Study on the Travelling Wave Solutions of the KdV Burgers Equation

With the aid of the Lax Niouver transformation,the exact travelling wave solutions and the asymptotic travelling wave solutions of the KdV Burgers Equation are obtained.Furthermore,the series solutions are constructed with the Adomian integration.The relations of the travelling wave solutions between the KdV Burgers equation and the RLW Burgers equation are found.Moreover,a class of known exact solutions of the KdV Burgers equation are analysed.     

Vatiational Methods for Anti periodic Traveling Wave Solutions to a Forced Two dimensional Generalized KdV Equation

Using variational methods,we study the existence of the anti periodic traveling wave solutions to a forced two dimensional generalized KdV equation.     

MODIFIED BURGERS MODEL AND ITS APPLICATON TO HARDENED CONCRETE

In this paper, an exponential function is introduced to modify the viscous element of Burgers model. The result shows modified Burgers model is advantageous to describe the creep behavior of hardened concrete and the creep test results are in good agreement with the theoretical predictions of creep equations derived from modified Burgers model.     

The Initial Value Problem of Nonlinear Evolution Equation

This paper discusses the initial value problem of the nonlinear evolution equation. The uniqueness and stability of the solutions for the problem are proved. It is also obtained that the solution of the problem blows up in a finite time.     

Analysis of diffusion equation with the second and third boundary conditions based on steady state approximation

One dimensional diffusion equation is widely used to describe mass transfer in particles or droplets in a reactor. The length of the definition domain of the one-dimension Fick equation is limited, because it is determined by the scale of the particles or the droplets. The diffusion equation with a certain length of definition domain has no analytic solution unless series solution. So, to obtain approximate solutions of diffusion equation is of theoretical significance and practical significance. Firstly, assumption of constant concentration variance ratio is used instead of assumption of constant concentration frequently used in kinetics of process metallurgy. Secondly, a detail process to deal with diffusion equation based on steady state approximation is given, and the approximate solutions of the diffusion equation at certain conditions are obtained at the same time. By comparing the approximate solutions with the numerical solutions, it is concluded that the diffusive process of non-steady state is considerably well predicted by the approximate solutions, and approximate solutions accord with the situations being close to the final steady state a little better than accord with the situations being close to the begin of the diffusion, and it fairly satisfies the total mass balance.     

Existence and Stability of Periodic Solutions for Reaction-diffusion Systems with Time Delays

Periodic solutions of reaction-diffusion systems with time delays are investigated. It is constructed that the - per and lower control function of nonmonotone reaction term, and it is showed that the function satisfies a global Lipschitz condition and quasimonotone. A sort of effective method of studying differential equation with nonmonotone reaction term is gained. By using the method of upper and lower solutions and fixed point theorem, it is shown that periodic solutions of this system exist when reaction-term is not monotone and the boundary value system has a pair of coupled-upper and lower solutions. Some methods for proving the stability of the periodic solution are also given. And some known resuits are extended.     

Positive Solutions of a Kind of Special Nonlinear Neumann Boundary Value Problems

The purpose of this paper is to consider a kind of special nonlinear Neumann boundary value problems. The kind of boundary value problems has not Green function. Using suitable transformation,we can change these problems to general Neumann boundary value problems. By applying integral equation and degree theory on cone,the existence of n positive solutions is proved for the kind of problems,where n is an arbitrary natural number.     

Existence of Periodic Solutions for Reaction-diffusion Systems with Time Delays

Periodic solutions of reaction-diffusion systems with time delays are investigated. The upper and lower control function of nonmonotone reaction term is constructed. It is showed that the function satisfies a global Lipschitz condition and quasimonotone. A sort of effective method of studying differential equation with nonmonotone reaction term is gained. It is shown that periodic solutions of this system exist when reaction-term is not monotone and the boundary value system has a pair of coupled to-upper and lower solutions.     

A THEORETICAL BASIS OF EQUATION OF CORRELATION BETWEEN STRENGTH AND ELASTIC MODULUS OF CONCRETE

The equation of correlation between compressive strength and elastic modulus of concrete is derived on the basis of modified Burger's model. The result shows that the derived equation is similar to the empirical equation of correlation between compressive strength and elastic moulus of concrete. So this empirical equation is confirmed by rheology theory of concrete.     

The existence of limit cycles of some non-linear differential equations

The existence of limit cycles for the nonlinear oscillation equation is discussed, in which some hypothesis is omitted. The results of theorem 1 generalized the corresponding results for\.     

MAXIMUM PRINCIPLE AND NONTRIVAL SOLUTION FOR A STATIONARY WAVE EQUATION

The boundary-value problem of a non-linear equation is discussed. A necessary condition for existence of nontrival solution and a maximum priciple are proved.     

Research on a Risk Investment Portfolio with Stochastic Character

With the theory of stochastic differential equation, the authors discuss a problem of a class of risk investment portfolio with stochastic character. With the selection of appropriate utility function and combines the Hamilton-Jacobi-Bellman equation, under the assumption that an optimal portfolio exists, and by using the Homologous Lagrangian function, some quantitative results of this risk optimal investment portfolio are given. With these quantitative results, some qualitative results are got. These results concord with the results of the theory of risk investment.     

水平荷载作用下单桩的虚拟桩解法及参数

根据Muki&Sternberg的虚拟桩方法，将水平荷载作用下单桩的问题分解为弹性半空间扩展土和一根虚拟桩的叠加，其中虚拟桩的弹性模量等于桩的弹性模量与土的弹性模量之差。基于水平位移协调条件推导出求解桩土间相互作用所需要的第二类Fredholm积分方程，通过广义胡可定律推导出该积分方程间断点的显式解，从而提高了Fredholm积分方程的数值计算精度并简化了计算程序的编写，根据Mindlin解推导出位移影响函数，简化了位移函数的推导过程。参数分析表明，桩土弹性模量比对单位水平力作用下桩身最大弯矩的位置有明显的影响，随着桩刚度的增加，桩身最大弯矩的位置随之加深。     

Analytic Solution of Anchor Bolts with Dynamic Detection

Sonoprobe method has been applied in non-destructive inspection of anchorage project. Its fundament is that to use dynamic transient excitation for inducing anchor bar's elastic vibration. The flaws in the bar can be estimated or deduced by determining transient response of anchor bar. Based on the theory of elasto-dynamics, in this paper, a theoretical model of acoustic detection of anchor bar has been built up. On the mechanics field, this method means that if information of disturbance resource, boundary conditions and initial conditions has been given, the dominant equation describing medium motion would be established. That is, it leads to the problem of initial value or initial boundary value of hyperbolic type or hyperbolic-diffusibility type equation. Thereby the dynamic response could be solved. As an example, analytic solution of heterogeneous wave equation is deduced in case of bounded region.     

Remarks for Various Boundary IntegralEquations Reduced from the ExteriorNeumann Problem of Helmholtz Equation

This paper presents a discussion on various boundary integral equations reduced from the exterior Neumann problem of Helmholtz equation.The author analyses how the famous difficulty that some equations have no unique solution when the wave number k is an eigenvalue of an interior problem is arised in the course of reducing these equations from Helmholtz representations,and proposes a method of overcoming the difficulty,that is,introducing a direct boundary integral equation which has unique solution for all wave numbers k and is equivalent to the original boundary value problem.Besides,advantages and shortcomings for these integral equations are estimated respectively.     

用数学模型方法选择人工薪炭林树种

人工薪炭林是当前人工林建设中的重要林种,它与人民生活息息相关。笔者拟通过寻找区域内各主要适生薪炭林树种,对其采样的重量和样本燃烧的热值建立多元回归方程的数学模型的思想,从而找出燃烧热值最高的一种或者几种优势薪炭林树种,为科学准确选择合理的人工薪炭林树种提供理论依据。     

棉子油分近红外光谱测定技术研究

以近红外光谱分析技术无损、快速和高效等优点,建立棉籽油分含量的近红外分析模型,进行棉籽油分快速大批测定,提高分析水平和效率。218份陆地棉的脱绒光籽为定标样品,通过不同的光谱数学预处理和光谱反射方式,优化棉子含油量近红外光谱法所建立的回归方程。结果表明,采用(2,4,4,1)光谱数学预处理和散射校正(SNV)得到的回归方程效果最好,回归决定系数(RSQ=0.9773)和验证决定系数(1-VR=0.9646)最高,回归标准误差(SEC=0.6977)和交互验证标准误差(SECV=0.8714)最小。对30份验证样品的化学测定值和近红外光谱预测值相关系数高达0.9882,平均偏差0.65%,回归标方程具有很好的预测效果,可以在实践中应用。长江流域棉花杂交种棉子含油量平均值为28.05%,含油量在26.50%~30.05%区间的品种居多,具有很大的改良潜力。     

Equivalent Coustitutive Equation of Honeycomb Materials with Equivalent Couple Stresses within Plane Deformation

Equivalent couple stresses and non-symmetric equivalent stresses are introducedto describe the equivalent constitutive equation of honeycomb materials within plane deformation.Itis necessary for the materials of macroscopic polarity induced by some mesostructures.     

THE BASIC PROPERTIES OF CONDITIONAL EQUATION WITH ACCUMULATIVE STATE

Several aspects of the conditional equation derived from the accumulative equation are discussed in detail. The results indicate that the conditional equation not only is well consistent with the principles of electronegativity and absolute hardness equalization, but also satisfies the bonding of a full -prerequisite condition, e. g. two like electronic charge species repel and unlike attract each other'. In addition these principles are in the accumulative state. Mathematically, some other aspects of the conditional equation are worth studying based on the generalization of this equation.