP) method has been successfully applied to the investigation of mercury flow contained in a stainless steel wall in the configuration of a liquid metal target of a spallation neutron source called SINQ at the Paul Scherrer Institute. One- and two-dimensional stationary flow has been fully investigated in the form of velocity profiles. Using velocity profiles obtained by the UVP method, a two-dimensional flow map was efficiently produced. A steady state vector map was successfully made and time dependent flow mapping is feasible. Received: 17 May 2000 / Accepted: 27 December 2000 Published online: 29 November 2001     

A formula of solution to the integral of rational functions

ＡＦＯＲＭＵＬＡＯＦＳＯＬＵＴＩＯＮＴＯＴＨＥＩＮＴＥＧＲＡＬＯＦＲＡＴＩＯＮＡＬＦＵＮＣＴＩＯＮＳＧｕｉＺｕ－ｈｕａ（桂祖华）（ＴｈｅＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ＳｈａｎｇｈａｉＪｉａｏ－ｔｏｎｇＵｎｉｖｅｒｓｉｔ...