查询词典 existence theorem of implicit function

For the theorem 4 on DEA efficiency (C~2R) in reference ,this paper gives its inverse theorem under a condition in order to be easy to discriminate DEA efficiency (C~2R).

对文[1]中有关DEA有效(C2R)的定理4，本文给出了在某种条件下的逆定理，以便简化DEA有效性(C2R)的判断。

Lagrange value theorem is an important one of the Mean Value Theorem.

拉格朗日中值定理是重要的微分中值定理之一。

In Chapter 4, by some important summation formulas, we prove some results of number theory, such as Jacobi two square numbers theorem and Lagrange four square numbers theorem.

第四章：应用第二章介绍的几个重要求和公式，证明了数论中的若干结果。

Then using Hahn-Banach separation theorem, we obtain Lagrange multiplier theorem.

再利用Hahn-Banach分离定理，得到Benson真有效解的Lagrange乘数定理。

The differential theorem of mean is called "the Lagrange theorem of mean" generally, is in the differential calculus one of most important conclusions.

微分中值定理一般称为"Lagrange中值定理"，是微分学中最重要的结论之一。

This article is divided into several categories of questions, focus on a typical example of the Lagrange Mean Value Theorem to prove the application of the inequality summarized in the hope that readers can better grasp the Lagrange mean value theorem in the inequality in the application of skills .

本文将题型分成几类，集中典型例题，对拉格朗日中值定理在不等式证明的应用中进行归纳总结，希望读者能够更好的掌握拉格朗日中值定理在不等式中的应用技巧。

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 article will write divides into several kinds, the centralism typical sample question, carries on the induction to the Lagrange theorem of mean in the application which the inequality proved to summarize, hoped that the reader can better grasp the Lagrange theorem of mean in the inequality application skill.

本文将题型分成几类，集中典型例题，对拉格朗日中值定理在不等式证明的应用中进行归纳总结，希望读者能够更好的掌握拉格朗日中值定理在不等式中的应用技巧。

Based on the outcome of Xu Yang and Qin Keyun about lattice implication algebra and lattice-valued prepositional logic LP with truth-value in a lattice implication algebra, the author studied the properties of lattice implication algebra and the α-automated reasoning method based on α-resolution principle of LP. The specific contents are as follows: The Study of Lattice Implication Algebra On the basis of previous results of lattice implication algebra, this part consists of the following three points: 1. Some properties of lattice implication algebra L were discussed, and some important results were given if L was a complete lattice implication algebra. 2. The properties of left idempotent elements of lattice implication algebras were discussed, and the conclusion that lattice implication algebra L was equals of the directed sum of the range and dual kernel of a left map constructed by a left idempotent element was proved. 3. The properties of the filters of lattice implication algebra were discussed, the theorem was shown that they satisfy the hypothetical syllogism and substitute theorem of the propositional logic. 4. The concept of weak niters of lattice implication algebras and their properties and structures are discussed. It is proved that all weak filters of a lattice implication algebra form a topology and the the implication isomorphism betweem two lattice implication algebras is a topological mapping between their topological spaces. The Study of α-automated reasoning method based on the lattice-valued propositional logic LP In this part, the author given an a-automated reasoning method based on the lattice-valued propositional logic LP.

本文基于徐扬和秦克云的关于格蕴涵代数和以格蕴涵代数为真值域的格值命题逻辑系统LP的研究工作，对格蕴涵代数以及格值命题逻辑系统LP中基于α-归结原理的自动推理方法进行了系统深入的研究，主要有以下两方面的研究成果：一、关于格蕴涵代数的研究 1、对格蕴涵代数的格论性质进行了研究，得到了当L为完备格蕴涵代数时，关于∨，∧，→运算的一些结果； 2、对格蕴涵代数的左幂等元进行了研究，证明了格蕴涵代数L可以分解为任何一个左幂等元所对应的左映射的像集合与其对偶核的直和； 3、对格蕴涵代数的滤子的性质进行了研究，证明了滤子的结构相似于逻辑学中的Hypothetical syllogism规则和替换定理； 4、给出了格蕴涵代数中弱滤子的概念，对弱滤子的性质个结构进行了研究，证明了格蕴涵代数的全体弱滤子构成一个拓扑结构，格蕴涵代数之间的蕴涵同构是相应的拓扑空间之间的拓扑映射。

There are proved the theorems on convergence of sequences of the integral, which are similar to Levi's theorem, Fatou's theorem and so on in Lebesgue's integral.

4中引进了一类特殊的所谓λ次可加模糊测度空间，给出了这种测度空间上收敛性的Егоров定理和Riesz定理并得到了该空间上的模糊积分在积分号下取极限的一些充分条件。

The studies on the developing of new media are very important to the increasing of the area density of HDD and to the implementation of hybrid recoding technology.

光磁混合记录方法，是一种可以突破超顺磁极限的限制，并进一步提高硬盘记录密度和读写速率的一种新型超高密度信息存储方式。

In io, mTOR inhibition promotes T cell anergy under conditions that would normally induce priming.

体内研究中，在正常可激发免疫反应的条件下，抑制mTOR可促使T细胞无能。