定理

Arad and Blau proved that an abelian table algebra can be viewed as a group algebra of some abelian group G. Chapter 3 of this paper gives the structural theorem of abelian table algebras by defining a group structure in table basis. Furthermore, the structure of elementary abelian table algebras is discussed using the number of composition series of table algebras.

Arad和Blau证明了abel表代数等价于某个有限生成abel群G的群代数，受此启发本文第3节通过定义表基的一个群结构给出了abel表代数的结构定理，并从合成列数目的角度对初等abel表代数进行了细致刻画。

The existence and convergence theorem of Newton method and quasi Newton method solving nonlinear equation with parameters F = 0 is obtained under point estimates and weak conditions.

在点估计条件下给出用Newton法及拟Newton法求解带参数非线性方程F = 0解的存在性定理和收敛性定理，以及误差估计。

The paper de-duced the kinematically admissible plastic strain rate cycles of scattered structuresproceeding from Betti′s reciprocal theorem and the principle of virtual work.A fi-nite element formula of upper shakedown analysis of shells is given.Computerprograms are coded to resolve the problems of lower shakedown limit andoptimum shakedown design of plate structures and the lower and uppershakedown limits of combined rotation shells with initial geometric imperfections.The computing results show the correctness and effectiveness of the methods pro-posed by this paper.

本文还从Betti互换定理和虚功原理出发推导出离散结构中可能的塑性应变率循环，将其应用于安定上限定理，首次给出了壳体安定上限分析的有限元列式；编制了板的安定下限分析和板的安定优化设计程序及有初始几何缺陷的组合旋转壳体安定上下限分析的样条有限元程序，计算结果表明本文提出的方法正确、可行。

The paper, taking Pythagorean Theorem for example, analyzes the function, effect and the practice in the modern teaching.

分析了数学定理演变的原因及其对数学发展的作用，并以数学教材中典型的定理&勾股定理&为例，分析其在历史演化中的作用与影响，以及在现代中学里的教学。

The study of lattice-valued resolution principle based on lattice-valued logic with truth-value in lattice implication algebras Because of it concise, resolution principle is an implication direction in automated theorem proving, and it will be of significance to establish resolution principle based on non-classical logics.

基于格蕴涵代数的格值逻辑中归结推理的理论与方法研究归结原理由于其简洁性一直是自动定理证明中一个受到广泛重视的研究领域，因而建立基于非经典逻辑的归结方法对于非经典自动定理证明有着重要的意义。

Interpret conjunctions and disjunctions in terms of.

定理证明。定理1 对于给定集合A 和A上的二元运算，如果存在。。。。

It proved that the intersection of hyperplanes corresponding to the edges of a clique in a simple graph is a modular...

并利用上面证明的定理及Stanley定理给出此类图构形的Poincaré多项式的一个因式分解。

Secondly,we improved the related inclusion region for it,which is based on the eigenvalue inclusion region theories such as Gerschgorin theory and ovals of Cassini theory.

其次，基于齐次特征值问题诸如Gerschgorin圆盘定理及Cassini卵形域等特征值包含定理，我们对于矩阵非齐次特征值问题的包含域问题做了一些相应的讨论。

In chapter 3, as the direct application of the resonance theorems what discussed in chapter 2, we estaiblish corresponding the resonance theorems in Menger probabilistic normed spaces and fuzzy normed spaces.

第三章 作为第二章中给出的共鸣定理的直接应用，建立Menger概率赋范空间和模糊赋范空间中相应的共鸣定理。

So, many scientists set out to consider how we can probabilistically or approximately clone quantum states, because these are not forbidden.

这一定理使得人们对于量子信息处理的能力很受限制，但是信息处理的需求总是很强烈的，这就导致了很多科学家转向考虑如何绕过这条定理，进行概率克隆或者不精确克隆，因为这两种方式的量子态操作并未被禁止。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。