查询词典 equations

This thesis is divided into six parts. The first chapter is preface, the current status of research in the inverse problems for parabolic partial differential equations is reported; the second chapter is "regularization methods for numerical differentiation and their applications ", in this chapter we investigate many regularization methods from a viewpoint of regularization theory and algorithm, some applications in the inverse problems for parabolic partial differential equations are given; the third chapter is "spectral regularization methods". Based on Fourier analysis, within the framework of regularization theory, we apply the spectral methods to some ill-posed problems. Many numerical experiments are done in order to show the validity of the methods; the fourth chapter is devoted to wavelet dual least squares method and a revised wavelet method; in the fifth chapter,we combine finite difference method with method of lines and apply it to the backward heat conduction problem in time; in the sixth chapter "identification problems for unknown source ", the essence and the degree of two problems related to source identification are pointed out, at the same time, some numerical methods are reported.

本文分为六个部分，第一章前言简要分析了国内外抛物型偏微分方程反问题的研究现状；第二章数值微分的正则化及其应用从正则化理论和算法的角度出发，考察了许多正则化方法，还给出了数值微分在抛物型偏微分方程反问题的一些应用；第三章谱正则化方法是在Fourier分析的基础上，在一般正则化理论的框架下，给出了这种方法在各种不适定问题中的应用，数值实验表明谱方法是有效的；第四章研究了小波对偶最小二乘方法和改进的小波方法；第五章主要研究了有限差分方法结合线方法在时间反向热传导问题中的应用；第六章是未知源识别问题，主要指出了两类未知源问题的不适定程度和不适定本质，同时报告了一些数值方法。

By adapting the existed numerical methods for ordinary and delay differential equations, and matching certain suitable numerical quadrature formulas, Rosenbrock methods are constructed for delay integro-differential equations, the stability criteria of the methods are derived.

通过改造现有常及离散型延迟微分方程的数值方法，并匹配以适当数值求积公式，构造了求解时滞积分微分方程的Rosenbrock方法，导出了其稳定性准则。

In this paper,the method of interpolation for the numerical solution of tridiagonal system of linear equations is popularized,and another method of interpolation for quasi-tridiagonal system of linear equations is proposed.

文章将求解三对角线性方程组数值解的插值法进行推广，得到一种求解拟三对角方程组的插值算法。

The last one is to study the relation between the discrect process and the iteration theory for some derivative equations(for example,equations with conservation law) and to make benefit analysis of methods.

结合具体问题的数值求解，探求迭代理论和实际离散方法的有机结合，研究算法的效益分析。

This paper is composed of three chapters, which respectively discusses the following impulsive delay difference equations with discrete variables and continuous variables:In chapter 1, we investigate the oscillation and nonoscillation of equation and some sufficient conditions for oscillation and nonoscillation are obtained. Consequently we extend these results to the difference equations with several delays and with nonlinear impulsive perturbations and with variable delays respectively.

本篇论文由三章组成，分别讨论下面四类具离散变量和连续变量的脉冲差分方程这里p≥0，Q＞0，当n∈N(0)时；p∈C(-1，∞)，R~+，Q∈C

The results show that the equations have benefit to the deduction of the pantograph's mechanical differential equations.

研究结果表明：利用升角与升弓高之间的关系，可简化受电弓运动微分方程的推导；应用所建立的力学模型、实测数据以及简化公式可更准确地分析和计算弓网系统的力学行为。

This article bases on the knowledge of ordinary differential equation, mathematical and physical equations and equation of reactive pervasion. It researches the blow-up critical exponents of heat conduction type which is parabolic equations with nonlinear boundary constraints.

本篇论文以常微分方程与数学物理方程，反应扩散方程的知识为理论基础，讨论了热传导问题的临界指数问题，该问题是一个带齐次边界条件的非线性抛物型问题。

The viscosity solutions for partial differential equations of parabolic type havethree different basic definitions.The three definitions are equivalent when the equa-tions are continuous.But for the discontinuous equations,the equivalence of themare still unknown.

因为抛物型方程粘性解有三种基本定义法，它们在方程为连续时相互等价，对于不连续情况，它们间关系尚不明确，因而在本章里，我们特别证明了其中二个定义：定义1，定义2之间的关系。

This paper stated the application of parallel link mechanism in modern machine tools,set up the error analysis as to parallel link mechanism in the virtucal-axis machine tool,derived the double triangular error equations of parallel link mechanicsm in its horizontal posture,analyzed the linearity and non-singularity of the error equations,thus giving the normal splution to the horizontal posture error.

该文对并联机构在现代机床上的应用作了论述，建立了虚拟轴机床并联机构的一种误差分析方法，应用坐标变换原理导出了双三角并联机构水平姿态时的误差方程组；分析了误差方程组的线性和非奇异性，给出了水平姿态时的位姿误差正解；对工作空间中心线的误差分布规律进行了仿真，绘制了其误差分布曲线。

Chapter 2, we investigate the existence of multiple positive solutions of the neutral partial difference equations on the base of the existed results of partial difference and difference equations, and obtain some sufficient conditions for the existence of multiple positive solutions.

第二章，基于已有的偏差分方程和差分方程的结果，我们研究了高阶非线性中立型偏差分方程多正解的存在性问题，建立了判断多正解存在的充分条件，对前人的结果进行推广。

In this new architectural plan the Garden of Golgotha came to be at the centre of the new city.

Aelia 是高举他自己，并在此城内朝拜罗马诸神。

The continuous nature of peat accumulation means that terrestrial coaly rocks may provide a higher resolution and more complete record of base-level change than the time-equivalent shallow-marine strata, thus enabling the identification of highfrequency cycles that are not recorded in themarine strata.

泥炭积累的持续性质的手段，陆地coaly岩石可提供较高的分辨率和更完整的记录基准面变化的影响时，相当于浅海阶层，从而使确定的高频周期，不记录在themarine 阶层。