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And then the influence of two of the damage models, the Kachanov and the gradient-dependent constitutive equations, on the well-posed properties of the fundamental equations in continuum damage mechanics is studied according to the characteristic method of the quasi-linear partial differential equations under the case of one dimension elastic damage.

首先从非局部理论出发，推导了应变梯度损伤本构方程；然后利用一阶拟线性偏微分方程组的特征理论，在一维弹性损伤情况下分析了两种不同的本构模型，即Kachanov损伤本构方程与应变梯度损伤本构方程，对连续介质损伤力学基本方程适定性的影响。

Synthesizing the degrees of freedom of both rotor and helicopter body, and involving time derivatives of flap motion coefficient and induced velocity model derived from vortex theory, the governing equations of helicopter maneuvering flight are derived properly, with combination of kinematic equations and dynamic equations.

集旋翼和机体之自由度并计及挥舞运动系数对时间的导数和涡流理论的诱速模型，把运动学方程和动力学方程组合起来，从而导出了机动飞行的控制方程。

The numerical model of non-linear wave in harbor, including the non-coupled and non-linear wave numerical model, the numerical model combined Boussinesq equations with Laplace equation and the coupled numerical model combined Boussinesq equations with Euler's equations, are studied.The studies on non-coupled and non-linear wave numerical model are following.

本文分别以Boussinesq方程，二维和三维Laplace方程，欧拉方程和牛顿第二定律作为基本控制方程，分别从非耦合非线性波浪计算模型(指单独采用一个计算模型：本文指Boussinesq方程，或边界元法解Laplace方程，或有限元法解Laplace方程)、Boussinesq方程与Laplace方程耦合计算模型、Boussinesq方程与欧拉方程耦合计算模型三个方面对港口非线性波浪计算模型展开了研究。

In the fourth chapter, some general equations are studied, of which Abel equation and some equations that have been intensively studied are the special cases.

第三章利用Abel方程已有的结果来讨论多项式系统的极限环的存在性，个数和稳定性，推广了水树良和蔡燧林的相关工作。

In addition,Various methods of stability analysis of wakes behind bluff bodies arediscussed,among which the general theory of absolute/convective instability is strictlyformulized from stability equations of viscous flow;the theoretical foundation of stabil-ity analysis of time-average flows is also discussed from basic equations of fluids,andthe reason for the stability analysis of time-average flow can predict the frequency inthe saturation state is explaned.

此外，讨论了钝体尾迹稳定性分析的各种方法，其中从粘性流的稳定性方程出发严格推导了绝对/对流不稳定性的理论公式；从基本方程出发探讨了采用时均流场作稳定性分析的可行性，并解释了用时均流场作稳定性分析可以更好地预示饱和频率的原因。

Taking into account the absorption of Cr 4+∶YAG in excitaion state,the Q switching rate equations are given and the equations are solved numerically by using computer.

在考虑Cr4＋∶YAG激发态吸收的情况下，给出调Q 速率方程组，并且利用计算机对该方程组进行数值求解。

Core saturation and the rotor bar skin effects were directly taken into account in the field calculation. The adopted circuit equations are suitable for describing the stator windings and the special rotor-bar connections of BDFM. The waveform of supplied voltage source may be an arbitrary. Three-dimensional end effects were considered in the circuit parameter corrected by classical formulas. In addition, the coupling and constraint equations were used to handle rotor rotation without any process of remeshing.

其特点是：铁心饱和以及转子导条集肤效应可以直接在场的计算过程中加以考虑；采用的电路方程可以方便地处理无刷双馈电机定子绕组和转子端环的各种特殊连接方式，电压源可以是任意电压波型；三维端部效应可以通过传统的方法在电路参数中加以修正；采用耦合与约束方程来处理转子转动问题，而无须不断地对转子重新进行刨分。

The Steady-state model is based on the PENG-ROB equation, that is, the material balance equations, Phase equilibrium equations, component additivity and the enthalpy balance equation.

稳态模型建立的基础是 PENG-ROB 方程，即物料平衡方程、相平衡方程、组分加和方程和焓平衡方程。

Aiming at the shortage of traditional numerical methods, the Adomian Decomposition Method is introduced to solve the nonlinear model equations in reaction engineering. ADM can give the approximate analytical solutions in a form of algebraic expressions for nonlinear equations.

针对传统数值求解方法存在的不足，将Adomian分解法(Adomian Decomposition Method，ADM)引入到反应工程非线性数模求解中，可给出非线性数模逼近解析解的代数表达式。

First,the basic formulas solving the artificial earthquake wave compatible with object response spectra are established;the integration equations are translated into the algebraic equations by interpolation function.

首先，从单质点系在地震作用下的反应出发，直接推导了求解与目标反应谱拟合的人造地震动基本公式；随后，利用插值函数将积分方程变换为代数方程组，进而从反应谱的变分求得人造地震动的时域变分。

We stopped by the old fashion ice cream parlor Manhattan Beach Creamery for some refreshment. The "No Shoes, No Shirt, No Problem" sign on the wall epitomizes the beach lifestyle.

我们去商店区的一家老式冰淇淋店坐坐，墙上挂著「没鞋，没上衣，没问题」的牌子完全捕捉了海滩生活的随性及风格。

"If therefore", argues Bellarmine we can offer our prayers and our satisfactions in behalf of those detained in purgatory, because we are members of the great body of Christ, why may not the Vicar of Christ apply to the same souls the superabundant satisfaction of Christ and his saints--of which he is the dispenser?

" "因此，如果"，认为贝拉明（德indulgentiis ，十四）"我们可以提供我们的祈祷和我们满意的代表那些被拘留在炼狱，因为我们是成员的伟大基督的奥体，为什麼可能不是牧师基督适用於同样的灵魂满意的过剩是耶稣和他的圣人-他是在配药？