查询词典 comparison theorem

this article discusses the integral theorem of mean the promoted question, mainly has two aspects: On the one hand in analyzes in the teaching material under the first integral theorem of mean condition, had proven lies between the value spot to have to be possible to obtain in the open-interval, further discusses this knot promotes to the generalized Riemann integral, and further proved the conclusion also establishes to the promoted first integral theorem of mean; Promotes on the one hand in addition the integral theorem of mean to in the curve and the curved surface, and has proven the curvilinear integral theorem of mean and the surface integral theorem of mean.

本文讨论积分中值定理的推广问题，主要有二个方面：一方面在分析教材中第一积分中值定理的条件下，证明了介值点必可在开区间内取得，进一步将这个结论推广到广义Riemann积分，并进一步证明结论对推广的第一积分中值定理也成立；另一方面，将积分中值定理推广到曲线和曲面中，并证明了曲线积分中值定理和曲面积分中值定理。

The thesis will introduce, respectively, relevant concepts of residue theorem and its promotion and application in two parts In the basic concepts of chapter II, the definition, classification and relationship between function zero and pole of the isolated singular point are given to lead out relevant definition, theorem and solving method, while the core content of this paper is promotion and application of residue theorem, including calculation of integration by using residues, application in diagonal theorem and argument theorem, application in electromagnetism and theorem promotion and relevant application of extension theorems

本文将从两大部分分别引入和浅析了留数定理的相关概念及其推广和应用在第二章的基本概念部分中，给出了孤立奇点的定义和分类、函数零点与极点的关系，从而引出留数定理的相关定义与定理及其求法而本文的核心内容也就是留数定理的推广和应用，包括运用留数来计算积分、体现在对角定理与辐角定理中的应用、在电磁学中的应用及其定理的推广和推广定理的相关应用

Differential intermediate value theorem and the Taylor formula In this paper, leads to Fermat's theorem Rolle Mean Value Theorem, and then constructing auxiliary function of the Lagrange mean value theorem and Cauchy's Mean Value Theorem to prove that.

微分中值定理和泰勒公式本文通过费马定理引出罗尔中值定理，再构造辅助函数对拉格朗日中值定理和柯西中值定理进行证明。

In part 1, we explore some properties of solution y of a backward stochastic differential equation, such as comparison theorem, reverse comparison theorem and uniqueness theorem of generator.

第一部分研究了倒向随机微分方程的解中y的性质，其中包括解的比较定理，逆比较定理，生成元的唯一性定理。

The study of lattice-valued propositional logic system based on lattice implication algebra.On the bases of previous study, by using the concepts and methods of T algebras we established the lattice-valued propositional logic system LP , whose truth values domain is a lattice implication algebra, and discussed systematically the semantical and syntactical properties of LP , proved the soundness theorem 、consistency theorem、deduction theorem and the decidability of validity of the system when the truth values lattice is finite. We also discussed the relationship between the α-theorem of some premise, say A, and the closed sets that contain A.

本文在前人研究工作的基础上，利用T代数的概念与方法，建立了真值取于格蕴涵代数的格值命题逻辑系统LP，对它的语义及语法性质进行了较系统的研究，得到了它的可靠性定理、协调性定理及演绎定理等，证明了值格有限时系统"有效性"的可判定性并讨论了某一前提A下的α定理与包含A的闭集之间的关系。

To the problem of unbiasedness of L 1 estimation,basing on uniqueness of solution,Zhou Shijiang proved it according to dual theorem of linear programming; and Wang Zhizhong proved it according to probability statistics theorem by using the method from special to general; also,basing on error distribution theorem and probability statistics theorem,the authors proved it.

对于L1 估计的无偏性问题，周世健基于解法的惟一性，根据线性规划的对偶理论，证明了L1 估计的无偏性[5] ；王志忠根据数理统计理论，采用由特殊情形推广到一般情形的方法，证明了L1 估计的无偏性[6] 。

Based on much knowledge, contrasting to linear programming; we extend duality theorem (including weak duality theorem and strong duality theorem), complementary slack theorem to conic optimization. Hence we find out some significative conclusions and existing conditions under which their duality gap is zero of two optimizations.

在此基础上，通过与线性规划作对比，将对偶定理、互补松弛定理等推广到锥规划问题中，得到了一些有意义的结论，并且得到了这两个规划的零对偶间隙的存在条件。

By using the partition theorem of unity, a continuous selection theorem for a multimap from a compact Hausdorff topological space to a finitely continuous topological spaces (simply, FC-spaces) without any convexity structure was obtained, and from which and Tychonoff fixed point theorem, a collectively fixed point theorem for a family of multimaps on the product space of compact FC-spaces and several collectively fixed point theorems for a family of multimaps on the product space of non-compact FC-spaces were given.

利用单位分解定理得到从紧的Hausdorff拓扑空间到没有任何凸结构的有限连续拓扑空间的集值映射的连续选择定理，并从该结果和Tychonoff不动点定理，得到紧的FC-空间的乘积空间上映射族的集族不动点定理和若干个非紧的FC-空间的乘积空间上的映射族的集族不动点定理，对文献中的相应结果进行了改进和一般化。

Chapter 2 deals with some refinements of the central limit theorem for a class of non-uniformly hyperbolic dynamical systems called Youngs system, such as local central limit theorem and so-called Berry-Esseen theorem giving the rate of convergence in the central limit theorem.

在第二、三章中，我们考虑一类重要的非一致双曲动力系统的统计性质-中心极限定理，及其进一步的精细结果如局部中心极限定理，带有收敛速度的中心极限定理。

The paper consists of six chapters. Chapter One is the theoretical background, we review the course of mechanical theorem proving and briefly introduce the main mechanical theorem prover of the last decade, Among them, we stress on the Boyer-Moore theorem prover and its throretical foundation a computational logic. In Chapter Two, we discuss two theorem proving tactics. One is the rippling-out tactic, which is a tactic for manipulating the induction conclusion to enable the induction hypothesis to be used in its proof, because it extremely restricts the search space, so it has high efficiency.

全文共分六章，第一章是理论背景知识，回顾了定理机器证明的历程，并对近十年来的主要定理证明器作了扼要的介绍，其中，着重介绍了计算逻辑及Boyer-Moore定理证明系统；第二章讨论了两种定理证明策略，一种是波动策略，它是一种在证明中通过处理归纳结论来激活归纳假设的策略，由于极大的限制了搜索空间，因此搜索效率高。

The statistical analysis of this large set of mutations has led us to propose a diagnostic strategy that should help with the molecular work-up of optic neuropathies.

这一大系列基因突变的统计学分析引导我们提出一个诊断策略，可以帮助我们对视神经病变进行分子学的诊断检查。

The results show that the pipe grouting changes the mechanical parameters of surrounding rocks to achieve the security of engineering objectives by reinforcing surrounding rocks and bolcking the water.

研究表明：小导管注浆一方面改变了围岩的力学参数，另一方面利用浆液的固结特性可以实现堵水和加固围岩的工程目标，使隧道在开挖过程中的安全得到保障。