BASIC EQUATIONS, THEORY AND PRINCIPLE OF COMPUTATIONAL STOCK MARKET (Ⅰ)──BASIC EQUATIONS

IntroductionComputationaleconomicwillbethetendencyofmodemeconomicanalysis,nevedhelessthereisalongwaytoachievethelevelofcomputationalmathematicsandcomputationalmechanicsatpresent.Stockmarketisasensiblebarometermeasuredtheweatherofmarketeconomicactivities.Althoughtherearemanypapersoncomputationaleconomic(forexampleRefs.[l,2])butpaperconcernedwithstockmarketisrarelyseen.InChina,mostpublicationsonstockmarket(forexampleRefs.[3~5])arequotationdata,predicationoftendency,skillsorexperiencesforgainin…     

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

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｒｉｃｅｏｆｇｏｏｄｓｖａｒｙｉｎｇａｒｏｕｎｄｉｔｓｖａｌｕｅｉｓｃｏｎｓｉｄｅｒｅｄｔｏｂｅａｂａｓｉｃｒｕｌｅｏｆｇｏｏｄｓ,ｉ.ｅ .,ｔｈｅｌａｗｏｆｖａｌｕｅｏｆｇｏｏｄｓ.Ａｓｔｏｃｋｉｓａｋｉｎｄｏｆｇｏｏｄｓ ,ｉｔｎａｔｕａｌｌｙｏｂｅｙｓｔｈｅｌａｗｏｆｖａｌｕｅｏｆｇｏｏｄｓ.Ｓｏｔｈａｔｔｈｅｐｒｉｃｅｏｆｓｔｏｃｋｖａｒｉｅｓａｒｏｕｎｄｉｔｓｖａｌｕｅ.Ｔｏｄｅｔｅｒｍｉｎｅｔｈｅｖａｌｕｅｏｆｓｔｏｃｋｉｓｖｅｒｙｉｍｐｏｒｔａｎｔｆｏｒｔｈ…     

BASIC EQUATIONS, THEORY AND PRINCIPLES OF COMPUTATIONAL STOCK MARKET (Ⅱ)——BASIC PRINCIPLES

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｒｅａｒｅｍａｎｙｐｒｉｎｃｉｐｌｅｓｉｎｍｅｃｈａｎｉｃｓ,ｓｕｃｈａｓｔｈｅＳａｉｎｔ＿Ｖｅｎａｎｔ’ｓｐｒｉｎｃｉｐｌｅ,ｔｈｅＤ’Ａｌｅｍｂｅｒｔ’ｓｐｒｉｎｃｉｐｌｅ,ｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｓ...     

EXACT SOLUTION OF LARGE DEFORMATION BASIC EQUATIONS OF CIRCULAR MEMBRANE UNDER CENTRAL FORCE

Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of the solution were discussed by using of modern immovable point theorems. Although specific problem is treated, the basic principles of the methods can be applied to a considerable variety of nonlinear problems.     

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

By basic equations, two basic theories are presented: 1. Theory of stock’s value v^*(t)=v^*(0) exp (ar₂^*t);2. Theory of conservation of stock’s energy. Let stock’s energy Φbe defined as a quadratic function of stock’s price v and its derivative v, Φ=Av²+Bv+Cv²+Dv, under the constraint of basic equation, the problem was reduced to a problem of constrained optimization along optimal path. Using Lagrange multiplier and Euler equation of variation method, it can be proved that Φkeeps conservation for any v,v. The application of these equations and theories on judgement and analysis of tendency of stock market are given, and the judgement is checked to be correct by the recorded tendency of Shenzhen and Shanghai stock markets.     

SIMPLIFICATION OF THE EXPANSIONS OF VISCOUS TERMS IN BASIC AERODYNAMIC EQUATIONS IN NON-ORTHOGONAL CURVILINEAR COORDINATE SYSTEM

The application of non-orthogonal curvilinear coordinate system to the calculation ofthe flow field inside the channel,with complex boundary geometry,can effectively simplifythe work of designing the calculation program and improve the accuracy of calculation.Therefore, it is obviously necessary to expand the viscous terms,i.e.viscous force,rate ofwork done by viscous stress and dissipation, in basic aerodynamic equations in the non-orthogonal curvilinear system. However, each of these expansions consistes of tens oreven hundrede of algebraic terms.The expansions of these three viscous terms discribed inthis paper are considerably simplified by analysing their order of magnitude.     

MULTI-SOLITARY WAVE SOLUTIONS FOR VARIANT BOUSSINESQ EQUATIONS AND KUPERSHMIDT EQUATIONS

Ｒｅｃｅｎｔｌｙ,ＷａｎｇｐｒｅｓｅｎｔｅｄａｈｏｍｏｇｅｎｅｏｕｓｂａｌａｎｃｅｄｍｅｔｈｏｄｆｏｒｃｏｎｓｔｒｕｃｔｉｎｇｓｏｌｉｔａｒｙｗａｖｅｓｏｌｕｔｉｏｎｓｆｏｒｔｈｅｖａｒｉａｎｔＢｏｕｓｓｉｎｅｓｑｅｑｕａｔｉｏｎｓ[1].Ｉｎｔｈｉｓｐａｐｅｒ,ｗｅｗｉｓｈｔｏｇｉｖｅｇｅｎｅｒａｌｍｕｌｔｉ＿ｓｏｌｉｔｏｎｓｏｌｕｔｉｏｎｓｆｏｒｔｈｅｖａｒｉａｎｔＢｏｕｓｓｉｎｅｓｑｅｑｕａｔｉｏｎｓａｎｄｔｈｅＫｕｐｅｒｓｈｍｉｄｔｅｑｕａｔｉｏｎｓ.Ｔｈｅｆｉｒｓｔｔｙｐｅｏｆｖａｒｉａｎｔ…     

SINGULAR PERTURBATION OF LINEAR ALGEBRAIC EQUATIONS WITH APPLICATION TO STIFF EQUATIONS

In this paper the singular perturbation problem of linear algebraic equations with asmall parameter is presented by an example in practice.The existence and uniquenesstheorem of its solution is proved by the perturbation method and the estimation of error forits approximate solution is given.Finally,the example mentioned above explaining how toapply the theory to solve the stiff equations is shown.     

SOME SOLUTIONS OF MAXWELL EQUATIONS

This article gives a class of solution of Maxwellequations which implies the solution of arbitrary ho-lomorphic hypercomplex functional with brief discus-sion of their physical meaning.It exhibites somewider nature than classical electromagnetic theory:(l)An electromagnetic field may spread non-periodically and may have the holographic nature andfree shape.(2)The electromagnetic field may spread more slow-ly,equally or more quickly than light speed.(3)The electromagnetic field may spread in arbi-trary curved direction.(4)There is a branch electromagnetic field in in-tergrowth space.An intergrowth world may exist.This article also makes an inference and a descrip-tion about the example of the above-mentioned strangeelectromagnetic field.It relates to some hard-to-explain phenomena through different physical models.     

SEVERAL CLASSES OF INTEGRABLE NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS(Ⅰ)FIRST-ORDER EQUATIONS

In this paper we give some results of integrability and several classes of integrableequations of first-order nonlinear ordinary differential equations.Many known results ofintegrability and integrable equations are special cases of them.They may be applied inphysics and mechanics,and to derive soliton equations and find soliton solutions.     

SEVERAL CLASSES OF INTEGRABLE NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS(Ⅱ)—HIGHER-ORDER EQUATIONS

In this paper,several classes of integrable nonlinear higher-order ordinary differentialequations are given.It is pointed out that some known results of integrability or integrableequations are all special cases of them.These equations have a wide-ranging appliedbackground in physics and mechanics.     

SEVERAL CLASSES OF INTEGRABLE NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS(Ⅱ)—HIGHER-ORDER EQUATIONS

In this paper, several classes of integrable nonlinear higher-order ordinary differential equations are given. It is pointed out that some known results of integrability or integrable equations are all special cases of them. These equations have a wide-ranging applied background in physics and mechanics.     

FUNDAMENTAL EQUATIONS OF TURBULENT TWO-PHASE FLOW

A new set of Keynolds equations for predicting turbutent two-phase flows has beendeveloped by means of Reynolds averaging method on the unsteady laminar equations oftwo-phase flow.These equations involve average terms of products of turbulent fluctuationsin some physical parameters in a large degree.The interaction forces between two phases,thepressures for dispersed phase,extra stresses except for pressure and the expressions forenergy interchange between two phases have been discussed.     

CONDITIONAL RECURSIVE EQUATIONS ON EXCESS-OF-LOSS REINSURANCE

The marginal recursive equations on excess-of-loss reinsurance treaty are investignted, under the assumption that the number of claims belongs to the family consisting of Poisson, binomial and negative binomial, and that the severity distribution has bounded continuous density function. On conditional of the numbers of claims associated with the reinsurer and the cedent, some recursive equations are obtained for the marginal distributions of the total payments of the reinsurer and the cedent.     

ATTRACTORS OF NONAUTONOMOUS SCHR?DINGER EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＡｔｔｒａｃｔｏｒｓｏｆａｕｔｏｎｏｍｏｕｓｅｖｏｌｕｔｉｏｎｅｑｕａｔｉｏｎｓｈａｖｅｂｅｅｎｉｎｔｅｎｓｉｖｅｌｙｓｔｕｄｉｅｄｉｎｍａｔｈｅｍａｔｉｃａｌｌｉｔｅｒａｔｕｒｅ (ｓｅｅ,ｆｏｒｅｘａｍｐｌｅ ,ｂｏｏｋｓ [1 ] ,[2 ] ,[3 ] ,[4 ]ａｎｄｔｈｅｌｉｔｅｒａｔｕｒｅｃｉｔｅｄｔｈｅｒｅ) .Ｔｈｅｎｏｎａｕｔｏｎｏｍｏｕｓｉｎｆｉｎｉｔｅ＿ｄｉｍｅｎｓｉｏｎａｌｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓｗｅｒｅｌｅｓｓｗｅｌｌｕｎｄｅｒｓｔｏｏｄ .Ｉｎ 1 994 ,Ｃｈｅｐｙｚｈ…     

CONCENTRATION OF COUPLED CUBIC NONLINEAR SCHRODINGER EQUATIONS

A coupled nonlinear Schrodinger equations is considered in 2-D space. Based upon the conservation of mass and energy, local identities is established by the study of the limit behavior of the solutions, and L^2-concentration for the blow-up solutions with radially symmetry is obtained.     

ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of the solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the well-known classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.     

烟囱抗震动力计算的BASIC程序

利用虚功法,并不考虑纯弯曲型杆件的剪切影响,求出烟囱各分段质量处的位移。再利用柔度矩阵列出多自由度体系的自由振动方程[u] {A~(r)}=入{A~(r+1},式中[u]为质量柔度矩阵,仅与质量分布及刚度有关。按照所要求的精度反复迭代,并利用振型正交性,求得第一、二、三振型的频率ω_j及周期T_j。最后按振型组合求出各截面的内力。     

REMABKS ON THE STRUCTURE OF EVOLUTION EQUATIONS

ＲＥＭＡＢＫＳＯＮＴＨＥＳＴＲＵＣＴＵＲＥＯＦＥＶＯＬＵＴＩＯＮＥＱＵＡＴＩＯＮＳＪ．Ｂａｄｕｒ；ＳｕｎＢｏｈｕａ（孙博华）（Ｒｕｈｒ－ＵｎｉｒｅｒｓｉｔＢｏｃｈｕｍ，ＬｅｈｒｓｔｕｈｌｆｒＡｌｌｇｅｍｅｉｎｅＭｅｃｈａｎｉｋＤ－４４７８０Ｂｏｃｈｕ...