查询词典 implicit function theorem

Theorem 3 Let be a continuous function on the interval and let be a number between and , then there is at least one number , such that.

定理 3 设函数在闭区间上连续，且在这区间的端点取不同的函数值及，那么，对于与之间的任意一个数，在开区间内至少有一点使。

Theorem 2 If the functionis continuous and increasing on the interval, then its inverse function is also continuous and increasing on the corresponding interval.

定理 2 如果函数在区间上单调增加且连续，那么它的反函数也在对应的区间上单调增加且连续。

The total energy of the system is employed to show the passivity property of TORA, and then a proper Lyapunov function including energy item is designed. Based on Lyapunov theory, a state feedback control algorithm is achieved. The stability of the control system is based on LaSalle invariance theorem.

基于拉格朗日方程，建立了TORA的动力学模型，从能量的角度出发，说明了系统的无源特性，在此基础上设计了一个合适李亚普诺夫函数，从而得到了系统的控制算法；采用拉萨尔不变性原理分析了控制系统的稳定性。

In this method, an interim variable is defined by combining one variable of each subsystem. The interim variable is used to construct the sliding-mode function and the total control law can be derived to guarantee the equilibrium point is reachable in finite time. Using LaSalle invariance theorem, it can be proved further that the equilibrium field only includes one equilibrium point and the equilibrium point is asymptotically stable.

该方法将各个子系统的一个变量进行组合定义成一个中间变量，然后从这个中间变量出发构造滑模函数，通过求取总的控制量保证中间变量在有限时间内收敛到平衡点；进一步利用LaSalle不变性原理证明该收敛域内只有一个平衡点且是渐近稳定的。

In the third part we investigate a kind of two-dimensional non-product-type operators on continuous function space and some important properties and a locally inverse theorem are obtained.

其中第三节在连续函数空间上研究这类非乘积型二元算子，讨论了该算子的一些重要性质，给出局部意义下的一个逆定理。

In the present work,the existence and uniqueness results aboutperiodic boundary value problems for different kinds of the nonlin-ear periodically perturbed nonconservative systems are establishedthrough the discretization technique,under suitable assumptions,by using global inverse function theorem and result about the ex-istence and uniqueness of periodic solution for nonhomogeneouslyfirst order linear periodic boundary value problem.

本文的第一章概述了在讨论原问题解的存在唯一性过程中以及构造和分析相关的数值求解方法时将要用到的全局反函数定理、有关矩阵特征值的若干重要引理、线性常微分方程非齐次周期问题解的存在唯一性定理和单参数影射方法及有关结论，并简单回顾了已有的证明非线性微分方程周期边值问题解的存在唯一性的方法，其中包括谱理论、最大最小化形式方法、摄动技术和全局反函数理论方法，最后，介绍了两类数值求解非线性微分方程问题的方法。

Lagrange mean value theorem is to examine the function of the characteristics of a powerful tool.

拉格朗日中值定理是研究函数特性的一个有力工具。

The Lagrange theorem of mean studies a function characteristic powerful tool.

拉格朗日中值定理是研究函数特性的一个有力工具。

We establish a Lagrange multiplier theorem for strict efficiency in convex settings and express strict points as saddle points of an appropriate Lagrangian function.

讨论凸多目标最优化问题的严有效解，建立了拉格朗日乘子定理，并把严有效解表示为一个适当的拉格朗日函数的鞍

By using Mawhin\'s continuous theorem and liapunov function, sufficient conditions for the existence and globally asymptotic stability of positive periodic solutions of three systems are derived, respectively.

我们还利用Mawhin连续性定理分别建立了两个系统正周期解存在的充分条件。

Don not attempt to do something which you can not to do.

不要企图做那些办不到的事情。

The expression of CTGF and TNF-αweredetected by immunochemistry and the number of Clara Cells was calculated.

光镜下观察肺组织的病理变化，采用免疫组化染色观察肺组织中结缔组织生长因子和肿瘤坏死因子-α的表达和Clara细胞的数量。