数学物理学报(英文版)

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PARTIAL ELIMINTATION ALGORITHM FOR A LINEAR RECURRENCE SYSTEM R(n, m) OF ORDER m

郑慧娆, 黄传河, 樊戊

数学物理学报(英文版). 1993 (3): 241-250.

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This paper presents an algorithm for computing a linear recurrence system R(n, m) of order m for n equations on MIMD parallel system. This algorithm is not only easy to be programmed on a parallel computer system, but also reduces the data-waiting time due to compute-ahead strategy. The paper analyses how to achieve maximal load balancing when the algorithm is implemented on MIMD parallel system. By the end of the paper, an analysis on the speedup and parallel efficiency are given. The results indicate that the new parallel elimination algorithm has great improvement compared with the old ones.

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EXPONENTIALLY BOUNDED C-SEMIGROUP AND INTEGRATED SEMIGROUP WITH NONDENSELY DEFINED GENERATORS I:APPROXIMATION

郑权, 雷岩松

数学物理学报(英文版). 1993 (3): 251-260.

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In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.

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ON DENSITY OF SMOOTH ELEMENTS FOR AN ACTION OF AN AMENABLE GROUP

颉火安

数学物理学报(英文版). 1993 (3): 261-265.

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The aim of this paper is to prove the problem 2.2.2 in Braiteli's paper. It is proved that the problem is true for amenable group action.

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ON THE REGULARITY OF THE MINIMUM SOLUTION OF THE RESTRAINED VARIATIONAL PROBLEMS

沈尧天, 郭信康

数学物理学报(英文版). 1993 (3): 266-272.

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This paper is concerned with the regularity of minimum solution u of the following functional
L(u)=∫₀a_αβ(x)g_ij(u)D_auⁱD_βvⁱdx
on the restraint E={u∈W₀^1,2(Ω,R^N)||u|_{L_p}=1}Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Hölder continuous.

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CHAOTIC MOTION PRODUCED IN FREE CONVECTIVE AND INERTIAL MOTION OF ATMOSPHERE

朱凯成, 李湘如

数学物理学报(英文版). 1993 (3): 273-281.

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In this paper a nonlinear model of convective and inertial motion of atmosphere with damping is studied with Melnikov's function method, The results show that in the atmospheric motion under periodic forcing chaos can occur independently whether the atmospheric motion is stable or not; and it is the key to produce chaos that the distribution of relevant physical quantity is nonlinear and periodically driven exists. The formulae calculating the parameter ranger in which chaos occur are given as well.

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THE WEAK DETONATION SOLUTIONS TO THE SIMPLEST COMBUSTION MODEL

谭得春, 张同

数学物理学报(英文版). 1993 (3): 282-292.

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In the present paper the authors prove that all the generalized entropy solutions of the CJmodel, which for the given Riemann initial data are a oneparameter family u^η characterised by weak detonation discontinuity point η, are just the limits of the admissible solutions u_ek of the selfsimilar combustion model. In fact, the authors prove that for any possible η, there exists a constant B>0 s.t.
u^η=lim_{εk-e,e→0⁺,k→+m} u_εk

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THE CONDENSATION EXTENSION AND THEMULTIPLE POSITIVE FIXED POINTSOF THE CONDENSING MAPPING

刘清荣, 仝松林, 巩馥州, 孙万贵

数学物理学报(英文版). 1993 (3): 293-307.

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In the paper the authors present some formulae to the condensation extension and k-set contractive extension of a condensing mapping and a k-set contractive mapping respectively, and obtain the sufficient conditions for a condensing mapping to have two or three fixed points. At last they apply their results to solve the generalized H-equation and two-points boundary value problems.

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COPLANAR CRACKS IN A FINITE TRANSVERSELY ISOTROPIC ELASTIC SLAB UNDER ANTIPLANE SHEARL STRESSES

洪怀忠

数学物理学报(英文版). 1993 (3): 308-315.

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An antiplane crack problem concerning a pair of coplanar cracks in a finite transversely isotropic elastic slab is considered. Using Fourier integral transform together with singular integral equation which can be solvel numerically by suing a collocation technique. Once the integral equation is solved, the relevant crack energy and stress intensity factors of the problem are given. The analysis present can be easily extended to include cases where there are two or more pairs of coplanar cracks in the slab.

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ASYMPTOTIC AND OSCILLATORY BEHAVIOURS OF SOLUTIONS OF THE 1ST ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH SEVERAL DELAY ARGUMENTS

俞元洪, 傅希林

数学物理学报(英文版). 1993 (3): 316-322.

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In this paper authors consider a class of the first order nonlinear neutral differential equations with several delay arguments. Sufficient conditions are obtained which ensure that all nonoscillatory solutions tend to zero as t→+∞. Criteria are established for all solutions to oscillate.

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THE WELL-POSEDNESS OF THE ABSTRACT KINETIC EQUATION BOUNDARY VALUE PROBLEMS

许跟起

数学物理学报(英文版). 1993 (3): 323-334.

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In this paper the abstract boundary value problem on Hilbert space H is studied:
T d/dx=-A(x)ψ(x)+f(x) 0 < x < a Q+ψ(0)=a₁Q+ψ(a)+g₊ 0<a₁,a₂ ≤ 1 Q-ψ(a)=a+2Q-ψ(0)+g_-
where Q₊/Q_- are the maximum positive/negative spectral projections of self-adjoint operator T. Under suitable conditions, it is shown that the boundary value problem of abstract kinetic equation is well-posed and can be applied to transport theory.

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MAXIMUM NORM ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF THE STATIONARY AND NONSTATIONARY NAVIER-STOKES PROBLEMS

沈树民, 邓庆平

数学物理学报(英文版). 1993 (3): 335-349.

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This paper deals with maximum norm error estimates of conforming finite element approximate solutions for the stationary and nonstationary Navier-Stokes problems in a plane bounded domain, using the so-called velocity-pressure mixed variational formulation. Quasi-optimal maximum norm error estimates of the velocity and its first derivatives, and the pressure are obtained for conforming finite element approximations of the stationary Navier-Stokes problem by some estimates of the Green function and their finite element approximations for Stokes problem. Moreover, with the method of Navier-Stokes projection, quasi-optimal maximum norm error estimate results are shown for semidiscrete conforming finite element approximations of the nonstationary Navier-Stokes problem.

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THE BIFURCATION ANALYSIS OF EXISTENCE AND TABILITY OF POSITIVE STEADY-STATE SOLUTION FOR A ONE-PREDATOR-TWO-PREY SYSTEM

宋开泰, 周笠

数学物理学报(英文版). 1993 (3): 350-360.

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This paper discusses the existence and stability of steady-states for a three-dimensional system ef parabolic partial differential equations subject to Dirichlet boundary conditions, i.e. the situation in which a predator feeds on twoprey species. Resultts are obtained by the use of spectral analysis and bifurcation theory.

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