Analytical solution of basic equations set of atmospheric motion

On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.

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

This paper studies computational stock market by using network model and similar methodology used in solid mechanics. Four simultaneous basic equations, i. e., equation of interest rate and amount of circulating fond, equations of purchasing and selling of share, equation of changing rate of share price, and equation of interest rate, share price and its changing rate, have been established. Discussions mainly on the solution and its simple applications of the equation of interest rate and amount of circulating fond are given. The discussions also involve the proof of tending to the equilibrium state of network of stock market based on the time discrete form of the equation by using Banach theorem of contraction mapping, and the influence of amount of circulating fond with exponential attenuation due to the decreasing of banking interest rate.Keyworks: stock market; network model; differential equation; contraction mapping; elasticity; methodology

BASIC EQUATIONS OF TURBULENT FLOW FOR VARIABLE DENSITY AND VARIABLE VISCOSITY NEWTONIAN FLUID IN OPEN CHANNEL

In this paper, using Navier-Stokes equations and Reynolds time-averaged rules, the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid have been presented, and the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid in open channel have been further proposed. The concepts of the density turbulence stress and the viscosity turbulence stress have been firstly presented in the paper.

BASIC EQUATIONS OF THE PROBLEM OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE WITH VARIABLE THICKNESS

Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given;then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given.

Stability for basic system of equations of atmospheric rhotion

The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate system the basic system of equations of atmospheric motion is stable in infinitely differentiable function class. In the sense of local solution, the necessary and sufficient conditions by which the typical problem for determining solution is well posed were also given. Such problems as something about ＂speculating future from past＂ in atmospheric dynamics and how to amend the conditions for determining solution as well as the choice of underlying surface when involving the practical application were further discussed. It is also pointed out that under the usual conditions, three motion equations and continuity equation in the basic system of equations determine entirely the property of this system of equations.

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅴ)--POLAR THERMOMECHANICAL CONTINUA

The purpose is to reestablish rather complete basic balance equations and boundary conditions for polar thermomechanical continua based on the restudy of the traditional theories of micropolar thermoelasticity and thermopiezoelectricity . The equations of motion and the local balance equation of energy rate for micropolar thermoelasticity are derived from the rather complete principle of virtual power. The equations of motion, the balance equation of entropy and all boundary conditions are derived from the rather complete Hamilton principle . The new balance equations of momentum and energy rate which are essentially different from the existing results are presented. The corresponding results of micromorphic thermoelasticity and couple stress elastodynamics may be naturally obtained by the transition and the reduction from the micropolar case , respectively . Finally , the results of micropolar thermopiezoelectricity are directly given .

A STABILITY STUDY OF NAVIER-STOKES EQUATIONS (Ⅲ)

In this paper, the necessary conditions of the existence of C￣2 solution. in someinitial problems of Navier-Stokes equations are given. and examples of instability ofinitial value (at t=0) problems are also given. The initial value problem ofNavier-Stokes equation is one of the most fundamental problem for this equationvarious authors studies this problem and contributed a number of results .J.Leray .aFrench professor, proved the existence of Navier-Stokes equation under certain definedinitial and boundary value conditions .In this paper,with certain rigorously definedkey.concepts,based upon the basic theory of J.Hadmard partial differentialequanous￣[1], gives a fundamental theory of instability of Navier-Stokes equations.Finally,many examples are given,proofs referring to Ref.[4] .