共查询到20条相似文献,搜索用时 109 毫秒
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就连续函数应用问题的教学内容进行探讨.介绍数列和连续函数的压缩映射原理及其在方程求解,数学建模等方面的应用,并给出压缩映射的一般形式.续而通过压缩映射原理在图像处理和导航系统中的应用,阐明创新思想的重要性,以求开拓学生的思路和想象空间. 相似文献
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在映射与函数概念的教学中,由映射的基本概念和性质出发给出了函数的概念.从映射的角度扩展函数的概念,引出了高等数学及相关后续课程中的一些基本内容,帮助学生了解多元函数、复变函数、线性代数和泛函分析等相关后续课程. 相似文献
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两个微分中值定理证明中辅助函数的多种作法 总被引:6,自引:1,他引:5
李君士 《数学的实践与认识》2004,34(10):165-169
在数学分析中 ,三个微分中值定理极为重要 .在证明 Lagrange中值定理和 Cauchy中值定理时 ,都少不了作辅助函数 ,各种版本的《数学分析》或《高等数学》书本中 ,都只给出了一种形式的辅助函数 .为了扩展思路 ,给出了多种形式的辅助函数 ,并得出了一般形式 . 相似文献
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首先讨论了一个非线性标量化函数的基本性质并给出了其对偶形式.在此基础上建立了对向量值映射的恰当锥拟凸性的刻画.然后提出了锥形邻域的概念并给出了向量值映射的一类新的锥半连续性的统一定义.最后通过两个非线性标量化函数得到了对向量值映射的锥半连续性的完整刻画. 相似文献
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求递推数列的极限是数列极限中一个非常重要的内容,常用单调有界定理,压缩映射原理解决.本文利用不动点给出该类数列的解法,在解决复杂问题中有一定的优越性. 相似文献
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B-vexFuzzyMappingsandItsApplicationtoFuzzyOptimizationProblems¥LiuDefeng(InstituteofQuantitativeEconomics,DongbeiUniversityOf... 相似文献
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Indicator functions have been in the literature for several years, and yet only a few of their properties have been examined.
In this paper, we study some properties of indicator functions of two-level fractional factorial designs. For example, we
show that there is no indicator function with only two words, and also classify all indicator functions with only three words.
The results imply that there is no valuable non-regular design with only three or less words in its indicator function. 相似文献
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Alexander I. Molev Bruce E. Sagan 《Transactions of the American Mathematical Society》1999,351(11):4429-4443
We give a combinatorial rule for calculating the coefficients in the expansion of a product of two factorial Schur functions. It is a special case of a more general rule which also gives the coefficients in the expansion of a skew factorial Schur function. Applications to Capelli operators and quantum immanants are also given.
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Steven Nahmias 《Fuzzy Sets and Systems》1978,1(2):97-110
The purpose of this study is to explore a possible axiomatic framework from which a rigorous theory of fuzziness may be constructed. The approach we propose is analogous to the sample space concept of probability theory. A fuzzy variable is a mapping from an abstract space (called the pattern space) onto the real line. The membership function is obtained as the extension of a special type of capacity (called a scale) from the pattern space to the real line via the fuzzy variable. In essence we are proposing an entirely new definition of a fuzzy set on the line as a mapping to the line rather than on the line. The current definition of a transformation of a fuzzy set is obtained as a derived result of our model. In addition, we derive the membership function of sums and products of fuzzy sets and present an example which reinforces the credibility of our approach. 相似文献
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In this paper, the definition of the Shapley function for fuzzy cooperative games is given, which is obtained by extending the classical case. The specific expression of the Shapley function for fuzzy cooperative games with multilinear extension form is given, and its existence and uniqueness are discussed. Furthermore, the properties of the Shapley function are researched. Finally, the fuzzy core for this kind of game is defined, and the relationship between the fuzzy core and the Shapley function is shown. 相似文献
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Mira Sarkar 《Journal of Mathematical Analysis and Applications》1981,79(2):384-394
In this paper, a few separation properties and some aspects of subspace fuzzy topology have been studied, where both the crisp and the fuzzy elements have been taken into consideration. Since the conventional definition of compactness is not quite meaningful in Hausdorff fuzzy spaces (as introduced by us), a new more natural definition of proper compactness is given and a few properties resulting from this are established. 相似文献
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Examples of fuzzy metrics and applications 总被引:1,自引:0,他引:1
In this paper we present new examples of fuzzy metrics in the sense of George and Veeramani. The examples have been classified attending to their construction and most of the well-known fuzzy metrics are particular cases of those given here. In particular, novel fuzzy metrics, by means of fuzzy and classical metrics and certain special types of functions, are introduced. We also give an extension theorem for two fuzzy metrics that agree in its nonempty intersection. Finally, we give an application of this type of fuzzy metrics to color image processing. We propose a fuzzy metric that simultaneously takes into account two different distance criteria between color image pixels and we use this fuzzy metric to filter noisy images, obtaining promising results. This application is also illustrative of how fuzzy metrics can be used in other engineering problems. 相似文献
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Fuzzy measures are used in conjunction with fuzzy integrals for aggregation. Their role in the aggregation is to permit the user to express the importance of the information sources (either criteria or experts). Due to the fact that fuzzy measures are set functions, the definition of such measures requires the definition of 2n parameters, where n is the number of information sources. To make the definition easier, several families of fuzzy measures have been defined in the literature.In this paper m-separable fuzzy measures are introduced. We present some results on this type of measures and we relate them to some of the previous existing ones. We study generating functions for m-separable fuzzy measures and some properties related to these generating functions. 相似文献