应用数学和力学

1991 Vol. 12, No. 11

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Probabilistic Contractor Couple and Solutions for a System of Nonlinear Equations in Non-Archimedean Menger Probabilistic Normed Spaces

Zhang Shi-sheng, Peng Yong-cheng

1991, 12(11): 965-972.

Abstract(2459) PDF(487)

Abstract:
The purpose of this paper is to introduce the concept of probabilistic contractor couple in non-Archimedean probabilistic normed spaces and to study the existencc and uniqueness of solutions for a system of nonlinear operator equations with probabilistic contractor couples in non-Archimedean probabilistic normed spaces. The results presented in this paper improve and extend the corresponding results in [1-5].

Analysis of Characteristics of Pressure Curve in Gas-Condensate Wells

Xu Xian-Zhi, Liu Ci-qun

1991, 12(11): 973-978.

Abstract(2031) PDF(403)

Abstract:
This paper utilizes a flow equation with a sink item that describes the characteristics of pressure-lime chart when the pressure is higher than the maximum condensate pressure. We have established a sink item to show the influence of accumulation of condensate liquid according to Duhamet Principle of Superposition, and introduced two coefficients for it: condensing strength R_D and condensing relaxation time λ_D. This paper gives the principle and the quantitative expression of the well pressure influenced by condensate function in the flow equation. An analytical solution for an infinite system is obtained (constant rate). These results can be used to analyse the unsteady flow test of constant production.

The Numerical Solution of a Singularly Perturbed Problem for Semilinear Parabolic Differential Eqnation

Su Yu-cheng, Shen Quan

1991, 12(11): 979-988.

Abstract(1959) PDF(498)

Abstract:
The numerical solution of a singularly perturbed problem for the semilinear parabolic differential equation with parabolic boundary layers is discussed. A nonlinear two-level difference scheme is constructed on the special non-uniform grids. The uniform con vergence of this scheme is proved and some numerical examples are given.

The Theorem of the Stability of Linear Nonautonomous Systems under the Frequently-Acting Perturbation and Its Application in the Stability Analysis of Robot

Zhang Shu-shun

1991, 12(11): 989-995.

Abstract(2088) PDF(470)

Abstract:
The necessary and sufficient condition of the stability of linear nonautonomous system under the frequently-acting perturbation has been given and proved on the basis of [1] and [2], and the theorem of the equivalence on the uniform and asymptotical stability in the sense of Liapunov ami the stability under the frequently-acting perturbation of linear nonautonomous system has been given in this paper. Besides, the analysis of the dynamic stabilitv of robot has been presented by applying the theorem in this paper, which is closer to reality.

An Exact Element Method for the Bending of Nonhomogeneous Reissner’s Plate

Ji Zhen-yi

1991, 12(11): 997-1005.

Abstract(1874) PDF(522)

Abstract:
In this paper, based on the step reduction method and exaet analytic method, a new method, theexacl element method for constructing finite element, is presented. Since the near method doesn't need varialional principle, it can he applied to solve nun-positive and positive definite partial differcntial equations with arbitral varutble coefficients. By this method, a triangle noncompatible element with 15 degrees of freedom is derived to solve the bending of nonhomogenous Reissner's plate. Because the displacement parameters at the nodal point only contain deflection and rotation angle, it is convenient to deal with arbitrary boundary conditions. In this paper, the convergcnce of displacement and stress resultants is proved. The element obtained by the present method can be used for thin and thick plates as well, hour numerical examples are given at the end of this paper, which indicates that we can obtain satisfactory results and have higher numerical precision.

On Diffusion Velocity and the Mass Conservation Equation for Components

Liu Da-you, Wu Bang-xian

1991, 12(11): 1007-1013.

Abstract(2083) PDF(489)

Abstract:
The mass migration velocity(absolute velocitv) of component i in a multicomponent flow is equal to the convection velocity (frame velocity) plus the diffusion velocity (relative velocity). The diffusion velocity as well as the corresponding diffusion coefficient depends on how the convection velocity is adopted.

The Theory and Applications of Generalized H-Space

Che Su-bing

1991, 12(11): 1015-1022.

Abstract(2399) PDF(502)

Abstract:
This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces. In this paper, the uniformity and properties far generalized H-space are considered. The conditions of metrization and the form of metric functions for generalized H-spaces, H-spaces and Menger PM-spaces are given and the characteristics of completeness and compactness for generalized H-spaces are presented. The results of this paper generalize and unify some recent results of [1-2, 8, 10].

The Symmetrical Bending of an Elastic Circular Plate Supported at k Internal Points

Li Nong, Fu Bao-lian

1991, 12(11): 1023-1028.

Abstract(2804) PDF(544)

Abstract:
This paper treats the symmetrical bending of a uniformly loaded circular plate supported at k internal points. The boundary displacement and slope are expanded in Fourier seriesr. The method proposed by [6] is applied. As both the governing differential equation and boundary conditions are satisfied exactly, we therefore obtain the analytic expression of the transverse deflectionul equation of the circular plate. This is an easy and effective methed.

Integrable Types of Nonlinear Ordinary Differential Equations of Higher-Orders

Tane Guang-song, Dong Ju-qing

1991, 12(11): 1029-1036.

Abstract(2280) PDF(602)

Abstract:
In this paper some integrable types of more general nonlinear ordinary differential equatients of higher-orders are proposed in virtue of Leibnite formula and fornudas of higher-order derivatives of the composite functions as well as substitution varable.The experssions for the general integrations of some of the equations are presented.The veenlts abtained are the generalization of those in the references.Finally some examples are also given.

Singular Perturbation of Boundary Value Problems for Second Order Nonlinear Ordinary Differential Equations on Infinite Interval (Ⅱ)

Zhao Wei-li

1991, 12(11): 1037-1048.

Abstract(2319) PDF(523)

Abstract:
In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameter is ε>0: examined, where α_i, β are constants, and i=0,1. Moreover, asymptotic estimates of the solutions for the above problems are given.

Some New Results about Fixed Pansystems Theorems

Liu Huai-jun

1991, 12(11): 1049-1053.

Abstract(1694) PDF(433)

Abstract:
In this paper the fixed pansy stems theorems concerning the composition-complement-operators are discussed. Some existence conditions of panchaos and strange panat tractor are given. And using the results, some fixed point theorems for many-valued mappings are also proved, which complement and develop the results obtained by Kakutani.

1991, 12(11): 1054-1054.

Abstract(1456) PDF(472)

Abstract: