应用数学和力学

1996 Vol. 17, No. 9

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Notes on a Study of Vector Bundle Dynamical Systems(Ⅱ)──Part1

Liao Shantao

1996, 17(9): 759-771.

Abstract(2060) PDF(470)

Abstract:
The study of linear and global.properties of linear dynamical systems on vector bundles appeared rather extensive already in the past.Presently we propose to study perturbations of this linear dynamics The perturbed dynamical system which we shallconsider is no longer linear.while the properties to be studied will be still global in general.Moreover.we are interested in the nonuniformly hyperbolic properties.In this paper,we set an appropriate definition for such perturbations.Though it appears somewhat not quite usual yet has deeper root in standard systens of differential equations in the theory of differentiable dynamical systens The general problen is to see which property of the original given by the dynamical system is persistent when a perturbation takes place.The whole contenl of the paper is deyoted to establishing a theorem of this sort.

On a Class of New KKM Theorem with Applications

Zhang Shisheng, Zhang Xian

1996, 17(9): 773-780.

Abstract(2246) PDF(504)

Abstract:
In this paper,a class of new KKM theorem is obtained which unifies and improves the correspontiling results in [2,3,6,7,11].As applications.we utilize our resultto obtain some matching theorem,coincidence theorem,coincidence theorem.fixed point theorem,mini-max inequality theorem and section theorem.

Hamiltonian System and the Saint Venant Problem in Elasticity

Zhong Wanxie, Xu Xinsheng, Zhang Hongwu

1996, 17(9): 781-789.

Abstract(2197) PDF(697)

Abstract:
The traditional semi-inverse solution method of the Saint tenant problem.whichis described in foe Euclidian space under the Lagrange syslemformulation,is updated to be solved in the symplectic space under foe conservative Hamiltonian system.It isproved in the present paper that all the Saint Venant solutions can be obtained directlyvia the zero eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian operator matrix.

Local Bifurcation Analysis of Strongly Nonlinear Duffing System

Bi Qinsheng, Chen Yushu, Wu Zhiqiang

1996, 17(9): 791-799.

Abstract(2653) PDF(492)

Abstract:
By using coordinate and nearly,identical transformations.the strongly nonlinear Duffing system is reduced to normal form in this paper.and then the bifurcation equations with different resonant conditions and their solutions are obtained.The local bifurcation diagrams and the transition sets on unfolding parmeter and physical parameter plane are analysized by singularity theory.

Pareto Equilibria of Multicriteria Games without Compactness,Continuity and Concavity

Ding Xieping

1996, 17(9): 801-808.

Abstract(1954) PDF(688)

Abstract:
In this paper.by using a minimax inequality obtained by the author,some existence theorems of Pareto equilibria for multicriteria games without compactness,continuity and concavity are proved in toplogical vector spaces and reflexive Banach spaces.

The Interaction of Plane SH-Waves and Non-Circular Cavity Surfaced with Lining in Anisotropic Media

Shi Shouxia, Han Feng, Wang Zhenqing, Liu Diankui

1996, 17(9): 809-820.

Abstract(2140) PDF(722)

Abstract:
This is an expand of the complex function method in solving the problem of interaction of plane.SH-waves and non-circular cavity surfaced with linig in anisotropic media.the use the method similar to that incorporated in [2] added with Savin's method for solving stress concentration of non-circular cavity surfaced with lining in elasticity.Anisotropic media can be used ic simulate the conditions of thegeology.The solving proceeding for this problem can be processed conveniently in the manner similar to that introduced in [2].In this paper.as illustrated in example numerical studies have been done for a square cavity surfaced with lining in anisotropic media.

Stability Analysis of Linear and Nonlinear Periodic Convection in Thermohaline Double-Diffusive Systems

Zhang Diming, Li Lin, Huang Hai

1996, 17(9): 821-828.

Abstract(1943) PDF(563)

Abstract:
A shortout analytic method of stability in Strong non-linear autonomous system is introduced into stability analysis of the themohaline double-diffusive system.Using perturbation technique obtains conditions of existence and stability for linear and nonlinear periodic solutions.For linear periodic solution in infinitesimeal motion the existence range of monotomic branch and oscillatory branch are outilined.The oscillatory branch of nonlinear periodic solution in finite-amplitude motion has unstable periodic solution when μ is smaller than critical value μ_c in this case of 0s-r_sc<<1.The stability conclusions under different direction of vortex are drawn out .

Fourier Nonlinear Galerkin Approximation for the Two Dimensional Navier-Stokes Equations

Hou Yanren

1996, 17(9): 829-836.

Abstract(2050) PDF(588)

Abstract:
In this paper,for viscous incompressible Navier-Stokes equations with periodic bonndary conditions,we prove the existence and uniqueness ot the solution corresponding to its Fourier nonlinear Galerkin approximation.At the same time we give its error estimates.

Forced Oscillations of Boundary Value Problems of Higher Order Functional Partial Differential Equations

Jin Mingzhong, Dong Ying, Li Chongxiao

1996, 17(9): 837-847.

Abstract(1952) PDF(573)

Abstract:
In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequalities.

Lagrangian Vector Field on Kahler Manifold

Zhang Rongye

1996, 17(9): 849-855.

Abstract(2080) PDF(535)

Abstract:
In this paper.we discuss Lagrangian vector field on Kähler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kähler Manifold.