Oscillation Theorems of Systems of High Order Nonlinear Delay Partial Differential Equations

Partial functional differential equations come from many mathematical models in physics,biology,engineering and other fields,which have strongly practical background.The oscillation theory is the one of the important branches of qualitative theory of partial functional differential equations. Therefore,it is of great theoretical and practical value to research the oscillation of partial functional differential equations.The anthors study the oscillation of the systems of a class of high order nonlinear delay partial functional differential equations.By using Green's theorem and Riccati transformation,they obtain some sufficient criteria for oscillation of all solutions of the systems under two kinds of different boundary value conditions,which are illustrated by some examples.These results offer the foundation of mathematical theory for solving the practical problems of the above fields.     

Optimization Method of Turbine Impeller''s Stress and Deformation Calculation

Taking into the feature of computer computing method, using Stress solution of elasticity theory and according to different method of solving of system of second order ordinary differential equations , this article provides two numerical value computing method as for the stress and deformation of the turbine impeller which is within the scope of elasticity . One combines the initial value computing method of system of ordinary differential equations (Runge-Kutta Method) with optimization method, another combines the boundary value computing method of system of ordinary differential equations difference method-with optimization method and three points interpolation method . The proposed method can eliminate the deficiencies of Secondary Calculation method and is particularly suited for programmable computer-based solution . The sample show that results gotten by two methods is nearly equal to the precise results,so they are practicable. They completes the quick and precise calculating of stress and deformation . They have some general meaning , large commonality and the project employing value.     

Slip Line Field of Plane Strain Problem Obeying the GeneralizedHoek Brown Failure Criterion

According to the characteristics of plane strain problem of elastic and plastic mechanics, the bi parametric expressions were derived for stress components satisfying the generalized Hoek Brown failure criterion. Being substituted into the static equilibrium partial differential equations, a group of first order hyperbolic pseudo linear differential equation partial differential equations was obtained. Utilizing the determinant method and proper variable transformation, the characteristic direction and the differential relation equation for the stress partial differential equations were acquired. The characteristic direction indicted that in plastic zone obliquely intersecting conjugate shear slip surfaces formed two families of non orthogonal slip lines, in which conjugate angle varied with the limit stress state and the material physical properties of Hoek Brown rock mass. Since the principal direction of the maximum principal stress was circumferential in perfectly elasto plastic surrounding rock of the plastic zone around a circular opening suffering the symmetric initial stress field, the angle between the tangential direction of slip line with the principal direction of the maximum principal stress was the function of the minimum principal stress(i.e. the radial stress). Combined with the analytical solution, the polar coordinate differential equation was derived and furthermore, the polar coordinate curve equation for the slip line was obtained.     

A NEW BOUNDARY INTEGRAL EQUATION METHOD FOR SOLVING EXTERIOR BOUNDARY VALUE PROBLEMS OF THREE-DIMENSIONAL HELMHOLTZ EQUATION

This paper pressnts a new boundary integral equation method for solving exteri-or boundary value problems of three-dimensional Heimheltz equation by using the multiple reciproc-ity method.Firstly,integral representations of the solution in an exterior domain as well as on itsboundary,which have the peculiarity that integral kernels are infin ite seriesea developed from thenormal fundamental solution of Laplace equation and independent of the wavenumber,are given andproved under the Dirichlet condition.Then,based on the representation of the solution on the bound-ary,boundary integral equations for solving the Dirichlet and the Neumann boundary value prob-lems are obtained,and remarks for some problems concerned with solving these integral equationsnumerically are made.Finally, the advantages of the proposed method,as compared with the conven-tional boundary element methods,are summarized.     

THE EQUATION OF STBING IN THE EXTERNAL FIELDS

The classical equations of string in the external fields deduced with Kaluza's method. A solution of the equations for uniform magnetic field is got by means of differential geometry technlqde.     

THE CALCULATION OF INTERNAL FORCES AND DISPLACEMENTS IN FRAME-SHEARING WALL STRUCTURE UNDER THE HORIZONTAL LOADS

In general,the calculating result of a comparatively regular frame-shearing wall system in tall buildings,a 4-order differential equations are established according to the deformation-coordination of beams,columns and four boundary conditions.Then a series of formulas concerning internal forces and displacement is obtained These formulas are hyperbolic functions.This paper presents a method,which changes 4-order differential equations into 2-order and solves them by the expressions of new homogeneous solutionThen the formulas of internal forces and displacements become exponential functions By this method,the calculation is very convenient The result of suggested method agrees well with the general by comparison This paper is also applicable to buildings with some part of different height of storey or stiffness.     

PROPERTIES OF HOMOGENEOUS FUNCTION AND ITS APPLICATIONS

This paper proves some properties of homogeneous function. Mainly, it proves that a sufficient condition of a parahomogeneous function is a subhomogeneous function. From which the relations of homogeneous function and partial derivatives of its respective variables are obtained. By these properties, this paper finally solves spcial first order total differential equations and obtains the quadrature of total differential of some function with n-variables. The obtained method of solution is simpler than usual one.     

LARGE DEFLECTION OF A CIRCULAR PLATE ON PASTERNAK FOUNDATION UNDER A CONCENTRATED LOAD AT THE CENTER

Based on Karman's nonlinear foundamental differential equations, the new method combines perturbation method with integral equation method is forward to solve nonlinear bending of a clamped circular plate on Pasternak foundation under a concentrated load at the center. This method is simple and easy to use. The numerical results show that the present solution is reliable.     

PREDICTIVE INTELLIGENT CONTROL OF THE COLD STORAGE

The predictive intelligent control scheme is proposed, which is based on approximation theory and numerical method of Chcbyshev orthogonal polynomial. It has the practical value to the cold storge using widely electromagnetic valve and can be also applied similar systems in orther area.     

A NEW APPROACH OF OPTIMIZATION

In this paper, a necessary optimality condition of problems with equality constraints is investigated by the implicit function theorem in n-dimensional Euclidean space. A new approach solving these problems is obtained. The number of dimensions of corresponding system of equations is less than the classic Lagrangian multiplier method.     

A FAST ALGORITHM FOR DIGITAL SIMULATTON OF HVDC SYSTEMS

After considering the features of the differential equations which have described the dynamic behaviours of HVDC systems, a fast algori -thm is presented for these equations. Compared with the fourth Runge-Kutta Method,this method has less amount of calculation with the same precision, numerical stability and other properties. Therefore, the use of the method has greatly increased the speed of the digital simulation of HVDC systems.In this paper an example of calculation is given, and the results obtained hv using this example are compared with the results obtained by calculating with the fourth Runge-Kutta Method. The speed of simulation by using this method is about 1.8 timss as fast as that by using the fourth Runge-Kutta Method.     

AN OPTIMIZATION METHOD FOR SOLVING THE BOUNDARY WALUE QUESTION OF DIFFERENTIAL EQUATIONS

This paper presents an optimization method for solving the boundary value question of a differential equation on the basis of the trial-and-error method and the optimization method. As compared with the differential method, this method has some advantages such as quiker velocity at count, higher precision(especially at the boundary points) and can be widely used.     

Boundary Element Methods with Overlapping Domain Decomposition for Parabolic Problem

Boundary element method is a numerical method for solving partial differential equations. There are several formulations of boundary element method (BEM) applied to solve a parabolic differential equation.The approach,which employs time- dependent fundamental solution,allows longer time steps in time integration than other approaches,and this can cut down on time for computer implementation with high precision.Domain decomposition method,which decompose the domain that a given problem is to be solved into subdomains,has the advantages of reducing the large problem into smaller ones and reducing the complex problem into simpler ones,and allows parallel computing.An overlapping domain decomposition method is applied combining a boundary element formulation with time-dependent fundamental solution to solve a diffusion equation. Firstly, by domain decomposition, the problem divided into two problems on subdomains, and then the initial-Boundary problems are solved by boundry element method on each subdomain.Some numerical examples are presented to illustrate feasibility and efficiency of the method. The numerical experiments show that the convergence rate of the method is dependent with the overlapping degree of the subdomains.     

The Differential Scheme of Pricing for American Put Options

Based on the differential scheme,presents a numerical method of pricing for American put options.Firstly,the partial differential equation satisfied by the option price is transformed into a series of differential equations.Then,these differential equations are solved by the iterative method.The numerical method includes the implicit finite difference method and the explicit finite difference method and these two methods are compared.Finally,a numerical example is given and the validity of the algorithm is checked by a series of experiments.Some useful results are obtained for its application in the option markets.     

Information Structures in Portfolio Selection

This paper gives a brief presentation of the influence of different information structures on portfolio selection and some simple examples to demonstrate their basic algorithms. The first is the familiar mean_variance model. The model does not need more hypotheses on the motion of the asset price along the full continuous time axis,but sometimes many unanticipated computation problems may be involved because of the difficulty in computing the inverse of some matrices with high dimension. The second is the stochastic optimal control model. It is to solve a stochastic optimal control problem,which is often related to Hamilton_Jacobi_Bellman eqution.It results in solving partial differential equations of Riccati matrix differential equations. Their closed_form solutions are usually very hard to obtain. The last is the differential game model. The existence,uniqueness,and the computation for its equilibrium solution are all very difficult mathematical problems.     

THE CALCULATION OF FLOW USING SEMI-IMPLICIT METHOD FOR PRESSURE-LINKED EQUATIONS

This paper briefly introduces Patankar-Spalding Method, which is systematical, active and widely applicable in numerical heat transfer and fluid flow. The corresponding dependent variables, diffusivities and source terms for the general differential equations under all circumstances are explained. By using this method the calculation of two-dimentional Poiseuiue Flow and Couette Flow compared with exact solutions are proved to be high precision. with two-dimentional path-flow in the heat convertor intersification devices as an example, the tilted method is used with FORTRAN 77 programming, and the calculation is done on a SIEMENS 7570c minicomputer.     

ANALYSIS OF NONLINEAR PROBLEMS OF LAMINATED PLATES BY USE OF PERTURBATION AND WEIGHTEDRESIDUAL METHOD

This paper solves the geometrically nonlinear problems of symmetric, cross-ply laminated anisotropic rectangular plates subjected to uniformly distributed load by the higher-order shear deformation theory and taking an advantage of the perturbation and the weightedresidual method. First, with the help of the perturbation, the nonlinear partial equations have been changed into linear ones. This paper can solve these linear ones by the weighted-residual method. The combination of quintic B-spline functions are chosen as the basis of trial function and Dirac delta functtion, the weighted function. The method used in this paper is simple, direct and efficient. The numerical results show a good convergence and they are in good agreement with the available data.     

Singularly Perturbation of the Nonlinear Three Species Prey-predator Reaction Diffusion System

A class of nonlinear three species in the biomathematics is considered with the prey-predator singularly perturbed problems for the reaction diffusion system method of differential inequalities. Under suitable conditions, the existence and asymptotic behavior of solution for the initial boundary value problems are studied with the theory of differential inequalities. The theory of differential inequalities is really to constructing two auxiliary functions, which are super and lower solutions of the system respectively. And then the super and lower solutions are satisfied corresponding inequalities. Finally, there is a solution of the system between the super solution and lower solution. Then the existence of the solution for the system is proved and the asymptotic estimation is obtained.     

NONLINEAR ANALYSIS OF LAMINATED ANGLE-PLY PLATE USING A HIGHER-ORDER SHEAR DEFORMATION THEORY

A higher-order shear deformation theory is used to analyse nonlinear bending of symmetrically laminated angle-ply rectangular plates. The nonlinear governing differential equations are solved here by using perturbation method. Numerical rerults are presented graphically for vairous parameters of laminated plate. The present solutions are compared with those obtained using the classical plate theory. A lot of significient conclusions are obtained.     

紫黑色作物花色苷实验室定量检测方法研究

为了寻求快速、经济地测定自然界中紫黑色作物总花色苷含量的方法,利用酸性乙醇对黑元麦、茄子、葡萄3种不同作物进行花色苷提取,并采用pH示差法和差减法2种不同的实验室方法对3种样品总花色苷含量进行留样分析再测定。结果表明,黑元麦、葡萄采用pH示差法和差减法这2种测定方法的结果精确度和准确性没有显著性差异,且样品进行留样再检测时发现,2种样品测定结果之差的绝对值均小于测定结果质量不确定度,可以说明黑元麦、葡萄花色苷实验室定量检测pH示差法和差减法均适用。茄子采用pH示差法测定值相对标准偏差为2.20%,精确度明显好于差减法;从质控图看,茄子检出值出现1次连续4个点上升的情况,说明茄子皮利用差减法测定结果准确性差;从留样再检测结果可以看出,利用差减法测定2次结果之差的绝对值为0.023 mg/g,小于测定结果质量不确定度0.011 mg/g,说明茄子花色苷pH示差法检测结果可信赖,差减法检测存在问题。