等价方程

The first is based on the algebraically equivalent transformation to the standard centering equation xs=μe.

首先通过对中心化方程xs=μe实施代数等价变换，得到了新的不同的摄动方程组。

Then by using the Riemann's function of the operator and constructing an auxiliary problem, an integrodifferential equation equivalent to former problem is got.

然后利用该算子的Riemann函数，通过构造辅助问题，得到了一个等价积分微分方程。

Then by using the Riemanns function of the operator and constructing an auxiliary problem, an integrodifferential equation equivalent to former problem is got.

然后利用该算子的Riemann函数，通过构造辅助问题，得到了一个等价积分微分方程。

This article investigates the two-point boundary value problem to a coupled system of nonlinear fractional differential equations. By applying growth conditions on the nonlinear terms, we obtain an existence result of solutions. Our analysis relies on the Schauder fixed-point theorem and the reduction of the considered problem to the equivalent coupled system of integral equations.

本文讨论非线性分数阶微分方程耦合系统的两点边值问题，应用Green函数，将其转化为等价的积分方程耦合系统，并设非线性项在无穷远处有增长条件，应用Schauder不动点定理证明解而非限于正解的存在性。

First, we have proved that the constraint of local constant gradient angles is equivalent to the minimization of total variation. Based on this, a stronger continuity constraint of gradient angle is presented. The interpolation formula (a 3-degree-PDE) derived from the constraint can ensure the continuity of level lines and reduce the width of edges. The contrast invariant of the regularizer of the formula is also proved.

首先证明了局部恒定的梯度角约束插值等价于总变分最小化；在此基础上，提出一个具有更强连续性的梯度角约束，由这个约束条件导出的三阶偏微分方程使插值的图像既可以保证水平线方向的连续性，又减小图像边缘的宽度；最后证明了插值方程中正则项的对比不变性。

Firstly, we give out a reduction way for quasilinear generalized system A〓=G , and the concept of the index κ geometrically nonsingularity, where A is singular and of smooth kernal space. By using the canonical projection mappings onto the space of ker A , a class singular pointimpasse point only owned by nonlinear generalized system is also studied and we also prove that the regular index κ quasilinear generaized system A〓=G defined on the region W is equivalent with an ODEs 〓 defined on a submanifold W〓 of the W, so we reduce the problem of quasilinear generalized system to the problem of an ODEs.

首先利用投影函数，给出了拟线性广义系统A〓=G的一种归约方法，提出了指数κ几何非奇异的概念，同时对广义系统特有的一类奇点-寂点进行了研究，证明了正则指数κ的拟线性问题A〓=G等价于在其定义域W中某一个子流形W〓上的正常微分方程〓，从而将拟线性广义系统的问题归结为常微分方程问题。

Based on the equivalence between transformation equation and constrained equation consisting of times explicitly,the unified description of criteria for scleronomic constraint and scleronomic system is proposed.

根据变换方程与约束方程显含时间的等价性，提出了定常约束与定常系统判据的等同表述。

Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated.

针对弹塑性接触问题所构造的等价变分不等式，解除了弹塑性本构状态约束方程和接触状态约束方程的约束。

Stability of solutions of the cavitated bifurcation equation is discussed in each region by using the minimal potential principle, and the catastrophic phenomenon of cavity formation is explained. 2. In Chapter 4, problems of cavitated bifurcation for two spheres, which are composed of two different kinds of imperfect compressible hyper-elastic materials, were examined, respectively. The parametric analytic solutions of the radially deformed function and the parametric cavitated bifurcation solutions are all obtained for the two spheres.

利用奇点理论给出了空穴分岔方程在分岔点的等价正规形，将缺陷参数分成若干个区域，证明了当缺陷参数属于某些区域时，具有缺陷的超弹性材料球体发生空穴分岔时的临界载荷比无缺陷的小；并利用最小势能原理讨论了空穴分岔方程的解在各个参数区域内的稳定性，解释了空穴生成的突变现象。

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