应用数学和力学

2003 Vol. 24, No. 6

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Safety Margin Criterion of Nonlinear Unbalance Elastic Axle System

CHEN Yu-shu, LI Yin-shan, XUE Yu-sheng

2003, 24(6): 551-558.

Abstract(2319) PDF(652)

Abstract:
The safety margin criterion of nonlinear dynamic question of an elastic rotor system are given. A series of observing spaces were separated from integral space by resolving and polymerizing method. The stable-state trajectory of high dimensional nonlinear dynamic systems was got within integral spac...

Research on the Flow Stability in a Cylindrical Particle Two-Phase Boundary Layer

LIN Jian-zhong, NIE De-ming

2003, 24(6): 559-564.

Abstract(2696) PDF(532)

Abstract:
Based on the momentum and constitutive equations, the modified Orr-Sommerfeld equation describing the flow stability in a cylindrical particle two-phase flow was derived. For a cylindrical particle two-phase boundary layer, the neutral stability curves and critical Reynolds number were given with nu...

Bifurcation of a Shaft With Hysteretic-Type Internal Friction Force of Material

DING Qian, CHEN Yu-shu

2003, 24(6): 565-571.

Abstract(2644) PDF(719)

Abstract:
The bifurcation of a shaft with hysteretic internal friction of material was analysed. Firstly, the differential motion equation in complex form was deduced using Hamilton principle. Then averaged equations in primary resonances were obtained using the averaging method. The stability of steady-state...

On Reich’s Open Question

ZHANG Shi-sheng

2003, 24(6): 572-578.

Abstract(2261) PDF(733)

Abstract:
Under more general form and more general conditions an affirmative answer to Reich's open question is given. The results presented also extend and improve some recent results of Reich, Shioji, Takahashi and Wittmann.

Simplest Differential Equation of Stock Price,Its Solution and Relation to Assumption of Black-Scholes Model

YUN Tian-quan, LEI Guang-long

2003, 24(6): 579-582.

Abstract(2285) PDF(1074)

Abstract:
Two kinds of mathematical expressions of stock price, one of which based on certain description is the solution of the simplest differential equation(S. D. E.) obtained by method similar to that used in solid mechanics, the other based on uncertain description(i. e., the statistic theory)is the assu...

Maximal Elements for G_B-Majorized Mappings in Product G-Convex Spaces and Applications(Ⅰ)

DING Xie-ping

2003, 24(6): 583-594.

Abstract(2437) PDF(713)

Abstract:
A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set-valued mappings were proved...

The Existence of Time Periodic Solutions for a Damped Generalized Coupled Nonlinear Wave Equations

FANG Shao-mei, GUO Bo-ling

2003, 24(6): 595-604.

Abstract(2487) PDF(863)

Abstract:
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to prove t...

Fracture Calculation of Bending Plates by Boundary Collocation Method

WANG Yuan-han, WU You-lun, YU Fei

2003, 24(6): 605-610.

Abstract(2564) PDF(783)

Abstract:
Fracture of Kirchhoff plates is analyzed by the theory of complex variables and boundary collocation method. The deflections, moments and shearing forces of the plates are assumed to be the functions of complex variables. The functions can satisfy a series of basic equations and governing conditions...

Propagation of Electromagnetic Wave in the Three Phases Soil Media

CHEN Yun-min, BIAN Xue-cheng, CHEN Ren-peng, LIANG Zhi-gang

2003, 24(6): 611-618.

Abstract(2470) PDF(737)

Abstract:
The fundamental parameters such as dielectric permittivity and magnetic permeability are required to solve the propagation of electromagnetic wave(EM Wave) in the soil. Based on Maxwell equations, the equivalent model is proposed to calculate the dielectric permittivity of mixed soil. The results of...

A Variation Method for Acoustic Wave Imaging of Two Dimensional Targets

FENG Wen-jie, ZOU Zhen-zhu

2003, 24(6): 619-623.

Abstract(2592) PDF(564)

Abstract:
A new way of acoustic wave imaging was investigated. By using the Green function theory a system of integral equations, which linked wave number perturbation function with wave field, was firstly deduced. By taking variation on these integral equations an inversion equation, which reflected the rela...

The Controllability of Delay Degenerate Control Systems With Independent Subsystems

JIANG Wei

2003, 24(6): 624-630.

Abstract(2488) PDF(784)

Abstract:
The controllability of delay degenerate differential control systems is discussed. Firstly, delay degenerate differential control system was transformed to be canonical form, and the connected terms were gotten rid of, had delay degenerate differential control systems with independent subsystems. Fo...

Soliton-Like Thermal Source Forcing and Singular Response of Atmosphere and Oceans to It

ZHANG Ren, SHA Wen-yu, JIANG Guo-rong, WANG Ji-guang

2003, 24(6): 631-636.

Abstract(2634) PDF(619)

Abstract:
Non-linear dynamic study is undertaken of the response of atmospheric and oceanic flow fields to local thermal source forcing in the context of a generalized geophysical fluid dynamic barotropic quasi-geostrophic model, discovering a good relation between thermal disturbance and flow field response ...

Crack Problem Under Shear Loading in Cubic Quasicrystal

ZHOU Wang-min, FAN Tian-you, YIN Shu-yuan

2003, 24(6): 637-643.

Abstract(2554) PDF(536)

Abstract:
The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function. Based on the work, the analytic solutions of elastic field of cubic quasicrystal with a penny-shaped crack under the shear loading are f...

The Dynamic Model of Crop Growth System and Numerical Simulation of Crop Growth Process Under the Multi-Environment External Force Action

LI Zi-zhen, WANG Wan-xiong, XU Cai-lin

2003, 24(6): 644-652.

Abstract(2418) PDF(852)

Abstract:
According to the biomechanic theory and method, the dynamic mechanism of crop growth under the external force action of multi-environment factors (light, temperature, soil and nutrients etc.) was comprehensively explored. Continuous-time Markov(CTM) approach was adopted to build the dynamic model of...

Global Linear and Quadratic One-Step Smoothing Newton Method for Vertical Linear Complementarity Problems

ZHANG Li-ping, GAO Zi-you

2003, 24(6): 653-660.

Abstract(2128) PDF(690)

Abstract:
A one-step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so-called aggregation function. The proposed algorithm has the following good features: (i) it solves only one linear system of equations and does only one line search at each iteratio...