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In order to illustrate the exponential function and the homogeneous balance method effectiveness, were cited in this (2 +1)-dimensional Burgers equation and the promotion of the Burgers-Kdv equation for example, comparing the pros and cons of the two methods.

为了说明指数函数法和齐次平衡法的有效性，在此分别引用(2+1)维推广的 Burgers 方程和Burgers-Kdv方程举例说明，对比此两种方法的利与弊。

To investigate the mechanism of the origination of combustion noise, a three dimensional wave equation is derived by using the control equation set of KIVA for deduction.

由于这些振荡受到很多因素影响，其复杂性导致了对燃烧过程中的噪声至今仍未有一个实时计算的手段。

The results show that the one dimensional model equation is compatible with Burgersequation and can be used to describe a flow in which large scale motion and small scale mo-tion exist simultaneously,the computation is convergent,the solutions have the same na-ture of that of Burgers equation but contain more informations.

一维模型的计算表明，求解是收敛的，模型方程与Burgers方程相容，解的性质与Burgers方程解的性质是一致的，但包括更丰富的信息。

Considering that the temperature gradient through thickness is much higher than that through width and length of plate, in this model, the governing equation of heat transfer was simplified as a one dimensional differential equation, and the series function solution for temperature is established in Lagrangian coordinate setting.

在该模型中，考虑到轧件厚度方向的温度梯度远大于沿宽度和长度方向的温度梯度，因而将热传导方程简化为一维微分方程，基于拉格朗日坐标建立了温度场的级数解法。

The proposed methods avoid the Riccati equation and Diophantine equation and can reduce the on-line computational burden.

本文提出的方法避免了求解Riccati方程和Diophantine方程，减小在线计算负担。

Diophantine equation is an old problem, especially, its more difficult to apply primary method to resolve the problems related to Diophantine equation.

不定方程是一个古老的丢番图问题，特别是应用初等方法去解决不定方程的有关问题更是不宜；许多解法很简单也易看懂，但却不宜想到。

Diophantine equation is an old problem, especially; it's more difficult to apply primary method to resolve the problems related to Diophantine equation. There are many solutions, which are very simple and also easy to understand, but hard to think out.

不定方程是一个古老的丢番图问题，特别是应用初等方法去解决不定方程的有关问题更是不易；许多解法很简单也易看懂，但却不易想到。

There are many solutions, which are very simple and also easy to understand, but hard to think out. Another name of indeterminate equation is Diophantine equation, its an important branch of the number theory, and also the most active in the field of mathematics through the whole history.

不定方程又称为丢番图方程，是数论的重要分支学科，是历史上最活跃的数学领域之一。1980年，著名的数学家柯召和孙琦在我国出版了第一部专门研究不定方程的专著《谈谈不定方程》。

We also give some conservation and convergence analysis for the Dirac equation and the Korteweg-de Vries equation.

在第七章中，我们建立了全直线上不带权的Legendre有理谱逼近，并以Dirac方程作为实例，证明了谱格式的守恒性和收敛性。数值结果表明了算法是有效的。

The main advantages of using the Dirac equation in a description of electrons are the following:(1) The Dirac equation is compatible with the theory of relativity (2) it describes the spin of the electron and its magnetic moment in a completely natural way.

在电子的描述中用Dirac方程描述主要优势有：（1）Diarc方程同相对论理论是一致的；（2）它很自然地描写了电子自旋和自旋磁矩。

There are different types of personal loans available.

有许多不同类型的个人贷款优惠。

The above mentioned teaching model of spiral rising can be used to avoid rigidness in teaching.

上述螺旋式上升的教学模式，可以避免教学形成模式後的僵化现象。