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Stallard曾经用一族特殊的整函数说明了:超越整函数的Julia集的Hausdorff维数可以无限接近1.本文证明了该函数族的随机迭代的Julia集的Hausdorff维数也可无限接近于1.另一方面,对任意自然数M及任意实数d∈(1,2),本文给出了M个元素的整函数族其随机迭代的Julia集的Hausdorff维数等于d. 相似文献
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函数S-粗集(function singular rough sets)是用R-函数等价类定义的,函数是一个规律,函数S-粗集具有规律特征.函数S-粗集推广了Z.Pawlak粗集.利用函数S-粗集,给出规律生成,规律分离的讨论,提出规律分离定理.给出的结果在投资分险规律估计中得到了应用. 相似文献
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马立志 《纯粹数学与应用数学》1990,6(1):4-10
1.引言设f(z)为一超越整函数,考虑由这个函数经过逐次迭代所得到的函数:这个函数序列构成一个函数族。我们记J(f)为这个函数族的非正规点集。这个点集与f的各阶不动点有密切关系,因而引起了关于这个点集的一些研究工作。在这方面, 相似文献
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《数学的实践与认识》2017,(17)
一元粗糙函数及其数学分析性质具有意义,但当前研究主要局限于有限度量.基于无限度量研究一元粗糙函数及其数学分析性质.将度量从有限集扩展到无限集,讨论粗糙函数分类;基于无限度量研究粗糙函数的粗糙连续、粗糙极限、粗糙导数.采用无限度量,推进了一元粗糙函数及其分析性质. 相似文献
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Yulia Kempner 《Discrete Applied Mathematics》2008,156(4):492-499
This paper deals with maximization of set functions defined as minimum values of monotone linkage functions. In previous research, it has been shown that such a set function can be maximized by a greedy type algorithm over a family of all subsets of a finite set. In this paper, we extend this finding to meet-semilattices.We show that the class of functions defined as minimum values of monotone linkage functions coincides with the class of quasi-concave set functions. Quasi-concave functions determine a chain of upper level sets each of which is a meet-semilattice. This structure allows development of a polynomial algorithm that finds a minimal set on which the value of a quasi-concave function is maximum. One of the critical steps of this algorithm is a set closure. Some examples of closure computation, in particular, a closure operator for convex geometries, are considered. 相似文献
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Suppose that we are given a family of choice functions on pairs from a given finite set. The set is considered as a set of alternatives (say candidates for an office) and the functions as potential “voters.” The question is, what choice functions agree, on every pair, with the majority of some finite subfamily of the voters? For the problem as stated, a complete characterization was given in Shelah (2009) [7], but here we allow voters to abstain. Aside from the trivial case, the possible families of (partial) choice functions break into three cases in terms of the functions that can be generated by majority decision. In one of these, cycles along the lines of Condorcet’s paradox are avoided. In another, all partial choice functions can be represented. 相似文献
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Lynn Margaret Batten 《Discrete Mathematics》1984,49(2):113-116
We characterize those functions that are the rank functions of closure spaces of finite rank. In case such a function is defined on a finite set, we are able to improve this characterization. 相似文献
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In this paper, we propose a new modified proximal point algorithm for finding a common element of the set of common minimizers of a finite family of convex and lower semi-continuous functions and the set of common fixed points of a finite family of nonexpansive mappings in complete CAT(0) spaces, and prove some convergence theorems of the proposed algorithm under suitable conditions. A numerical example is presented to illustrate the proposed method and convergence result. Our results improve and extend the corresponding results existing in the literature. 相似文献
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A necessary condition is given on the Fourier transforms of a finite family of functions in Rsso that the finite family and their translates will approximate an arbitrary function within certain precision. 相似文献
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Saharon Shelah 《Discrete Mathematics》2009,309(8):2349-1352
Suppose we are given a family of choice functions on pairs from a given finite set (with at least three elements) closed under permutations of the given set. The set is considered the set of alternatives (say candidates for an office). The question is, what are the choice functions c on pairs of this set of the following form: for some (finite) family of “voters”, each having a preference, i.e. a choice from each pair from the given family, is chosen by the preference of the majority of voters. We give full characterization. 相似文献
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Prof. J. C. Harsanyi 《International Journal of Game Theory》1973,2(1):235-250
A new proof is offered for the theorem that, in “almost all” finite games, the number of equilibrium points isfinite andodd. The proof is based on constructing a one-parameter family of games with logarithmic payoff functions, and studying the topological properties of the graph of a certain algebraic function, related to the graph of the set of equilibrium points for the games belonging to this family. In the last section of the paper, it is shown that, in the space of all games of a given size, those “exceptional” games which fail to satisfy the theorem (by having an even number or an infinity of equilibrium points) is a closed set of measure zero. 相似文献
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本文研究了几何有限有理函数的复解析动力性质.利用Markov划分与共形迭代函数系统的理论,获得了几何有限有理函数Julia集的性质.如有理函数是几何有限的,且Julia集是连通的,则Julia集的Hausdorff维数为1当且仅当Julia集为一圆周或直线的一段. 相似文献
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A. A. Krokhin 《Algebra and Logic》1995,34(3):155-168
Suppose A is a finite set. For every clone C over A, the family C(1) of all unary functions in C is a monoid of transformations of the set A. We study how the lattice of clones is partitioned
into intervals, where two clones belong to the same partition iff they have the same monoids of unary functions. The problem
of Szendrei concerning the power of such intervals is investigated. We give new examples of intervals which are continual,
one-element, and finite but not one-element. Moreover, it is proved that every lattice that is not more than a direct product
of countably many finite chains is isomorphic to some interval in the lattice of clones, establishing, in passing, the number
of E-minimal algebras on a finite set.
Translated fromAlgebra i Logika, Vol. 34, No. 3, pp. 288-310, May-June, 1995. 相似文献
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David E. Hurtubise 《Transactions of the American Mathematical Society》1997,349(6):2493-2505
A family of Floer functions on the infinite dimensional complex Grassmann manifold is defined by taking direct limits of height functions on adjoint orbits of unitary groups. The Floer cohomology of a generic function in the family is computed using the Schubert calculus. The Floer homotopy type of this function is computed and the Floer cohomology which was computed algebraically is recovered from the Floer homotopy type. Certain non-generic elements of this family of Floer functions were shown to be related to the symplectic action functional on the universal cover of the loop space of a finite dimensional complex Grassmann manifold in the author's preprint The Floer homotopy type of complex Grassmann manifolds.