THE EXACT INTEGRAL EQUATION OF HERTZ’S CONTACT PROBLEM

This paper presents the exact integral equation of Hertz‘s contact problem,which isobtained by taking into account the horizontal displacement of points in the contactedsurfaces due to pressure.     

ANALYSIS OF FINANCIAL DERIVATIVES BY MECHANICAL METHOD (Ⅰ)—BASIC EQUATION OF PRICE OF INDEX FUTURES

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复合g-收缩映射不动点定理及其应用

任一几何平均收缩比率小于1(简称g-收缩映射)的由完备的非空度量空间M到M的复合序列映射,复合周期映射有在M中的唯一的不动点。文中给出定理应用于一组非线性微分方程以及扁壳轴对称弯曲的耦合的积分方程的解的存在和唯一性证明的应用例子。     

TORSION OF ELASTIC SHAFT OF REVOLUTION EMBEDDED IN AN ELASTIC HALF SPACE

The problem of torsion of elastic shaft of revolution embedded in an elastic half spaceis studied by the Line-Loaded Integral Equation Method(LLIEM).The problem isreduced to pair of one-dimensional Fredholm integral equations of the first kind due to thedistributions of the fictitious loads“Point Ring Couple(PRC)”and“Point Ring Couple inHalf Space(PRCHS”on the axis of symmetry in the interior and external ranges of theshaft occuied respectively.The direct discrete solution of this integral equations may beunstable,i.e.an ill-posed case occurs.In this paper,such an ill-posed Fredholm integralequation of first kind is replaced by a Fredholm integral equation of the second kind withsmall parameter,which provides a stable solution.This method is simpler and easier tocarry out on a computer than the Tikhonov’s regularization method for ill-posed problems.Numerical examples for conical,cylindrical,conical-cylindrical,and parabolic shafts aregiven.     

BASIC EQUATIONS, THEORY AND PRINCIPLE OF COMPUTATIONAL STOCK MARKET (Ⅲ)—BASIC THEORIES

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Pile Analysis by Simple Integral Equation Methods

Two simple integral equation methods are proposed for the analysisof vertical loaded pile.One of them is:let the axisymmetrical loads formedby Mindlin’s horizontal point forces be distributed along the axis z in[0,L]of the elastic half-space,and composed with the Boussinesq’s pointforce.The other is:in addition to the above fictitious loads,the Mind-lin’s vertical forces are distributed along the axis z in[0,L].The form-er reduces the problem of a vertical loaded pile embedded in a half-spacewith the following boundary conditions.     

SOLUTION OF SIMULTANEOUS EQUATIONS OF COSINE LAW ARISING FROM SUBJECTIVITY GEOMETRY

This paper discusses the solution of a group of two-order six elements rooted algebraicsimultaneous equations set up by cosine law arising from the application example ofsubjectivity geometry.By means of the implicit function theorem,this paper proves thatthere exists a unique real solution of those equations.Transforming this problem into anunconstrained nonlinear optimization problem,the solution can be found by knownmethods.A numerical example by descent method is given.     

金融衍生产品的力学方法分析（Ⅰ）——期指价格基本方程

类似连续介质力学方法,将期指价格变化看成是连续、有规律可寻的。根据期指特点,建立期指价格变化的基本方程。这是一个微分方程,其解显示时间与价格呈对数圆形关系。若将时间理解为相应价格的概率,则这一关系与基于统计理论分析的、著名的诺贝尔经济学奖（1997）获得者的期权定价Black-Scholes公式中主要假设-基础资产（在此为期指）价格呈对数正态分布-完全一致。表明了依据完全不同的两种分析方法,也会得到相同的结果。只是Black-Scholes是用假设给出,而作者则从微分方程的解推出。     

The Solution of Elastostatic Problems and the Principles of Minimum Potential Energy,Minimum Complementary Work,under Fuzzy Boundary Conditions

A Solution of elastostatic problem is defined on the basis of set theory andextended to the cases with fuzzy boundary conditions.Extension is alsogiven for the principles of minimum potential energy and minimum comple-mentary work with fuzzy boundary conditions.A quasisolution of an elasto-static problem is defined as an approximate solution with boundary conditionsmost close to the original.And the existance of quasisolution of an elasto-static problem can be proved on the basis of certain assumptions and thetheorem of minimum elementary potential energy.