应用数学和力学

1989 Vol. 10, No. 5

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Summation of Trigonometric Series By Fourier Transforms

Chien Wei-zang

1989, 10(5): 371-383.

Abstract(1594) PDF(590)

Abstract:
This paper gives the theorems concerning the summation of trigonometric series with the help of Fourier transforms.By means of the known results of Fourier transforms,many difficult and complex problems of summation of trigonometric series can be solved.This method is a comparatively unusual way to find the summation of trigonometric series,and has been used to establish the comprehensive table of summation of trigonometric series.In this table 10 thousand scries arc given,and most of them are new.

Fixed Point Indexes and Its Applications to Nonlinear Integral Equations Modeling Infectious Diseases

Zhang Shi-sheng, Bian Wen-ming

1989, 10(5): 385-392.

Abstract(1870) PDF(397)

Abstract:
In this paper the fixed point index problem for a class of positive operators with boundary control conditions is discussed,and some sufficient conditions for the fixed pointindex to be equal to 1 or 0 are given.Moreover,a general fixed point theorem of expansions and compressions for cone is obtained,which generalizes and improves the corresponding results of [3,8,9].As an application,we utilize the results presented above to study the existence conditions of positive solutions of nonlinear integral equations modelling infectious diseases.

Instability of Hagen-Poiseuille Flow For Non-axisymmetric Mode

Wang P.M., J. T. Stuart(F. R. S.)

1989, 10(5): 393-402.

Abstract(1552) PDF(383)

Abstract:
An investigation is described for instability problem of flow through a pipe of circular cross section.As a disturbance motion,we consider a general non-axisymmetric mode.An associated amplitude or modulation equation has been derived for this disturbance motion.This equation belongs to a diffusion type.The coefficient of it can be negative while Reynolds number increases,because of the complex interaction between molecular diffusion and convection.The negative diffusivily,when it occurs,causes a concentration and focussing of energy within decaying slugs,acting as a role of reversing natural decays.

The Continual Differentiate Peak-Unimodal Solutions of Feigenbaum’s Functional Equations

Cheng Bao-long

1989, 10(5): 403-409.

Abstract(1832) PDF(425)

Abstract:
For the famous Feigenbaum's equations,in this paper,we established its constructive theorem of the peak-unimodal,then we found out other paths to explore the peak-unimodal solutions.For example,we proceed on the direction to try the non-symmetrical continuous peak-unimodal solutions and C¹ solutions.

Classical Limits for the Coefficient of Variation for the Normal Distribution

Zhou Yuan-quan

1989, 10(5): 411-418.

Abstract(1632) PDF(524)

Abstract:
The exact classical limits for the coefficient of variation c for the normal distribution are derived.The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineering needs.Using Odeh and Owen's computational method and Brent's algorithm,the tables for the r-upper exact classical limits of coefficient of variation for normal distribution are calculated for the different confidence coefficient γ,the sample size n=1(1)30,40,60,120,the sample coefficient of variation ε=0.01(0.01)0.20.It is shown that if n<8,ε<0.20,then the γ-upper exact classical limits c_u for c are slightly higher than the exact fiducial limits c_u,F for c if.n>8,c<0.02,then c_u-c_u,F<5×10^-6.

Bending of Rectangular Thin Plates with Free Edges Laid on Tensionless Winkier Foundation

Bu Xiao-ming, Yan Zong-da

1989, 10(5): 419-436.

Abstract(1631) PDF(475)

Abstract:
In this paper,the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms.By assuming proper form of series for deflection,the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations.Because the boundary of contact region cannot be determined in advance,these equations are weak nonlinear ones.They can be solved by using iterative procedures.

Hopf Bifurcations of Nonautonomous Systems at Resonance

Cheng Chong-qing, Ji Wen-mei

1989, 10(5): 427-436.

Abstract(1606) PDF(538)

Abstract:
In this paper,Hopf bifurcations of nonautonomous systems at resonance are studied and similar results are obtained.

On the Method of Reciprocal Theorem to Find Solutions of the Plane Problems of Elasticity

Fu Bao-lian

1989, 10(5): 437-446.

Abstract(2038) PDF(691)

Abstract:
In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist,obtaining displacement expressions by means of the method of reciprocal theorem is actual.But in other conditions,when static force edge conditions or mixed ones exist,the obtained displacements are admissible.In order to find actual displacement,the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple,convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions.Evidently,it is a new method.

A High Accuracy Difference Scheme for the Slnuglar Perturbation Problem of the Second-Order Linear Ordinary Differential Equation in Conservation Form

Wang Guo-ying

1989, 10(5): 447-462.

Abstract(1660) PDF(391)

Abstract:
In this paper,combining the idea of difference method and finite element method,we construct a difference scheme for a self-adjoint problem in conservation form.Its solution uniformly converges to that of the original differential equation problem with order h³.

On the Singular Perturbation of a Nonlinear Ordinary Differential Equation with Two Parameters

Zhang Han-lin

1989, 10(5): 453-461.

Abstract(1724) PDF(521)

Abstract:
In this paper,the method of differential inequalities has been applied to study the boundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.

A Discussion about the Effectiveness on Using a Variate-Transformation to Find out Solutions of Mode Ⅲ Crack Problems in Power Hardening Media

Li Xiang-lin

1989, 10(5): 463-468.

Abstract(1437) PDF(374)

Abstract:
By the use of the transformations of physical plane to strain plane and physical planeto stress plane,an analytic expression of the asymptotic solution near a mode Ⅲ Crack tipin a power hardening medium can be obtained.In this paper the effectiveness of the transformation is discussed.Analytical results show that the transformation is effectiveexcept for a special limit case of power hardening media-the ideal plastic materials.