共查询到20条相似文献,搜索用时 93 毫秒
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从研究生试题看两个定理的重要性刘甸瑞(中国地质大学)极限的保号性与连续函数的有界性是高等数学中的两个重要定理。从分析1987—1994年历届研究生高等数学试题中我们看到需用这两个定理的试题多次出现,这本身也说明了这部分内容的重要性。这两个定理是:定理... 相似文献
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[1]中定理3.6是经典的Dini定理的推广。Wolk在证明了这个定理后指出,有例子说明,若将值域空间Y的全无序集(即反链)有限性条件去掉后,此定理将不成立。于是他提出了一个可供进一步思考的问题:是否可用另外一些拓扑代替Y中的Dedekind拓扑,去掉Y中全无序集有限性条件后,此定理或它的某种变形依然成立?按照这个思路我们将[1]中定理3.6和3.9进行了推广。为此,先摘录两个主要概念如下: 相似文献
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高等代数两个定理的证明曹重光(黑龙江大学数学系150080)本文给出高等代数中两个重要定理的新的证明方法.它们是诸多教材和文献中尚未见到的(看[1]-[6]).1行列式乘法定理设A,B为数域F上两个n阶方阵,则|AB|=|A||B证明设A=(aij)... 相似文献
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本文建立了两个积分学定理(定题1.1与定理2.1),应用它们可简化传统的关于曲线的弧长,第一型与第二型曲线积分以及第一型与第二型曲面积分计算公式的证明。 相似文献
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关于多项式因式分解的两个定理 总被引:1,自引:1,他引:0
关于多项式因式分解的两个定理彭明海(湖南吉首大学416000)我在《高等代数》教学中,发现下面两个定理,今介绍出来,供同行参考.定理1设f(x)=anxn+an-an-1n+…+(Z[x]表示整系数多项式集合)如果有一个素数p满足条件且则f(x)在有... 相似文献
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提出了两个基于不同张量乘法的四阶张量分解. 首先, 在矩阵乘法的基础上, 定义第一种四阶张量乘法(F-乘), 基于F-乘提出了第一种四阶张量分解(F-TD). 其次, 基于三阶张量t-product给出了第二种四阶张量乘法(B-乘)和分解(FT-SVD). 同时, 利用两种分解方法, 分别给出两个张量逼近定理. 最后, 三个数值算例阐明提出的两种分解方法的准确性和可行性. 相似文献
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A generalization of Simons's metaminimax theorem to a metaminimax theorem involving two functions is given. 相似文献
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S—R分解定理的唯一性,存在性和客观性 总被引:3,自引:0,他引:3
对于连续体的一切物理可能的变形场,其变形梯度张量F可被分解为一个对称张量S和一个正交张量R的直和,这便是S-R分解定理.本文通过矩阵方法和张量方法证明了S-R分解定理的唯一性、存在性和客观性. 相似文献
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Florin Panaite 《Czechoslovak Mathematical Journal》2012,62(1):187-195
The so-called “invariance under twisting” for twisted tensor products of algebras is a result stating that, if we start with
a twisted tensor product, under certain circumstances we can “deform” the twisting map and we obtain a new twisted tensor
product, isomorphic to the given one. It was proved before that a number of independent and previously unrelated results from
Hopf algebra theory are particular cases of this theorem. In this article we show that some more results from literature are
particular cases of invariance under twisting, for instance a result of Beattie-Chen-Zhang that implies the Blattner-Montgomery
duality theorem. 相似文献
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SU ZHONGGEN 《高校应用数学学报(英文版)》1995,10(4):367-378
ONTHECENTRALLIMITTHEOREMINPRODUCTSPACESSUZHONGGENAbstract:SupposethatEandFareseparableBanachspaces,XandYareindependentsymmetr... 相似文献
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Thierry Coquand 《Archive for Mathematical Logic》1998,37(3):143-147
Semantical arguments, based on the completeness theorem for first-order logic, give elegant proofs of purely syntactical
results. For instance, for proving a conservativity theorem between two theories, one shows instead that any model of one
theory can be extended to a model of the other theory. This method of proof, because of its use of the completeness theorem,
is a priori not valid constructively. We show here how to give similar arguments, valid constructively, by using Boolean models.
These models are a slight variation of ordinary first-order models, where truth values are now regular ideals of a given Boolean
algebra. Two examples are presented: a simple conservativity result and Herbrand's theorem.
Received December 5, 1995 相似文献
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A topological minimax theorem involving two functions is derived. It generalizes Greco and Horvath'minimax theorem given by them in 2002. 相似文献
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Algorithms are developed for computing generalized Racah coefficients for the U(N) groups. The irreducible representations (irreps) of the U(N) groups, as well as their tensor products, are realized as polynomials in complex variables. When tensor product irrep labels as well as a given irrep label are specified, maps are constructed from the irrep space to the tensor product space. The number of linearly independent maps gives the multiplicity. The main theorem of this paper shows that the eigenvalues of generalized Casimir operators are always sufficient to break the multiplicity. Using this theorem algorithms are given for computing the overlap between different sets of eigenvalues of commuting generalized Casimir operators, which are the generalized Racah coefficients. It is also shown that these coefficients are basis independent.
Mathematics Subject Classifications (2000) 22E70, 81R05, 81R40. 相似文献
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两个网络间的相互同步 总被引:2,自引:1,他引:1
本文研究了两个耦合网络的相互同步,利用线性化方法,我们给出了两个具有相同拓扑结构的网络实现同步的定理,最后用数值例子来验证得到的理论结果。 相似文献