应用数学和力学

1996 Vol. 17, No. 11

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New Version of KKM Theorem in Prohahilistic Metric Spaces with Applications

Zhang Shisheng, Yeol Je Cho, Wu Xian

1996, 17(11): 951-960.

Abstract(2253) PDF(413)

Abstract:
In this paper we first introduce the concept of probabilistic interval space. Under this framework a new version of KKM theorem is obtained. As application, we utilize this result to study some new minimax theorem. section theorem, matching theorem,coincidence theorem and fixed point theorem in probabilistic metric spaces. The results presented in this paper not only contain the main resull of von Neumann[7] as its special case but also extend the corresponding resulls of [1, 3, 4, 6, 8] to the case of probabilistic metric spaces.

A Non-lncremental Time-Space Algorithm for Numerical Simulation of Forming Process

Liu Baosheng, Chen Dapeng, Liu Yu

1996, 17(11): 961-968.

Abstract(1868) PDF(474)

Abstract:
A non-incremental time-space algorithm is proposed for numerical. analysis of forming process with the inclusion of geometrical, material, contact-frictional nonlinearities. Unlike the widely used Newton-Raphson counterpart, the present scheme features an iterative solution procedure on entire time and space domain. Validity and feasibility of foe present scheme are further justiced by the numerical investigation herewith presented.

The Proof of Fermat’s Last Theorem

Wong Chiahe

1996, 17(11): 969-978.

Abstract(1810) PDF(507)

Abstract:
(i) Instead of xⁿ+yⁿ=zⁿ,we Use as the generzl equation of Fermat's Last Theorem (FLT),where a and b are two arbitrary natural numbers.

On the Boundedness and the Stability Results for the Solution of Certain Fourth order Differential Equations via the Intrinsic Method

Cemil TUNC, Aydin TIRYAKI

1996, 17(11): 979-988.

Abstract(2127) PDF(403)

Abstract:
In this paper, we first present constructing a Lyapunov function for (1.1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p o,and the boundedness result of the solutions of (1.1) for case p=0. These results improve sveral well-known results.

Splitting Method for Two-Dimensional Phreatic Flow Equation

Xu Shaohui, Zhu Xueyu, Zhu Guorong

1996, 17(11): 989-995.

Abstract(1897) PDF(543)

Abstract:
In this paper, according to their difference in "physical meaning", twodimensional phreatic flow equation, which has been transformed, is devided into two parts──advection and dispersion by the splitting method. For the former, alternating direction finite difference method will be used and for the faller, it is resolved by altemating direction Picarditeration, therefore, the aim of computing the solution of whole problem will be reached. At last, the validitt of the algorithms is proved by the numerical example. The comparison of the proposed method with the conventional finite difference (linearized) is made. The results show that the precision of calculationby the method proposed in this paper is better than the conyentional methods.

Computer Simulation of the Motion of the Bullet Belt of Airplane Gun

Zhang Dingguo

1996, 17(11): 997-1004.

Abstract(1804) PDF(439)

Abstract:
With the dynamic theory of multi-rigidbody systems, first this paper establishes the mathematical amodel of dynamics and impact dynamics of the bullet belt of airplane gun, and then it carries cut the numerical and graphic simulation of the motion of the bullet belt by way of computer.

Quasi-Flow Corner Theory on Large Plastic Deformation of Ductile Metals and its Applications

Hu Ping, Liu Yuqi, Guo Wei, Tai Feng

1996, 17(11): 1005-1011.

Abstract(1815) PDF(515)

Abstract:
A quasi-flow corner theory on lalge plastic deformation if ductile metals is proposed in this paper. From orthogonal rule of plastic flow, the theory introduces a "modulus rethtced function" and a corner effect of yield surface into the constilulive model of elastic-plastic large deformation. Thereby, the smooth and continuous transitions from orthogonal constitutive model to non-orthogonal one, and from plastic loading to elastic unloading are realized. In addition, the theory makes it possible to connect general anisotropic yield functions with corner hardening effect. The comparison between numerical simulation and experimental observation for the uniaxial tensile instability and shear band deformation of anisotropic sheet metals shows the validity of the present quasi-flow corner theory.

A High-order Accuracy Explicit Difference Scheme for Solving the Equation of Two-Dimensional Parabolic Type

Ma Mingshu

1996, 17(11): 1013-1017.

Abstract(2091) PDF(649)

Abstract:
In this paper, a three explicit difference shcemes with high order accuracy for solving the equations of two-dimensional parabolic type is proposed. The stability condition is r=△t/△x²=△t/△y²≤1/4 and the truncation error is O (△t²+△x⁴).

Existence Theorems of Extremal Solutions for a Class of Nonlinear lntegro-Differential Equations

Song Guangxing

1996, 17(11): 1019-1024.

Abstract(2046) PDF(396)

Abstract:
In this paper, the following initial value problem for nonlinear integro-differential equationis is considered, where Using the method of upper and lower solutions and the monotone iterative technique.We obtain existence results of minimal and maximal solutions.

Further Study on Large Amplitude Vibration of Circular Sandwich Plates

Du Guojun, Chen Yingjie

1996, 17(11): 1025-1031.

Abstract(1812) PDF(557)

Abstract:
In this paper, a solution of axisymmetric large amplitude vibration is presented for a circular sandwich plate with the flexure rigidity of the face layers taken into account. In solving the problem, the modified iteration method is proposed. Then our results are compared with those from paper [1].

Singular Perturbation for a Nonlinear Boundary Value Problem of First Order System

Chen Songlin

1996, 17(11): 1033-1038.

Abstract(2184) PDF(482)

Abstract:
In this paper, we study the following perturbed nonlinear boundary value problem of the form:εx'=f(t,x,y,ε)εy'=g(t,x,y,ε)x(0)= A(ξ₁,ξ₂,x(1) -x(0),y(1)- y(0),ε)y(0)=B(ξ₁, ξ₂,x(1)-x(0),y(1)-g(0),ε) where ξ₁, ξ₂ are functions of ε. 0<ε<<1. Under some suitable conditions, we give the asymptotic expansion of solution of any order, and obtain the estimation of remaindet term by using the comparison theorem.

Blow-Up and Die-out of Solutions of Nonlinear PseudoHyperbolic Equations of Generalized Nerve Conduction Type

Wang Fanbin

1996, 17(11): 1039-1043.

Abstract(2732) PDF(415)

Abstract:
This paper considers the initial boundary value problems with three types of the boundary conditions for nonlinear pseudo-hyperbolic equations of generalized nerve conduction type, using foe eigenfunction method, the conditions for which the solutions blow-up and die-out in the finile time are got.