查询词典 gap theorem

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] 。

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。

Among which theorem 1 and theorem 2 are similar to the controlled convergence theorem and Lukin theorem in Lebesgue integral Theory.

定义μ=|G|／|Irr|。得到了定理1 若G是非交换有限群2。首先得到具有这种性质的非Abel有限单群的完全分类定理。

Finally, after defining an evaluation module of the corresponding Loop superalgebra (Section 4), two major results of the paper -Theorem 4.land Theorem 4.2 are proved: Theorem 4.1 reduces the irreducibility of the tensor product of finitely many evaluation modules to the irreducibility of the tensor product of finitely many irreducible modules of a nilpotent Lie superalgebra; Theorem 4.2 gives a criterion for the tensor product of such modules to be irreducible.

第4节在定义了相应的Loop超代数的赋值模之后，证明了本文的两个主要结论：定理4.1和定理4.2。定理4.1将有限多个赋值模其张量积的不可约性归结为一幂零李超代数的限多个不可约模其张量积的不可约性；定理4.2利用不可约指标给出了一幂零李超代数的限多个不可约模其张量积仍不可约的判别准则。

It includes luol theorem, Lagrange theorem and cauchy theorem, Taylor theorem.

它包括罗尔定理、拉格朗日定理、柯西定理、泰勒定理。

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。

Chapter 2 deals with some refinements of the central limit theorem for a class of non-uniformly hyperbolic dynamical systems called Young\'s 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。

On the other hand , illuminated by close relation between harmonic maps and sumanifold theory, we have also researched in-depth about some relative problems in submanifolds theory which include: the estimate of heat kernel and eigenvalue and it geometric application of submanifolds with or without boundary; many kinds of pinching problem of submanifolds which include the rigidity theorem, topological sphere theorem, differential sphere theorem and topological finite theorem.

另外，鉴于调和映照与子流形之间的密切关系，我们还要深入研究子流形几何中与之相关的一些问题，主要包括：带边与不带边子流形的热核与特征值估计及其几何应用；子流形的刚性定理、拓扑球定理、微分球面定理、拓扑有限性定理等各类Pinching问题。

For the head-teacher of the class said that I had seriously broken the school rules,which led me to a three-day suspend class.

为什么呢？因为我的班主任说我严重的违反了校规，于是让我停课三天。

Many of them believe that the conversion of thousands of working-class folk in England spared that nation from the mass carnage and the tyranny that came with the revolution in France.

他们之中有许多人相信，在英国数以千计的劳工阶级之悔改信主使英国免於遭受如法国大革命所造成的大屠杀和专制暴政。