查询词典 simultaneous equations

The distributions of transversal shearing and normal stresses obtained from constitutive equations and those from equilibrium equations agree with each other very well.

通过这部分的分析，得出了一个重要结论：根据该分析方法，由平衡方程与由物理方程得到的横向剪应力及横向正应力分布相当一致。

The variational principle of generalized potential energy is used to determine the unknown coefficients of above series. The distributions of transversal shearing and normal stresses obtained from constitutive equations and those from equilibrium equations agree with each other very well.

通过这部分的分析，得出了一个重要结论：根据该分析方法，由平衡方程与由物理方程得到的横向剪应力及横向正应力分布相当一致。

In the modeling of growth macroeconomic rational expectations , using the method of quadratic optimal dynamic programming, the steady state equations of Riccati equations under normal conditions is discussed, which makes a firm basis for the modeling of macroeconomic rational expectations .

针对采用二次最优动态规划建立的宏观增长经济合理预期模型，探讨了Riccati递推方程的稳态方程求取问题，推导出了一般情况下的Riccati稳态方程，为建立合理预期数量经济模型奠定了基础。

Now the scientific workers can evaluate them by Group contribution methods,some equations using other normal properties and some equations using the existed equation for other properties.

现有的估算方法主要分为基团贡献法，与某些常用物性相关联的经验或半经验估算式和基于某些求取其它物性的方程的经验或半经验估算式等。

For the LS problem, the method of normal equations needs less computation but its computed solution has poor accuracy. If QR factorization is used, more accurate solution can be got. However, its computation is nearly as twice as the method of normal equations.

对于线性最小二乘问题，混合方法的提出是企图在法方程法与QR分解方法之间取得某种平衡，希望能够节省计算量又同时保持计算解达到较高精度，但后者在理论上并未得到证明。

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

Don't listen to their haver, nothing of that sort.

别听他们胡说八道，根本就没那回事。

But bank's shares trade below their book value, suggesting that investors are skeptical.

但是，银行股票以低于账面价值的价格交易，这一点反应了投资者的怀疑。