查询词典 comparison theorem

This paper mainly introduces several different methods to prove the mid-value theorem, at the same time the mid-value theorem is applied in the mathematical theory, such as the application and mathematical modeling.

本文主要推荐几种不同的方法证明微分中值定理，同时对微分中值定理加以应用，如在数学理论中和数学建模中的应用。

When proving the differential mid-value theorem,"Higher Mathematics" does know to make the auxiliary function ф in order to apply Rolle Theorem.

在证明微分中值定理时，《高等数学》作辅助函数ф的目的是为了应用罗尔定理。

Equidistance point and difference theory in theory of function approximation are studied. Meanwhile, the relation among difference, difference quotient and derivate is revealed. By drawing Lagrange's and Cauchy's theorem of mean on difference and Taylor's formula into difference function, four theorems, such as Lagrange's theorem of mean on difference, are concluded in simple way. On the basis of these conclusions, the asymptotic property of middle point is studied, a series of new conclusions are drawn and the discussions on the asymptotic property of middle point in differential mid-value are summarized.

对函数逼近论中等距节点和差分理论进行了研究，揭示了差分、差商与导数之间的联系；将Lagrange中值定理、Cauchy中值定理、Taylor公式引入到差分函数中，简明地推导出Lagrange差分中值定理等4个定理，并在此基础上对&中间点&的渐近性进行了研究，得出了一系列&中间点&的渐近性的结果，概括了有关文献对微分中值公式的&中间点&的渐近性的讨论；给出的引理改进了函数逼近论的证明方法，精简了函数逼近论中的一些内容。

In chapter II,an extended strongly equivalent theorem forgerms with parameters is proved.The theorem is useful to constructthe factoring map between any unfoldings and universal unfolding.

在第二章中，对带有参数的核证明了一个推广的强等价性定理，这个定理在构造任意开折和普适开折因式相通的变换中有一定的应用。

Chapter 4 is devoted to the existence and multiplicity of homoclinic for self-adjoint nonlinear second order difference equations by using "Mountain Pass " theorem and "Symmetry Mountain Pass "theorem in critical point theory.

第四章应用临界点理论中的山路引理与对称山路引理研究了一类自共轭非线性二阶差分方程的同宿轨的存在性与多重性。

Based on the tree martingale decomposition theorem and the con-vergence of locally finite tree martingales,a tree martingale convergence theorem isverified.

再基于树鞅分解定理和局部有限树鞅收敛定理，证明了一个树鞅收敛定理。

In this paper, a fixed value theorem for direct areas of height triangle s in circular inscribed polygons is obtained, and some results, including the famous height theorem in a triangle, are deduced.

给出圆内接 2n +1边形中高线三角形有向面积的定值定理及其推论，其中包括著名的三角形的高线定

In chapter 2, we sets up the convergence theory of the alternating method for solving Hermitian positive definite systems of linear equations, and establishes the corresponding comparison theorem on its asymptotic convergence rate.

第二章首先介绍当系数矩阵是Hermitian正定矩阵时经典交替迭代法的收敛理论和相应的比较理论，同时我们给出了当分裂不同时对迭代渐进收敛率的影响。

This paper consists of three parts:We first consider the non-autonomous predator-prey system with both Beddirigton-DeAngelis functional response and dispersion. By using comparison theorem of differential equation, we study the permanance of the system. After that, by constructing suitable Lyapunov function, we obtain some sufficient condition which guarantee the existence of globally asymptotically stable almost periodic solution of the system.

本文研究三方面的内容：第一部分考虑具有扩散和Beddington—DeAngelis功能反应的捕食-食饵系统，利用微分方程比较原理得到该系统一致持续生存的条件；通过构造适当的Lyapunov函数得到了该系统存在全局渐近稳定概周期解的充分条件。

With the help of comparison theorem, sufficient conditions which guarantee permanence of the system are obtained. For the almost periodic case, by constructing a suitable Liapunov function, we obtained that the system has a unique globally asymptotically stable positive almost periodic solution. Finally, we study a multispecies predator-prey system with stage structure and Holling II type functional response.

第二部分考虑具有阶段结构的非自治扩散捕食系统，利用比较定理得到该系统持久生存的充分条件，其后在概周期情形下通过构造合适的Liapunov函数得到了保证该系统存在唯一一个全局渐近稳定的概周期解的条件。

Aquatic or marsh-growing fern allies; known to have existed since the Cenozoic; sometimes included in Lycopodiales.

生活于水中或湿地的蕨类；从新生代生存至今；有时归于石松目之中。

The engine was uprated from a 90hp Franklin to a 125hp Lycoming.

改良过的引擎是从90hp到125hp莱康明富兰克林。