等价的

Although the Preissman scheme of KP equation is multisymplectic, it took too efforts to realize, Hence we elimate the auxiliary variable by a trivial computation and obtained the multisymplectic forty-five points scheme of KP equation. And then, we test this forty-five points scheme on soliton and solitary waves over long time intervals, the numerical results shows the propagation and interact of soliton and solitary waves.

但是在实际的数值实验中，由于需要计算共轭动量的值，Preissman格式需要占用的计算内存比较大，计算时间比较长，因此我们在数值格式中消去共轭动量，最后得到与多辛Preissman格式等价的一个多辛45点格式，我们用这个格式进行了数值实验，数值实验结果很好地显示了孤立子和孤立波的传播与碰撞。

Finally, the equivalence properties between Boolean matrix representation and algebra representation of attribute reduction are proved.

建立了布尔矩阵与逻辑方程组的解和决策表中的属性集之间的关系；然后在此基础上给出了决策表中的粗糙集理论的布尔矩阵表示；最后证明了属性约简在布尔矩阵和代数两种不同表示下是等价的。

The thesis consists of the followingmain results:the Cauchy's integral formula on certain distinguished boundaryfor LR regular functions with values in a universal Clifford algebra 〓,theCauchy's integral theorem,the mean value theorem,the maximum modulus the-orem.the Taylor's expansion,the Laurent's expansion and the residue theoremetc..

第一章叙述了泛Clifford代数基本理论，其中，我们首先准确而又富有创造性地给出了在泛Clifford代数〓上的一个对合运算表示，由此，我们给出了在泛Clifford代数〓上的一个内积，然后，我们借此给出了在泛Clifford代数〓上的相应的两个等价的范数，并证明了若在〓上赋予其中的一个范数，则〓是一个Banach代数。

It shows that a remarkable advantage of the symplectic methods applied to the Schrodinger equation is the precise preservation of charge conservation law. In order to study the numerical stability, we also adopt the different time step sizes.

为了比较，我们还给出了同阶的非辛算法的数值模拟，从而得到辛摄动配置算法和其在理论上等价的辛龙格-库塔方法在数值上的等效性以及辛算法在数值计算中的优越性。

Inequality proof of various ways, they were: use derivative testify inequality nature, Includes using functional monotonicity and extreme value, the function and the concave and convex inequality, proving is concave and convex function in the original definition of equivalent definitions and a lemma is proposed on the basis of relevant concave and convex function of several theorems about inequality, and briefly discusses how to use the definitions and theorems in proof of inequality.

不等式的证明方法多种多样，它们分别是：用导数性质证明不等式；包括利用函数单调性，极值与最值，函数凹凸性证明不等式，其中在给出凹凸函数原始定义等价的解析定义和一个引理的基础上提出有关凹凸函数关于不等式的几个定理，并简要阐述了利用定义和定理在证明不等式中的运用。

By getting Lebesgue characteristic of integrable function of Riemann from the definition of gather zero measure, it discusses the relation between almost continuous everywhere and existent of limit, and gets that the almost continuous everywhere is equal to the almost limit existence everywhere in the integrable function of Riemann.

通过定义零测度集给出了可积函数的特征，讨论了其几乎处处连续与极限存在的关系，即可积函数中几乎处处连续与极限的几乎处处存在是等价的，得出了比正规函数更加广泛的统一条件，得出了有界变差函数是可积函数的结论。

A mathematical model of oil and water two-phase non-Darcy fluid flow in the direction of normal of the ellipses with initial pressure gradient is taken into account, which is a nonlinear equation with moving boundary and is established according to concepts of perturbable ellipses and equivalent developing regulations.

基于扰动椭圆的概念和等价的发展矩形的思想，建立了具有启动压力梯度的油水两相非达西椭圆二维渗流数学模型。

The researchers changed the 'trolley on a line' thought experiment to locally suitable equivalents, such as crocodiles swimming towards canoes.

研究者将'轨道上的电车'思维试验改成符合当地特征的等价的东西，比如向独木舟游来的鳄鱼。

In particular, the ability to express equivalences using owl:sameAs can be used to state that seemingly different individuals are actually the same.

特别地，owl：sameAs的表达等价的能力，可被用来表达表面上不同的个体实际上是相同的。

This paper presented a new method of generating synthetic, seismograms of wave theory in frequency domain and gave the diffraction equation in frequency domain, which is equivalent to Kirchhoff one.

本文提出一种新的方法，在频率域中制作波动理论的合成记录，给出了与克希霍夫绕射波方程等价的频率域中的绕射波方程。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失