查询词典 differential calculus

For the long composite cylindrical panels, including the influences of the transverse shear deformation, rotatory inertia and initial geometric imperfections, the nonlinear dynamic equations of the long composite cylindrical panels were derived from Hamilton's philosophy. The nonlinear partial differential equations were transformed to ordinary differential equations by expansion in series and solved numerically by fourthorder Runge-Kutta method.

针对含初始几何缺陷的复合材料圆柱曲板，考虑横向剪切变形、转动惯量、初始几何缺陷以及非扁壳等诸多因素，利用Hamilton原理导出复合材料长圆柱曲板的非线性动力方程；用级数展开把非线性偏微分方程组转化为二阶常微分方程组，并由四阶Runge-Kutta方法数值求解。

By changing differential equations into nonlinear integral equation,we study the existence of positive solution of a class of second order differential equations problems by the fixed point theorem of cone expansion and compression,and the fixed point index theorem,then we obtain two multiple positive .

通过将常微分方程转化为非线性积分方程，利用锥拉伸和锥压缩不动点定理和不动点指数讨论了一类二阶常微分方程的正解存在性问题，在一定条件下，得到了几个多重正解定理，同时证明了与此相关的主要引理

It is impossible to logically infer the classically expressed geodesic differential equation from the ontology differential geometry. Besides, the initial proposition how to construct a functional extreme value problem for the shortest curve on a surface, which was supposed first by Gauss, would be an improper formal expression with a wrong premise.

不仅仅无法由"实体论"微分几何逻辑地推导出经典的测地线方程，而且Gauss曾经为"曲面上最短线"问题所构造的泛函极值命题，实质上属于一个"前提认定"完全错误的不当表述。

Moreover,using Ito differential formul a to the constructed Lyapunov function along solutions of lto stochastic differential systems,Lyapunov method is adopted to set up the fundamental theory of dissipativity in the module corresponding to the theory on the dissipativity of deterministic ordinary dif- fere.

提出了有关Ito型随机微分系统耗散性理论的新概念：按模耗散、按模等度耗散和按模一致耗散，并利用Lyapunov方法，借助于Ito 微分公式沿着Ito型随机微分系统的解对所构造的Lyapunov函数求导数，给出了Ito型随机微分系统有关按模耗散理论的一些代数判据，获得了与确定性常微分系统耗散性理论相对应的结论，最后的算例证明了该方法的有效性和可行性。

Moreover, students should know some basic theories of initial value problem of differential equation, stability theory and first order linear or quasi-linear differential equations.

稳定性理论或一阶线性偏微分方程有所认识。

Using difference method, the first-order and the second-order differential equations of fractional derivative can become the first-order ordinary differential equation, and the high precision direct integration can be used for the solution.

所论方法首先引入差分格式，将含有分数阶导数的一阶和二阶微分方程变为一阶的常微分方程，然后再用精细积分方法逐步积分进行求解。

The stability of the complicated and high dimension stochastic functional differential systems with Markovian switching can be reduced to the stability of one dimension functional differential equation.

本文研究马尔可夫调制的随机泛函微分系统和脉冲泛函微分系统的稳定性。

In this thesis, we discuss several problems which exist to qualitative theory of the functional differential equation, within which we develop further two important theories, so-called the 3/2 - stability theory and the distribution of zeros of solutions of the functional differential equation.

本文中，我们对泛函微分方程定性研究中存在的若干理论问题进行探讨，对其中两个重要问题即3/2—稳定性理论和零点距估计问题，作了进一步推广。

In Chapters 3 and 4, we investigate the existence of periodic solutions of a class of second order functional differential equation and a class of third order functional differential equation, respectively, and obtain new sufficient conditions of their existence result of periodic solutions under growth conditions and linear growth condition, respectively.

第三章与第四章分别研究了一类二阶泛函微分方程及一类三阶泛函微分方程的周期解存在性，分别在增长条件及线性增长条件下，获得了这两类方程周期解存在性的新的充分条件，与文献中已知结果比较，我们所讨论的方程更为一般，所得结果较简洁且易于验证。

In Chapters 3 and 4, we investigate the existence of periodic solutions of a class of second order functional differential equation and a class of third order functional differential equation, respectively, and obtain new sufficient conditions of their existence result of periodic solutions under growth conditions and linear growth condition, respectively. Compared with some known results in the literature, the equations discussed by us are more general, and our results are concise and easy to be verified.

第三章与第四章分别研究了一类二阶泛函微分方程及一类三阶泛函微分方程的周期解存在性，分别在增长条件及线性增长条件下，获得了这两类方程周期解存在性的新的充分条件，与文献中已知结果比较，我们所讨论的方程更为一般，所得结果较简洁且易于验证。

Listen,point and check your answers.

听，指出并且检查你的答案。

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但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48