共查询到10条相似文献,搜索用时 62 毫秒
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讨论了具有无界变差的连续函数的结构.首先按照局部结构和分形维数对连续函数进行了分类,给出了相应的例子.对这些具有无界变差的函数的性质进行了初步的讨论.对于新定义的奇异连续函数,给出了一个等价判别定理.基于奇异连续函数,又给出了局部分形函数和分形函数的定义.同时,分形函数又由奇异分形函数、非正则分形函数和正则分形函数组成.相应于不连续函数的情形也进行了简单的讨论. 相似文献
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Oleg Khamisov 《Journal of Global Optimization》1999,14(1):79-101
We give a definition of the class of functions with a concave minorant and compare these functions with other classes of functions often used in global optimization, e.g. weakly convex functions, d.c. functions, Lipschitzian functions, continuous and lower semicontinuous functions. It is shown that the class of functions with a concave minorant is closed under operations mainly used in optimization and how a concave minorant can be constructed for a given function. 相似文献
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广义部分Bent函数和广义Bent函数的关系 总被引:5,自引:0,他引:5
Bent函数是一类特殊的布尔函数,因其非线性性和稳定性在密码学和通信等领域有很重要的应用,但它们数量少,不平衡且无相关免疫性,为了弥补Bent函数的不足,Claud Carlet提出了部分Bent函数的概念,部分Bent函数是包含Bent函数的更大的函数类,后来,人们又将这两种函数概念先后都拓广到了环zm^n(m为正整数)上,分别被称为zm^n上的广义Bent函数和广义部分Bent函数,本文利用zp^n(p为素数)上广义部分Bent函数的Chrestenson循环谱特征讨论了zp^n上的广义部分Bent函数和广义Bent函数之间的关系,给出了这两种函数之间的函数关系式和谱值关系式。 相似文献
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提出了一类新的广义凸函数——半严格-G-E-半预不变凸函数,它是一类非常重要的广义凸函数,为半严格-G-半预不变凸函数与半严格-E-预不变凸函数的推广.首先给出例子,以说明半严格-G-E-半预不变凸函数的存在性及其与其他相关广义凸函数间的关系.然后讨论了半严格-G-E-半预不变凸函数的一些基本性质.最后,探究了半严格-G-E-半预不变凸型函数分别在无约束和有约束非线性规划问题中的重要应用,获得一系列最优性结论,并举例验证了所得结果的正确性. 相似文献
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We consider multivariable hypergeometric functions related to Schur functions and show that these hypergeometric functions are tau functions of the KP hierarchy and are simultaneously the ratios of Toda lattice tau functions evaluated at certain values of higher Toda lattice times. The variables of the hypergeometric functions are related to the higher times of those hierarchies via a Miwa change of variables. The discrete Toda lattice variable shifts the parameters of the hypergeometric functions. We construct the determinant representation and the integral representation of a special type for the KP tau functions. We write a system of linear differential and difference equations on these tau functions, which play the role of string equations. 相似文献
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We initiate a study of harmonic functions on hypergroups. In particular, we introduce the concept of a nilpotent hypergroup and show such hypergroup admits an invariant measure as well as a Liouville theorem for bounded harmonic functions. Further, positive harmonic functions on nilpotent hypergroups are shown to be integrals of exponential functions. For arbitrary hypergroups, we derive a Harnack inequality for positive harmonic functions and prove a Liouville theorem for compact hypergroups. We discuss an application to harmonic spherical functions. 相似文献