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Not only that in the integral calculus, aspects and so on progression theory, as well as take the mathematical analysis as foundation many aspects, the Lagrange theorem of mean is also studies the question the important means that plays the pivotal role frequently.

不仅如此，在积分学，级数理论等方面，以及以数学分析为基础的许多方面，拉格朗日中值定理也是研究问题的重要手段，经常发挥举足轻重的作用。

This paper gives the new method to prove the Cauchy Mean Value Theorem ,which also may be deduced from the Lagrange Mean Value Theorem.

给出柯西中值定理的一个新的证法，说明柯西中值定理也可由拉格朗日中值定理导出。

This paper describes the content of the theorem, and theorems are given two proofs, cite the Lagrange mean value theorem in the mathematics major applications, including that inequality, identity, Limit, determine monotonicity, root The existence of such.

本文简要叙述了定理的内容，并且给出了定理的两种证明方法，例举了拉格朗日中值定理在数学中的主要应用，包括证明不等式，恒等式，求极限，判断单调性，根的存在性等。

Using LaGrange theorem on base of analyzing the elastic prop model tension system of band saw machine, the dynamics model of elastic prop tension system of band saw machine has been established and converted to mathematics model applying the modern control theory.

本文以MJ317型木工杠杆压砣张紧系统的带锯机改造成弹性挺杆张紧系统的带锯机为研究对象，通过对带锯机弹性挺杆式张紧系统的弹性动力学分析，运用拉格朗日定理建立了张紧系统的动力学模型，并应用现代控制理论将模型转换成数学模型。

The use of Differential Mean Value Theorem (Rolle theorem, Lagrange's theorem, Cauchy's theorem) to solve a number of derivative and limit the problem.

利用微分中值定理（罗尔定理，拉格朗日定理，柯西定理）解决一些导数和极限的问题。

Theorem of mean significance: The application derivative research function's nature wants directly or indirectly with the aid of Yu Zhongzhi,Specially Lagrange theorem of mean,Here is mainly from the equality proof, the inequality proof, existence asks some limits, the determination equation root and so on five aspects to carry on the discussion,so, The theorem of mean is transforms as the function in the sector research important tool, Must bring to the enough attention in the middle of ours study and the teaching.

中值定理意义：应用导数研究函数的性质都要直接或间接地借助于中值，特别是拉格朗日中值定理，这里主要是从等式的证明、不等式的证明、求一些极限、判定方程根的存在性等五个方面来进行讨论，因此，中值定理是转化为函数在区间上的研究的重要工具。在我们的学习与教学当中要引起足够的注意。

On the basis of these theories,Rolle mean value theorem,Lagrange mean value theorem and Cauchy mean value theorem are proved by constructing nested interval.

在此基础上通过构造区间套依次证明了罗尔中值定理、拉格朗日中值定理和柯西中值定理

In this paper,a threshold authentication scheme of ad hoe network based on elliptic curve is proposed,in using Lagrange Theorem to generate the group key and in using the digital signature algorithm based on elliptic curve to generate and merge the sub certificates.

论文提出一种基于椭圆曲线的门限身份认证方案，利用拉格朗日定理生成群密钥并利用椭圆曲线数字签名算法生成子证书并合成，该算法的安全性、高效率以及低计算复杂度特别适合Ad hoc网络移动自组的特点。

Based on maximum principles, Lagrangian function is adopted to obtain the weights of the indexes.

依据极值原理，利用拉格朗日函数得到各个指标的权重值。

It is well-known that reduced Hessian method is one of the most efficient methods for solving large scale constrained optimization problems. However, the convergence analysis for the method requires of the positive definiteness of the reduced Hessian of Lagrangian function.

众所周知，既约Hessian方法是求解较大规模约束优化问题的一类有效方法，但已有的这类方法的全局收敛性分析需假定拉格朗日函数的既约Hessian矩阵的一致正定性。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新