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集合是近代数学的一个重要概念 ,集合元素的任意性使得集合有着深刻的内涵 ,从而使集合的思想能渗透到数学的方方面面 .高中数学主要介绍了集合的五种关系“子集、相等、交集、并集、补集” .这些关系对于解决数学问题时有一定的启迪 .在此基础上进一步深化 ,还能发现其包含着丰富的数学思想和深刻的哲学原理 .1 子集关系中的特殊和一般集合中若A B 任意x∈A都有x∈B .所以探求具有A的性质的问题 ,可以利用子集的关系在B中加以讨论 .从哲学的观点来看 ,一般中包含着特殊 ,解决了一般的问题 ,特殊问题就迎刃而解 .这是数学解题的一种重… 相似文献
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一、对“包含”一词使用的看法全日制十年制高中《数学》第一册P10在介绍全集定义后补述了这样一句话:“也就是说,全集包含了我们所要研究的各个集合的全部元素”。同样的话也见中师《代数与初等函数》第一册P18。愚见以为此处用“包含”一词似有不妥。我们如将上句话省去定语变为“全集包含元素”。而书中介绍元素与集合关系时规定为“属于”与“不属于”,集与集的关系才是“包含”与“不包含”。倘若此处用“包含”一词,则使学生误为集与元素的关系也为“包含”或“不包含” 相似文献
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本文在广义模糊软集和犹豫模糊软集的基础上给出广义犹豫模糊软集的概念,并研究广义犹豫模糊软集的不确定性度量。首先在犹豫模糊集包含度的公理化定义基础上,建立犹豫模糊集合的三种包含度公式;然后给出广义犹豫模糊软集包含度的公理化定义,并利用犹豫模糊集合的包含度公式构造广义犹豫模糊软集间的包含度公式,这些公式可以计算参数集不同时两个广义犹豫模糊软集间的包含度。接下来给出广义犹豫模糊软集不确定性度量的公理化定义,并从其包含度出发来构造广义犹豫模糊软集的不确定性度量公式,这种不确定性度量的计算方法同样适用于参数集不同的广义犹豫模糊软集,最后利用广义犹豫模糊软集不确定性度量方法应用到聚类分析实例中,通过实例验证了所提出方法的可行性和有效性。 相似文献
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“集合与函数”是高中数学新课程必修模块《数学l》中的起始内容,人教A版教科书是以第一章“集合与函数概念”来编排的,鄂教版教科书是用了丽章,即第一章“集合”与第二章“函数及其基本性质”来编排的.本文主要以人教A版及鄂教版教科书为例,结合高中数学课程标准,对新教材中“集合与函数”这部分内容进行一些解读. 相似文献
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这样的映射有多少个? 总被引:2,自引:0,他引:2
集合单元中的重点内容之一就是关于集合之间的交集、并集、补集等运算,同时也是,同学们最感头疼的难点.实际上,在解题中借助数轴来完成无限数集之间的运算,借助平面直角坐标系中解决数对组成的集合之间的运算,是我们经常采用的“数形结合”的思想方法.但对一些有限数集之间的运算,却往往忽视了“韦恩图”(又称“文氏图”)所起到的辅 相似文献
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§1 介绍与基本概念最近,许多文章讨论r.e。集合的T-度与W-度之间的结构差别,例如Lerman和Remmel讨论USP性质以及UWP性质。1985年Downey证明每个度中都存在一个r.e。集合具有~USP和~UWP性质,并且猜想除contiguous度和完备度以外,所有度不包含具有USP(UWP)性质的r.e.集合。如果这样的话,contiguous集合具有的结构性质,具有USP性质的集合也应该具有。我们这里只讨论一种结构性质。Ambos,Spies和Fejer[ta]证明contiguous度在低度中 相似文献
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1 基本知识 1 )元素与集合的关系 .判断一个对象是否为某个集合的元素 ,就是检验这个对象是否具备这个集合的元素所共有的属性 .2 )两集合之间的关系 .两集合之间的关系主要是“相等”、“包含”、“真包含”关系 .3)映射 .映射是数学中的一个基本概念 ,几乎每一个数学分支都要用到它 .设A和B是给定的两个集合 ,如果有一个规则 f ,使得对于每一个x∈A ,通过 f ,唯一确定一个 y∈B ,那么 ,就称 f是A到B的一个映射 ,记为f :A| →B .我们称 y为x在 f作用下的象 ,记作 y =f(x) ,并用符号f :x| →y表示 ,称x为y的一个… 相似文献
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Nazan akmak Polat Gzde Yaylal Bekir Tanay 《Mathematical Methods in the Applied Sciences》2019,42(16):5607-5614
All over the globe, soft set theory is a topic of interest for many authors working in diverse areas because of its rich potential for applications in several directions since the day it was defined by Molodtsov in 1999. Moreover, soft set theory is free from the difficulties where as other existing methods viz. probability theory, fuzzy set theory. Considering to these benefits, soft set theory has became very popular research area for many researchers. To contribute this research area, in this paper, we examine some properties on soft topological spaces such as neighborhood structure of a soft element and soft interior, soft closure, and soft cluster element and so on that are based on soft element definition that gives us a different perspective for development of soft set theory. Moreover, we give some examples to clarify our definitions. 相似文献
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Computational and mathematical organization theory is an interdisciplinary scientific area whose research members focus on developing and testing organizational theory using formal models. The community shares a theoretical view of organizations as collections of processes and intelligent adaptive agents that are task oriented, socially situated, technologically bound, and continuously changing. Behavior within the organization is seen to affect and be affected by the organization's, position in the external environment. The community also shares a methodological orientation toward the use of formal models for developing and testing theory. These models are both computational (e.g., simulation, emulation, expert systems, computer-assisted numerical analysis) and mathematical (e.g., formal logic, matrix algebra, network analysis, discrete and continuous equations). Much of the research in this area falls into four areas: organizational design, organizational learning, organizations and information technology, and organizational evolution and change. Historically, much of the work in this area has been focused on the issue how should organizations be designed. The work in this subarea is cumulative and tied to other subfields within organization theory more generally. The second most developed area is organizational learning. This research, however, is more tied to the work in psychology, cognitive science, and artificial intelligence than to general organization theory. Currently there is increased activity in the subareas of organizations and information technology and organizational evolution and change. Advances in these areas may be made possible by combining network analysis techniques with an information processing approach to organizations. Formal approaches are particularly valuable to all of these areas given the complex adaptive nature of the organizational agents and the complex dynamic nature of the environment faced by these agents and the organizations.This paper was previously presented at the 1995 Informs meeting in Los Angeles, CA. 相似文献
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Togo Nishiura 《Applicable analysis》2013,92(2):141-144
The Geocze area theory for dimension two uses the geometrically simplest intervals on which area theory can he developed, These intervals are simple polygonal regions in the plane. For Geocze k-area with k > 2 it is shown in the present paper that the geometrically simplest interval arc not tue obvious generalizations of the- two dimensional case, that is, polyhedral regions in Rk which are topological K-cells. It is shown that the simplest interval is a polyhedral region in Rk whose complement is connected 相似文献
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The theory of crossed products of C~*-algebras by groups of automorphisms is a well-developed area of the theory of operator algebras. Given the importance and the success ofthat theory, it is natural to attempt to extend it to a more general situation by, for example,developing a theory of crossed products of C~*-algebras by semigroups of automorphisms, or evenof endomorphisms. Indeed, in recent years a number of papers have appeared that are concernedwith such non-classical theories of covariance algebras, see, for instance [1-3]. 相似文献
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A. M. Romanov 《Journal of Applied and Industrial Mathematics》2008,2(2):252-269
The theory of perfect codes is an area at the juncture of coding theory and design theory which is rather hard to explore. Linear perfect codes were constructed by M. Golay and R. Hamming in the end of the 1940s. Nonlinear perfect codes were discovered by Yu. L. Vasil’ev in 1961. At present, many different methods are known for constructing perfect codes. This article presents a survey of the methods for constructing nonlinear perfect binary codes alongside some open questions of the theory of perfect codes. 相似文献
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Jean-Marc Cordier Timothy Porter 《Transactions of the American Mathematical Society》1997,349(1):1-54
This article is an introduction to the categorical theory of homotopy coherence. It is based on the construction of the homotopy coherent analogues of end and coend, extending ideas of Meyer and others. The paper aims to develop homotopy coherent analogues of many of the results of elementary category theory, in particular it handles a homotopy coherent form of the Yoneda lemma and of Kan extensions. This latter area is linked with the theory of generalised derived functors.
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This contribution is located in the common area of operational research and economics, with a close relation and joint future potential with optimization: game theory. We focus on collaborative game theory under uncertainty. This study is on a new class of cooperative games where the set of players is finite and the coalition values are interval grey numbers. An interesting solution concept, the grey Shapley value, is introduced and characterized with the properties of additivity, efficiency, symmetry and dummy player, which are straightforward generalizations of the corresponding properties in the classical cooperative game theory. The paper ends with a conclusion and an outlook to future studies. 相似文献
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A generalization of multi-dimensional wavelet theory is introduced in which the usual lattice of translational shifts is replaced
by a discrete subgroup of the group of affine, area preserving, transformations of Euclidean space. The dilation matrix must
now be compatible with the group of shifts. An existence theorem for a multiwavelet in the presence of a multiresolution analysis
is established and examples are given to illustrate the theory with two dimensional crystal symmetry groups as shifts. 相似文献