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本文研究了Yang-Lee零点的Julia集的复解析动力系统问题.利用网格及共形迭代函数系统的方法,获得了Yang-Lee零点的Julia集及其Hausdorff维数连续性的结果,推广了乔建永教授在文献[1]中的结果, 相似文献
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本文研究了NCP映射的Julia集为Jordan曲线的问题.利用网格和共形迭代函数系统的方法,获得了Julia集在那种情况下为Jordan曲线的一般结果,推广了有理函数的Julia集为Jordan曲线的复解析动力系统方面的结果. 相似文献
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《数学物理学报(A辑)》2015,(4)
定义了螺形函数的新子族,即ρ次椭圆星形函数和ρ次椭圆形β型螺形函数,并将这些定义推广到多复变数空间中,得到推广的Roper-Suffridge算子在不同空间不同区域上保持ρ次椭圆星形映照和ρ次椭圆形β型螺形映照的性质,由此可以在多复变数空间中构造出许多ρ次椭圆形β型螺形映照.所得结论丰富了对螺形映照子族及推广的Roper-Suffridge算子的研究. 相似文献
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第一次世界大战期间,P.Fatou和G.Julia受Newton迭代法以及Mbius变换群的子群的极限集的启发,产生了Riemann球面上复解析动力系统的研究思想.当时,他们运用新的正规族理论(如Montel定理等)于动力系统,证明了一系列非凡、漂亮... 相似文献
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给定单位圆盘D={z||z|1}上调和映照f(z)=h(z)+g(z),其中h(z)和g(z)为D上的解析函数,满足f(0)=0,λf(0)=1,ΛfΛ.通过引入复参数λ,|λ|=1,本文研究调和映照Fλ(z)=h(z)+λg(z)和解析函数Gλ(z)=h(z)+λg(z)的性质,得到Fλ(z)和Gλ(z)单叶半径的精确估计.作为应用,本文得到单位圆盘D上某些K-拟正则调和映照Bloch常数的更好估计,改进和推广由Chen等人所得的相应结果. 相似文献
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本文研究了由m个超越整函数{fl,f2,…,fm}生成的随机迭代系统的Fatou集分支的某些动力学性质.运用复动力系统理论与双曲度量理论,得到了随机迭代系统有界Fatou分支不存在的一个判别准则,同时回答了Baker所提出的问题,且给出了随机迭代系统Fatou分支为单连通的一个充分条件,推广了Bergweiler的结果. 相似文献
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M. Oberguggenberger H. Vernaeve 《Journal of Mathematical Analysis and Applications》2008,341(1):649-659
This paper is devoted to the study of generalized functions as pointwise functions (so-called internal functions) on certain sets of generalized points (so-called internal sets). We treat the case of the Colombeau algebras of generalized functions, for which these notions have turned out to constitute a fundamental technical tool. We provide general foundations for the notion of internal functions and internal sets and prove a saturation principle. Various applications to Colombeau algebras are given. 相似文献
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A.R. Doagooei 《Optimization》2016,65(1):107-119
In this paper, we study sub-topical functions in the framework of abstract convexity and examine the relevant properties such as support sets, polar sets and sub-differentials for these functions. Plus-radiant and plus-co-radiant sets, and their relations with sub-topical functions are studied. Applying sub-topical functions, we present some separation theorems for both plus-radiant and plus-co-radiant sets. 相似文献
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Paolo Giordano Michael Kunzinger Hans Vernaeve 《Journal of Mathematical Analysis and Applications》2015
Based on a refinement of the notion of internal sets in Colombeau's theory, so-called strongly internal sets, we introduce the space of generalized smooth functions, a maximal extension of Colombeau generalized functions. Generalized smooth functions as morphisms between sets of generalized points form a sub-category of the category of topological spaces. In particular, they can be composed unrestrictedly. 相似文献
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In this paper we study relationships between CNF representations of a given Boolean function f and certain sets of implicates of f. We introduce two definitions of sets of implicates which are both based on the properties of resolution. The first type of sets, called exclusive sets of implicates, is shown to have a functional property useful for decompositions. The second type of sets, called essential sets of implicates, is proved to possess an orthogonality property, which implies that every CNF representation and every essential set must intersect. The latter property then leads to an interesting question, to which we give an affirmative answer for some special subclasses of Horn Boolean functions. 相似文献
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E-Convex Sets, E-Convex Functions, and E-Convex Programming 总被引:34,自引:0,他引:34
E. A. Youness 《Journal of Optimization Theory and Applications》1999,102(2):439-450
A class of sets and a class of functions called E-convex sets and E-convex functions are introduced by relaxing the definitions of convex sets and convex functions. This kind of generalized convexity is based on the effect of an operator E on the sets and domain of definition of the functions. The optimality results for E-convex programming problems are established. 相似文献
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T. Rapcsák 《Journal of Optimization Theory and Applications》2005,127(1):177-191
The Fenchel problem of level sets in the smooth case is solved by deducing a new and nice geometric necessary and sufficient
condition for the existence of a smooth convex function with the level sets of a given smooth pseudoconvex function. The main
theorem is based on a general differential geometric tool, the space of paths defined on smooth manifolds. This approach provides
a complete geometric characterization of a new subclass of pseudoconvex functions originating from analytical mechanics and
a new view on convexlike and generalized convexlike mappings in image analysis.
This paper is dedicated to the memory of Guido Stampacchia.
The author thanks K. Balla for assistance in solving the system of differential equations of Example 2.1 and for helpful remarks.
This research was supported in part by the Hungarian Scientific Research Fund, Grants OTKA-T043276 and OTKA-T043241, and by
CNR, Rome, Italy.
An erratum to this article is available at . 相似文献
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《International Journal of Approximate Reasoning》2014,55(3):908-923
Covering rough sets generalize traditional rough sets by considering coverings of the universe instead of partitions, and neighborhood-covering rough sets have been demonstrated to be a reasonable selection for attribute reduction with covering rough sets. In this paper, numerical algorithms of attribute reduction with neighborhood-covering rough sets are developed by using evidence theory. We firstly employ belief and plausibility functions to measure lower and upper approximations in neighborhood-covering rough sets, and then, the attribute reductions of covering information systems and decision systems are characterized by these respective functions. The concepts of the significance and the relative significance of coverings are also developed to design algorithms for finding reducts. Based on these discussions, connections between neighborhood-covering rough sets and evidence theory are set up to establish a basic framework of numerical characterizations of attribute reduction with these sets. 相似文献
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Analytical Linear Inequality Systems and Optimization 总被引:1,自引:0,他引:1
Goberna M. A. Jornet V. Puente R. Todorov M. I. 《Journal of Optimization Theory and Applications》1999,103(1):95-119
In many interesting semi-infinite programming problems, all the constraints are linear inequalities whose coefficients are analytical functions of a one-dimensional parameter. This paper shows that significant geometrical information on the feasible set of these problems can be obtained directly from the given coefficient functions. One of these geometrical properties gives rise to a general purification scheme for linear semi-infinite programs equipped with so-called analytical constraint systems. It is also shown that the solution sets of such kind of consistent systems form a transition class between polyhedral convex sets and closed convex sets in the Euclidean space of the unknowns. 相似文献