应用数学和力学

1996 Vol. 17, No. 6

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Solutions for a System of Nonlinear Random Integral and Differential Equations

Ding Xieping, Wang Fan

1996, 17(6): 471-481.

Abstract(2152) PDF(528)

Abstract:
In this paper we first prove a Darbao type fixed point theorem for a system of continuous random operators with random domains. Thenb, by using the theorem. wegive the existence criteria of solutions for a systems of nonlinear random volterraintegral equations and for the Cauchy problem of a system of nonlinear random differential equations. The existence of extremal random solutions and random comparison results for these systems of random equations are also obtained our theorems improve and generalize the corresponding results of Vaughn Lakshmikantham Lakshmidantham-Leela De blasi-Myjak and Ding.

An h-Type Adaptive Finite Element

Xu Xing, Ling Daosheng, Ding Haojiang, Du Qinghua

1996, 17(6): 483-489.

Abstract(2097) PDF(453)

Abstract:
For h-lype adaptive finite element method, the local mesh refinement introduces irregular nodes and destroys the standard continuity between elements. The reference nodes of the irregular are used to interpolate element coordinates and displacements.The improved shape functions, of which the conventional shape functions. are a particular case, are presented to guarantee the continuity, No changes but the shape functions are needed when the mcthod is applied in finite element programs.the computational results the features of the method higher accuracy,simplicity.fewer degrees of freedom and less computation effort.

(Φ, Δ)-Type Probabilistic Contractor and Solutions for a Nonlinear operator Equations in Menger PN-Spaces

Fang Jinxuan

1996, 17(6): 491-496.

Abstract(2036) PDF(438)

Abstract:
The purpose of this paper is to introduce the coneept of (Φ,△)-type probabilistic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with such probabilistic contractor in Menger PN-spaces.The results presented in this paper improve and extend the corresponding results in [1] and [4-8].

A K-εTwo-Equation Turbulence Model for the Solid-Liquid Two-Phase Flow

Liu Xiaobing, Cheng Liangjun

1996, 17(6): 497-505.

Abstract(2382) PDF(580)

Abstract:
A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carrier fluid in a two-phase flow The continuity, the momentum, K and ε equations are modeled. In this model,the solid-liquid slip veloeites, the particle-particte interactions and the interactions between two phases are considered,The sandy water pipe turbulent flows are sueeessfuly predicted by this turbulince model.

A Regularity Theorem for a Certain Fourth-order Differential Operator

Liu Yingfan

1996, 17(6): 507-514.

Abstract(1772) PDF(498)

Abstract:
This paper provides a regularity theorem for certain fourth-order differential operator B_λ with λ. from which we have obtained two homoeomorphism classes in "nonlinear case" or three linear isomorphism classes in "linear case" about this operator respectively It is useful and convenient to explain certain types of stability properties in both directions of some flying vehiele in its moving process.

On the Stability of Forced Dissipative Nonlinear System

Chen Daduan, Liu Xiaoming, Shi Weihui

1996, 17(6): 515-522.

Abstract(1720) PDF(638)

Abstract:
This paper, applying the stratification theory, proves the instability of certain initial (boundary) Value problem of forced dissipative nonlinear system in atmospheric dynamies. An example in given.

Free Boundary Problem of the 2D Seepage Flow

She Yinghe, Sun Ying, Guo Xiaoming

1996, 17(6): 523-527.

Abstract(1707) PDF(465)

Abstract:
The free boundary of the seepage flow is a problem of close consideration in engineering. So far. an estimation of the wet set region usually needs a priori beforethe numerical analysis. and the configuration of the free boundary is then obtained by Successive approximation, The authors of this paper benefit from a new mathematical expression——The variational Inequality——to formulate the free boundary problem,which is then solved by the finite element method Instead of the conventional way of discretization, here finite element mesh is generated in the entere domain of thestudied medin and the free boundary of the seepage region can be defined directlywithout any process of iteration. The investigation gives a new effective scheme for the seepage flow analysis.

A Three-Dimensional Solution of the Problem of Three Fixed Centres

Qin Yiping, Nie Zhaoming

1996, 17(6): 529-532.

Abstract(1905) PDF(447)

Abstract:
Based on the definitions of three fixed centres in a four-dimensional space, a three-dimensional solution of the problem of three fixed centres is presented,which develops the plane solution of the problem.

Jordan Canonical Forms of Matrices over Quaternion Field

Chen Longxuan, Hou Renmin, Wang Liangtao

1996, 17(6): 533-542.

Abstract(2499) PDF(699)

Abstract:
Using quaternion multiplication and the double determinant theory over quaternion field. we proved that an arbitrary quaternion square matrix is similar to a unique Jordan canonical form indicated by its principal characteristic watues.

Existence of Solutions of Three-Point Boundary Value Problems for Nonlinear Fourth order Differential Equation

Gao Yongxin

1996, 17(6): 543-550.

Abstract(2304) PDF(618)

Abstract:
In this paper.the author uses the methods in [1,2] to study the existence of solutions of three point boundary value problems for nonlinear fourth order differential equation.

A Method for Solving the Dynamics of Multibody Systems With Rheonomic and Nonholonomic Constraints

Shui Xiaoping, Zhang Yongfa

1996, 17(6): 551-557.

Abstract(2872) PDF(663)

Abstract:
The solution of the dynamic problem of multibody systems subject to rheonomic and nonholonomic constraints is achieved by applying singular value decomposition of the constraint matrix and projections of the dynamic equations of the systems along the feasible and unfeasible directions of the constraints. Formula to solve the constraint reaction forces and a method to avoid the violation of the constraints are also given.The solution does not rely on coordinates used to describe the systems and is computational efficitive example is finally presnted.

The Method of Derivation of Mac-Millan’s Equation for the Non-Linear Non-Holonomic System

Qiu Rong

1996, 17(6): 559-561.

Abstract(1922) PDF(412)

Abstract:
The Mac-Millan's equation for the non-linear non-holongmic system in one order is derived by using only principle of differential variation of Jourdain. Therefore definition of Niu Qinping for the virtual displacentent is unnecessary. This is the natural deduetion of the method in this paper and so with the non-linear and non holonomic system in high order.

The Lagrange Dynamic Equations of Multi-Rigidhody Systems with External Shocks

Zhang Dingguo

1996, 17(6): 563-568.

Abstract(2306) PDF(575)

Abstract:
This paper discusses the problems of dynamie response of multi-rigidbody systems with external impulsive forces, and presents a set of equations with form of Lagrange method.These equations are easy to be caleulated by computer.