应用数学和力学

1990 Vol. 11, No. 11

Select articles

Display Method:

Yeh Kai-yuan, Ji Zhen-yi

1990, 11(11): 937-946.

Abstract(2153) PDF(501)

Abstract:
In this paper, a new method, exact element method for constructing finite element, is presented.It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variable coefficient under arbitrary boundary condition.Its convergence is proved and its ...

Fixed Point Index of Uniform Limit of Set-Valued Strict Set-Contractive Mappings and Its Applications

Ding Xie-ping, Lan Kun-quan

1990, 11(11): 947-959.

Abstract(2085) PDF(525)

Abstract:
In this paper, the class of uniform limit mappings of set-valued, strick set-contractive mappings is discussed.Furthermore, the fixed point index theory for the uniform limit mappings is established.Using the fixed point index theory, some positive fixed point theorems are proved.Our theorems genera...

Some Further Generalizations of Ky Fan’s Minimax Inequality and Its Applications to Variational Inequalities

Zhang Shi-sheng, Yang Gan-shan

1990, 11(11): 961-968.

Abstract(2637) PDF(570)

Abstract:
The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general version of the famous KKM theorem and Ky Fan's minimax inequality.As applications, we utilize the results presented in this paper to study the saddle point problem and the existence problem of...

Singular Perturbation of Boundary Value Problem of Systems for Quasilinear Ordinary Differential Equations

Lin Zong-chi, Lin Su-rong

1990, 11(11): 969-976.

Abstract(2124) PDF(675)

Abstract:
In this paper, we study the singular perturbation of boundary value problem of systems for quasilinear ordinary differential equations: x′=f(t,x,y,ε),εy″=g(t,x,y,ε)y′+h(t,x,y,ε), x(0,ε)=A(ε),y(0,ε)=B(ε),y(1,ε)=C(ε) where x,f,y,h,A,B and C belong to Rⁿ and a is a diagonal matrix.Under the appropriate...

The Method of the Reciprocal Theorem of Force Vibration for the Elastic Thin Rectangular Plates (Ⅱ)——Rectangular Plates with Two Adjacent Clamped Edges

Fu Bao-lian, Li Nong

1990, 11(11): 977-988.

Abstract(2431) PDF(694)

Abstract:
In this paper, applying the method of reciprocal theorem, we give the distributions of the amplitude of bending moments along clamped edges and the amplitude of deflections along free edges of rectangular plates with two adjacent clamped edges under harmonic distributed and concentrated loads.

Numerical Solution of Nonlinear Ordinary Differential Equation for a Turning Point Problem

Lin Peng-cheng, Bai Qing-yuan

1990, 11(11): 989-998.

Abstract(2349) PDF(568)

Abstract:
By using the method in [3], several useful estimations of the derivatives of the solution of the boundary value problem for a nonlinear ordinary differential equation with a turning point are obtained.With the help of the technique in [4], the uniform convergence on the small parameter ε for a diffe...

Boundary and Interior Layer Behavior for Singularly Perturbed Vector Problem

Zhang Xiang

1990, 11(11): 999-1005.

Abstract(2149) PDF(655)

Abstract:
In this paper, we consider the vector nonlinear boundary value problem:εy″=f(x,y,z,y',ε), y(0)=A₁ y(1)=B₁ εz″=f(x,y,z,z',ε), z(0)=A₂ z(1)=B₂ where ε>0 is a small parameter,0≤x≤1 f and g are continuous functions in R⁴. Under appropriate assumptions, by means of the differential inequalities, we de...

Fractal Geometry Derived from Geometric Inversion

Zhang Yong-ping, Xie He-ping

1990, 11(11): 1007-1012.

Abstract(2160) PDF(907)

Abstract:
In this paper, the conception of fractal geometry derived from geometric inversion is introduced.A ramified self-inverse fractal with symmetry and a self-inverse fractal dust set are constructed.The authors extend the conception of the fractal osculation and propose a new notion——fractal envelope.Fi...

High-Order Boundary Conditions for the Problems of Laplace Equation in Infinite Region and Their Application

Huang He-ning, Wang Fa-jun

1990, 11(11): 1013-1018.

Abstract(2460) PDF(636)

Abstract:
The high-order boundary conditions for the problems cf Laplace equation in infinite region have been developed.The improvement in accuracy for numerical solution is achieved by imposing the high-order boundary conditions on the exterior boundarv of a reduced finite region in which the numerical meth...

The Inefficiency of the Least Squares Estimator and Its Bound

Yang Hu

1990, 11(11): 1019-1025.

Abstract(3048) PDF(687)

Abstract:
It was suggested by Pantanen^[1] that the mean squared error may be used to measure the inefficiency of the least squares estimator.Styan^[2] and Rao^[3] et al.discussed this inefficiency and it's bound later.In this paper we propose a new inefficiency of the least squares estimator with the measure of...