应用数学和力学

2000 Vol. 21, No. 8

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Research on the Effect of Particle of Two-Dimensional Shear Flow

LIN Jian-zhong, SHI Xing, YU Zhao-sheng

2000, 21(8): 771-776.

Abstract(2052) PDF(614)

Abstract:
The two-way coupling model was adopted to study the two-dimensional gas-solid mixing layer. The flow was simulated by pseudo-spectral method and particles were traced with Lagrangian method. It is found that the concentration and the Stokes number of the particles have distinct effect on the flow not only accounting for the influence of the flow on the particles, but also the particles' counteraction on the flow. The particles accelerate the dispersion of the vorticity and inhibit the variance of the flow and diminish the intensity of the coherent structure. The lifetime of the vortex is shortened. The pattern of particles' distribution is similar to the results from one-way coupling model.

Basic Equations, Theory and Principle of Computational Stock Market (Ⅲ)-Basic Theories

YUN Tian-quan

2000, 21(8): 777-782.

Abstract(2773) PDF(784)

Abstract:
By basic equations, two basic theories are presented:1.Theory of stock's value=v^*(t)=v^*(0)exp(ar₂^*t). 2. Theory of conservation of stock's energy. Let stock's energy φ be defined as a quadratic function of stock price v and its derivative,φ=Av²+Bv+Cv²+Dv, under the constraint of basic equation, the problem was reduced to a problem of constrained optimization along optimal path. Using Lagrange multiplier and Euler equation of variation method, it can be proved that φ keeps conservation for any v. The application of these equations and theories on judgement and analysis of tendency of stock market are given, and the judgement is checked to be correct by the recorded tendency of Shenzhen and Shanghai stock markets.

The Dimension of Spline Space S₃¹(Δ) on a Type of Triangulation

ZHANG Xiang-wei, LIN Yi

2000, 21(8): 783-791.

Abstract(2019) PDF(516)

Abstract:
A harmonic condition that can distinguish whether the dimension of spline space S₃¹(Δ) depends on the geometrical character of triangulation is presented, then on a type of general triangulation the dimension is got.

Persistence in a Three Species Lotka-Volterra Nonperiodic Predator-Prey System

ZHANG Yin-ping, SUN Ji-tao

2000, 21(8): 792-796.

Abstract(1980) PDF(772)

Abstract:
The predator-prey model for three species in which the right-hand sides are nonperiodic functions in time were considered. It's proved that the model is persistent under appropriate conditions.

Bianalytic Functions, Biharmonic Functions and Elastic Problems in the Plane

ZHENG Shen-zhou, ZHENG Xue-liang

2000, 21(8): 797-802.

Abstract(3348) PDF(1763)

Abstract:
Let the elastic body only be acted by gravity. By investigating the relations of bianalytic functions and biharmonic functions, the uniqueness and existence of the stress functions (Airy functions) are established in planar simple connected region. Moreover, the integral representation formula of the stress function in the unit disk of the plane is obtained.

Influence of Couple-Stresses on Stress Concentrations Around the Cavity

ZHAO Jian-bin, LI Zi-guo

2000, 21(8): 803-808.

Abstract(2227) PDF(863)

Abstract:
The complex function method was used in the solution of micropolar elasticity theory around cavity in an infinite elasticity plane. In complex plane, the general solution of two dimension micropolar elasticity theory is given. The solution comes from analytic function and "Zonal Function". The boundary conditions of non-circular cavity are satisfied by using the conformal mapping method. Based on the method, a general approach solving the stress concentration in micropolar elasticity theory is established. Finally, the numerical calculation is carried out to the stress concentration coefficient of circular cavity.

Stress in Transversely Isotropic Half-Space With Typical Loads Acting on Its Surface

WU Shi-ming, LIANG Jian, HU Ya-yuan

2000, 21(8): 809-816.

Abstract(2061) PDF(744)

Abstract:
Based on the results of Hu and Lekhnitskii, the united solution of additional vertical stress coefficient for both transversely isotropic and isotropic half space was obtained. Five typical load cases, namely, vertical circular uniform load, rectangular uniform load, linearly distributed rectangular load, uniform linear and strip loads are studied in detail. The final solutions are expressed in terms of elementary functions. Numerical results show that there are anisotropic effects on the variation of additional vertical stress coefficients.

Minimal Essential Sets and Essential Components of the Equilibria of Production Economies

XIANG Shu-wen

2000, 21(8): 817-822.

Abstract(1876) PDF(552)

Abstract:
The purpose of this paper is to give a further study on the stability of production economies. The new results were given by considering the "set-valued" stability of equilibria. It is proved that there exists at least one minimal essential set of equilibrium points of the economy and every minimal essential set is connected. Based on these results, it is easy to prove that there is at least one essential component of the set of equilibrium points.

On the Spectral Equivalence of Unconventional Finite Elements and Their Conventional Relatives

HUANG Jian-guo, MU Jian-fei

2000, 21(8): 823-828.

Abstract(1849) PDF(635)

Abstract:
With a generalized conforming element as a typical example, the spectral equivalence of unconventional finite elements and their conventional relatives is proved. This result is very important for the construction of domain decomposition parallel algorithms for unconventional finite elements.

The Survival Analysis for Gallopin’s System in a Polluted Environment

HE Ze-rong, MA Zhi-en

2000, 21(8): 829-835.

Abstract(2318) PDF(593)

Abstract:
The long-time behavior of the consumer population in a Gallopin's system, located in a polluted environment, was studied. Firstly, a mathematical model, i.e.,a nonlinear ordinary differential system, was made by taking a constant catch rate into account in model of MA Zhi-en. Secondly, using the extension theorem and the comparison theorem, the bound of the system was estimated. Then, the effect of the pollution on the consumer population was discussed by the use of calculus and qualitative theory of differential equation. Finally, some conditions for weak persistence in the mean and extinction are found out. The threshold between persistence and extinction can be established in some cases.

The Existence and Uniqueness of Solutions of Generalized Variational Inequalities Arising From Elasticity With Friction

FU Ming-fu, WU Hong-fei

2000, 21(8): 836-842.

Abstract(2605) PDF(948)

Abstract:
The existence and uniqueness of solutions of generalized variational inequalities arising from elasticity with friction, which is equivalent to corresponding elemental problems, is elucidated in detail, and then FEM approximation and discrete methods are proposed.

The Complementary Property of Lindel^Lf’s Work and Chaplygin’s Work

LIANG Li-fu, CHEN Wei-dong

2000, 21(8): 843-851.

Abstract(2611) PDF(610)

Abstract:
Lindel^Lf's equation is derived by using the Vakonomic model,which shows that Lindel^Lf's work coincides with Vakonomic model. Chaplygin's equation is derived by using Chetaev's model, which shows that Chaplygin's work coincides with Chetaev's model. On basis of these, by improving the expressions of Chaplygin's equation and Lindel^Lf's equation, the reasonable transition from Chaplygin's equation to Lindel^Lf's equation is realized, the reasonable transition from Lindel^Lf's equation to Chaplygin's equation is realized too. Finally, a typical example is given. The work of this paper shows that, just as the Vakonomic model and Chetaev's model are complementary to each other, Lindel^Lf's work and Chaplygin's work are complementary to each other too.

Spherical-Symmetric Steady-State Response of Piezoelectric Spherical Shell Under External Excitation

LI Hong-yun, LIU Zheng-xing, LIN Qi-rong

2000, 21(8): 852-860.

Abstract(2604) PDF(540)

Abstract:
Spherical-symmetric steady-state response problem of piezoelectric spherical shell in the absence of body force and free charges is discussed. The steady-state response solutions of mechanical displacement, stresses, strains, potential and electric displacement were derived from constitutive relations, geometric and motion equations for the piezoelectric medium under external excitation (i.e. applied surface traction and potential)in spherical coordinate system. As an application of the general solutions, the problem of an elastic spherical shell with piezoelectric actuator and sensor layers was solved. The results could provide good theoretical basis for the spherical-symmetric dynamic control problem of piezoelectric intelligent structure. Furthermore, the solutions can serve as reference for the research of general dynamic control problem.

Mathematic Description About Random Variable With Fuzzy Density Function(RVFDF)

LÜ En-ling, ZHONG You-ming

2000, 21(8): 861-869.

Abstract(2482) PDF(950)

Abstract:
The random variable with fuzzy probability caused by fuzziness of probability density function was studied. The basic concepts/definitions and calculating methods of the interval/fuzzy probability density function, the random variable with fuzzy density function(RVFDF) and its distribution function, mathematical expectation and variance are given and some theorems related to the RVFDF are proved.

On Very Rotund Banach Space

ZHANG Zi-hou, ZHANG Cong-jun

2000, 21(8): 870-874.

Abstract(2020) PDF(657)

Abstract:
Three characteristics of the very rotund space are proved and the relationships between the very rotund space and the geometrical properties of Banach space are discussed. Also connection between the weakly exposed points and Radon Nikodym-property is established.

On the Existence of Solutions of Boundary Value Problems of Duffing Type Systems

HUANG Wen-hua, SHEN Zu-he

2000, 21(8): 875-880.

Abstract(2126) PDF(661)

Abstract:
Several existence results of solutions of two-point boundary value problems of Duffing type systems with Dirichlet boundary conditions, Neumann boundary conditions and periodic boundary conditions are presented.