共查询到20条相似文献,搜索用时 484 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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本文提出了两类新的广义凸函数—强预拟不变凸函数与强拟不变凸函数.讨论了强预拟不变凸函数与强拟不变凸函数间的关系,强拟不变凸函数与强伪不变凸函数间的关系.研究了强预拟不变凸函数在多目标优化中的应用. 相似文献
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Subvexormal functions and subinvexormal functions are proposed, whose properties are shared commonly by most generalized convex functions and most generalized invex functions, respectively. A necessary and sufficient condition for a subvexormal function to be subinvexormal is given in the locally Lipschitz and regular case. Furthermore, subvex functions and subinvex functions are introduced. It is proved that the class of strictly subvex functions is equivalent to that of functions whose local minima are global and that, in the locally Lipschitz and regular case, both strongly subvex functions and strongly subinvex functions can be characterized as functions whose relatively stationary points (slight extension of stationary points) are global minima. 相似文献
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Constructions and equivalence of APN functions play a significant role in the research of cryptographic functions. On finite fields of characteristic 2, 6 families of power APN functions and 14 families of polynomial APN functions have been constructed in the literature. However, the study on the equivalence among the aforementioned APN functions is rather limited to the equivalence in the power APN functions. Meanwhile, the theoretical analysis on the equivalence between the polynomial APN functions and the power APN functions, as well as the equivalence in the polynomial APN functions themselves, is far less studied. In this paper, we give the theoretical analysis on the inequivalence in 8 known families of polynomial APN functions and power APN functions. 相似文献
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The study of moment functions on commutative topological groups leads to the study of systems of functional equations. Systems of functional equations characterizing moment functions and sequences of moment functions are closely related to exponential functions and additive functions. Here we describe moment functions and generalized moment functions on polynomial hypergroups.Received: 23 May 2003; revised: 20 September 2004 相似文献
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Hong-yong Wang Zong-ben XuDepartment of Mathematics Huaibei Coal Industry Teachers College Huaibei ChinaResearch Center for Applied Mathematics Faculty of Science Xi''''an Jiaotong University Xi''''an China 《应用数学学报(英文版)》2002,18(3):431-440
In this paper, we construct a class of nowhere differentiable continuous functions by means of the Cantor series expression of real numbers. The constructed functions include some known nondifferentiable functions, such as Bush type functions. These functions are fractal functions since their graphs are in general fractal sets. Under certain conditions, we investigate the fractal dimensions of the graphs of these functions, compute the precise values of Box and Packing dimensions, and evaluate the Hausdorff dimension. Meanwhile, the Holder continuity of such functions is also discussed. 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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XuZheng XuChengxian 《高校应用数学学报(英文版)》2000,15(3):307-318
The paper is concerned with the filled functions for global optimization of a continuous function of several variables. More general forms of filled functions are presented for smooth and nonsmooth optimizations. These functions have either two adjustable parameters or one adjustable parameter. Conditions on functions and on the values of parameters are given so that the constructed functions are desired filled functions. 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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A. Perotti 《Journal of Mathematical Analysis and Applications》2008,337(1):107-115
In this paper the Dirichlet problem for pluriholomorphic functions of two complex variables is investigated. The key point is the relation between pluriholomorphic functions and pluriharmonic functions. The link is constituted by the Fueter-regular functions of one quaternionic variable. Previous results about the boundary values of pluriharmonic functions and new results on L2 traces of regular functions are applied to obtain a characterization of the traces of pluriholomorphic functions. 相似文献
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R. A. Poliquin R. T. Rockafellar 《Transactions of the American Mathematical Society》1996,348(5):1805-1838
The class of prox-regular functions covers all l.s.c., proper, convex functions, lower- functions and strongly amenable functions, hence a large core of functions of interest in variational analysis and optimization. The subgradient mappings associated with prox-regular functions have unusually rich properties, which are brought to light here through the study of the associated Moreau envelope functions and proximal mappings. Connections are made between second-order epi-derivatives of the functions and proto-derivatives of their subdifferentials. Conditions are identified under which the Moreau envelope functions are convex or strongly convex, even if the given functions are not.
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Christophe Rabut 《Numerical Algorithms》2005,39(1-3):329-348
We present in this paper a family of functions which are tensor product functions in subdomains, while not having the usual drawback of functions which are tensor product functions in the whole domain. With these functions we can add more points in some region without adding points on lines parallel to the axes. These functions are linear combinations of tensor product polynomial B-splines, and the knots of different B-splines are less connected together than with usual polynomial B-splines. Approximation of functions, or data, with such functions gives satisfactory results, as shown by numerical experimentation.
AMS subject classification 41A15, 41A63, 65Dxx 相似文献
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Summary We introduce a new class of functions called strongly precontinuous functions in topological spaces. Some properties and several characterizations of this type of functions are obtained. We investigate the relationships between this class of functions and other classes of non-continuous functions. 相似文献
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Sorin-Mihai Grad 《Optimization》2015,64(8):1759-1775
We deliver formulae for the biconjugate functions of some infimal functions that hold provided the fulfilment of weak regularity conditions of both closedness and interiority types. As special cases, we obtain biconjugates of infimal convolutions of finitely many functions, of optimal value functions of both constrained and unconstrained optimization problems as well as of marginal functions associated with multifunctions (that can be, for instance, convex processes) and some given functions. Moreover, we rediscover or extend different results on biconjugate functions from the literature. 相似文献