应用数学和力学

1995 Vol. 16, No. 7

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Relativistic Absoluteness of Time-Space-Moving Mass

Chin Yuanxun

1995, 16(7): 573-576.

Abstract(1834) PDF(645)

Abstract:
A new theory of time-space-mass based on a mew invariant of special relativitv.

Inflation in Ω-Field Cosmology

Li Huacan, Yu Xin

1995, 16(7): 577-584.

Abstract(1872) PDF(404)

Abstract:
In thin paper.we shall apply the Ω-field theory as first proposed by Yu^[1] to cosmology.Under the assumption that the spacetime geometry of the Universe isdescribed by the Robertson-Walker metric and the matter temsor consists only of the Ω-field,the Universe is found to follow a de Sitter Expansion.The horizon and flatnes sproblems may thus be explained in a simple and natural way.

A General Topological Version of Minimax Theorem

Zhang Shisheng, Zhang Xian

1995, 16(7): 585-593.

Abstract(2056) PDF(501)

Abstract:
A more general topological version of minimax theorem inchuding the main resultsin König[3] as its special cases are given,and an open question suggested in König[3] is answered.

Stability for the Equilibrium State of Chaplygin’s systems

Zhu Haiping, Shi Rongchang, Mei Fengxiang

1995, 16(7): 595-601.

Abstract(2072) PDF(471)

Abstract:
The stability for the equitibrium states of Chaplygin's systems is considered.The equations of motion of Chaplygin's systems and the existence conditions of their equilibrium states are given.Some criteria of stability for the equilibrium.states of Chaplygin's systems are obtained.Two examples are finally given.

Increasing Property of Spectrum in the Vibrations of a Cyclic Chain of Masses Distributed According to the GTM Sequence

Shang Pengjian

1995, 16(7): 603-608.

Abstract(1733) PDF(443)

Abstract:
Generalized Thue-Morse sequences areint roduced into vibrational question of a hain of masses linked by springs of constant strength,and increasing property isproven of spectrum A_n of linear operator In about the vibrational model.

The Nonlinear Stability of Plane Poiseuille Flow for Non-Newtonian Power Series Fluid

Wang Zhendong, Zhou Zongke

1995, 16(7): 609-613.

Abstract(2455) PDF(513)

Abstract:
Non-Newtonan fluid is a kind of fluid whose components of stresstensor aren't theliear funtions of compoents of the strain rate tensor.Non-Newtonian fluid is being processed in many kinds of modern industry,Stability of flows for Non-Newtonian fluid is of important application,In this article we calculate subcritical thrdshold of flow which oecurs in polymer-processing when the melting substance is driven through two parallel fixed boundaries.

Series solution for Scattering of Plane SH-Waves by Multiple Shallow Circular-Arc Canyons

Fang Yingguang

1995, 16(7): 615-624.

Abstract(2127) PDF(638)

Abstract:
he analytcal method is used for the problem of seattering of plane SH-waves bymultiple shallow circur-are cangons.The solution of multiple scattering of plane SH-wares is first expressed as the sum of series of solutions im each of local coordinates using separation of variadles and is then converted into the form of dual infinite seriesof a local coordinate system by Graf's addition formula suitable for the interior and exterior problems.The solution of the problem is finally reduced to solving a set of infinite algbraic dquations:Numerical results of scattering influence on the motion on the earth surace are presented for the two adjacent shallow circular-arc canyons with the same diameter and variable depth-to-width ratio,and the effect of screening and interaction between canyons are discussed in the paper.

Hybrid Changeable Basis Galerkin Technique for Nonlinear Analysis of Structures

Zhao Qi, Ye Tianqi

1995, 16(7): 625-631.

Abstract(2029) PDF(557)

Abstract:
Based on the asynptotical perturbation method and the Galerkin Itechnique.thehybrid changeable basis Galerkin technique is presented for predicting the nonlinear response of structures.By the idea of changeable basis functions first proposed,itgreatly reduces calculation and is easily used in other numerical diseretization techniques,such as finite element method etc.,It appears to have high potential forsolution of nonlinear srtyctyrak oribkrbts.Finally,the effectiveness of this technique isdemonstrate by means of two numerical examples:the large deflection of circularplates objected to uniform normal load and the large deflection of spherical caps under centrally distributed pressures.

Parallel Multisplitting AOR Method for Solving a Class of System of Nonlinear Algebraic Equations

Bai Zhongzhi

1995, 16(7): 633-639.

Abstract(2207) PDF(617)

Abstract:
In this paper,we propose a class of parallel multisplitting AOR method for solving large-scale system of nonlinear algehraic equations Aφ(x)+Bφ(x)=b,Under certain conditions,we prove the exisrtence and uniqueness of the solution of thissystem of nonlinear equations and.set up thc globai convergence theory of the newmethod.

The Existence of the Solution for Linear Complementary Problem

Kou Shushun

1995, 16(7): 641-644.

Abstract(2266) PDF(1372)

Abstract:
This paper deals with the existince of the solulionlor linear complementaryproblern.The uniqueness theorem of lhe solution for linear compiementary.problem isproved.Two evaniples are given.They show that "Mis positive sermidefinite" neither sufficient nor necessary codition for the,existence to the solution of linear complementary problem.

Infinitely Many Solutions for Double Hamonic Perturbed Problem

Dai Qiuyi

1995, 16(7): 645-652.

Abstract(2046) PDF(572)

Abstract:
In this paper we consider the double hamonie perturbed problem on a bounded domain with boundary-value zero.the results which we have obtained havw improved the results obtained in [1].[3] and [4].

Nonlinear Oscillation Analysis by an Orthogonal Function Method

Sun Pizhong, Tang Qiangang, Sun Shixian

1995, 16(7): 653-661.

Abstract(2128) PDF(541)

Abstract:
In this paper an orthogonal function method is presented based on the idea to suppose perioche solution with the method of harmonie balance The displaeement is expressed in the form of trigonometric fumctions a group of simplified eigenequations are obtained by the use of orthogonarity of trigonometric fumetions and linear mondes The method overcomes the diffieulty of a drifi term existing in systems with quadratic nonlinearities.The ealeulation examples show that the method has thd advantages of high caleulation preeision high convergence speed and littld caleulation work.