共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper the properties of some maximum fractional [0, κ]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained. 相似文献
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In this paper the properties of some maximum fractional [0, κ]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional κ-factors is obtained. 相似文献
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分数因子和分数哈密顿图 总被引:1,自引:0,他引:1
本文介绍了图的分数方面,将图中基于整数的定义和变量转化为分数形式.介绍了分数图论的一些新结果,特别是关于分数因子和分数哈密顿图的新结果,其中包括了作者最近得到的一些关于分数(g,f)-因子的若干结果.进而,提出了还没有解决的几个新问题. 相似文献
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We prove that fractional k-factors can be transformed among themselves by using a new adjusting operation repeatedly. We introduce, analogous to Berge’s augmenting path method in matching theory, the technique of increasing walk and derive a characterization of maximum fractional k-factors in graphs. As applications of this characterization, several results about connected fractional 1-factors are obtained. 相似文献
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图的孤立韧度与分数因子的存在性 总被引:10,自引:1,他引:9
设G是一个简单无向图,若G不是完全图,G的孤立韧度定义为I(G)=min{|S|/I(G-S):S包含于V(G),I(G-S)≥2}。否则,令I(G)=∞。本文引入一个与图的孤立韧度I(G)密切相关的新参数I‘(G),若G不是完全图时,I‘(G)=min{|S|/(I(G-S)-1):S包含于V(G),I(G-S)≥2}。否则,I‘(G)=∞;本文研究了参数I(G)和I‘(G)的性质以及两者与图的分数k-因子的关系。给出了具有某些约束条件的图的分数因子存在的一些充分条件。并提出进一步的可研究的问题。 相似文献
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FRACTIONAL (g, f)-FACTORS OF GRAPHS 总被引:5,自引:0,他引:5
1 IntroductionThe graphs considered in this paper will be finite undirected graphs wllicll 11lay llavemultiple edges but no loops. Let G be a grapll with vertex set V(G) and edge set E(G). Fora vertex x of G, the degree of x in G is denoted by dG(z). Let g and f be two integer-valuedfunctions defined o11 V(G) such that 0 < g(z) 5 f(x) fOr all x E V(G). Then a (g, f)-factorof G is a spanning 8ubgraph F of G satisfying g(x) < dG(z) 5 f(x) for all x E V(F). Ifg(x) = f(x) for all x E V(… 相似文献
7.
Jinfa Cheng 《Annals of Differential Equations》2014,(1):5-14
This paper mainly discusses the problems of fractional variational problems and fractional diffusion problems using fractional difference and summation. Through the Euler finite difference method we get a variational formulation of the variation problem and the discrete solution to the time-fractional and space-fractional difference equation using separating variables method and two-side Z-transform method. 相似文献
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Udita N. Katugampola 《Applied mathematics and computation》2011,218(3):860-865
The paper presents a new fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form. Conditions are given for such a fractional integration operator to be bounded in an extended Lebesgue measurable space. Semigroup property for the above operator is also proved. We give a general definition of the fractional derivatives and give some examples. 相似文献
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分数k-因子临界图的条件 总被引:1,自引:0,他引:1
设G是-个连通简单无向图,如果删去G的任意k个项点后的图有分数完美匹配,则称G是分数k-因子临界图.给出了G是分数k-因子临界图的韧度充分条件与度和充分条件,这些条件中的界是可达的,并给出G是分数k-因子临界图的一个关于分数匹配数的充分必要条件. 相似文献
11.
Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk (type fractional differential equation). The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator. 相似文献
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Sabrine Arfaoui & Anouar Ben Mabrouk 《分析论及其应用》2022,38(4):394-416
In the present paper, by extending some fractional calculus to the framework of Clifford analysis, new classes of wavelet functions are presented. Firstly, some
classes of monogenic polynomials are provided based on 2-parameters weight functions which extend the classical Jacobi ones in the context of Clifford analysis. The
discovered polynomial sets are next applied to introduce new wavelet functions. Reconstruction formula as well as Fourier-Plancherel rules have been proved. The main
tool reposes on the extension of fractional derivatives, fractional integrals and fractional Fourier transforms to Clifford analysis. 相似文献
15.
Yi‐Fei Pu Patrick Siarry Ji‐Liu Zhou Ni Zhang 《Mathematical Methods in the Applied Sciences》2014,37(12):1784-1806
Traditional integer‐order partial differential equation based image denoising approach can easily lead edge and complex texture detail blur, thus its denoising effect for texture image is always not well. To solve the problem, we propose to implement a fractional partial differential equation (FPDE) based denoising model for texture image by applying a novel mathematical method—fractional calculus to image processing from the view of system evolution. Previous studies show that fractional calculus has some unique properties that it can nonlinearly enhance complex texture detail in digital image processing, which is obvious different with integer‐order differential calculus. The goal of the modeling is to overcome the problems of the existed denoising approaches by utilizing the aforementioned properties of fractional differential calculus. Using classic definition and property of fractional differential calculus, we extend integer‐order steepest descent approach to fractional field to implement fractional steepest descent approach. Then, based on the earlier fractional formulas, a FPDE based multiscale denoising model for texture image is proposed and further analyze optimal parameters value for FPDE based denoising model. The experimental results prove that the ability for preserving high‐frequency edge and complex texture information of the proposed fractional denoising model are obviously superior to traditional integral based algorithms, as for texture detail rich images. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
16.
Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy. 相似文献
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分数阶微分方程的理论和数值方法研究 总被引:3,自引:0,他引:3
分数阶偏微分方程的研究有很长的历史,并在最近十多年得到快速发展.相比极为有限的理论成果,数值方法的研究成果已经相当丰富,几个国际研究团队对此作出了贡献.本文旨在对分数阶微分方程的理论与数值方法研究成果做个简要的评价,聚焦总结评述与高阶方法发展密切相关的研究.主要内容为讨论最基本的三类方程:时间分数阶扩散方程、空间分数阶扩散方程、以及时空分数阶扩散方程的理论进展和数值方法研究在最近十年取得的结果.我们还有针对性地选择一些算例,用以说明几个重要方法的精度和有效性. 相似文献
19.
Csar T. Ledesma Josias V. Baca J. Vanterler da C. Sousa 《Mathematical Methods in the Applied Sciences》2022,45(1):49-76
In this present paper, we discuss some properties of fractional operators with fixed memory length (Riemann–Liouville fractional integral, Riemann–Liouville and Caputo fractional derivatives). Some observations and examples are discussed during the article, in order to make the results well defined and clear. Furthermore, we consider the fundamental theorem of calculus for fractional operators with fixed memory length. 相似文献
20.
Amir Hosein Hadian Rasanan Nastaran Bajalan Kourosh Parand Jamal Amani Rad 《Mathematical Methods in the Applied Sciences》2020,43(3):1437-1466
By the rapid growth of available data, providing data-driven solutions for nonlinear (fractional) dynamical systems becomes more important than before. In this paper, a new fractional neural network model that uses fractional order of Jacobi functions as its activation functions for one of the hidden layers is proposed to approximate the solution of fractional differential equations and fractional partial differential equations arising from mathematical modeling of cognitive-decision-making processes and several other scientific subjects. This neural network uses roots of Jacobi polynomials as the training dataset, and the Levenberg-Marquardt algorithm is chosen as the optimizer. The linear and nonlinear fractional dynamics are considered as test examples showing the effectiveness and applicability of the proposed neural network. The numerical results are compared with the obtained results of some other networks and numerical approaches such as meshless methods. Numerical experiments are presented confirming that the proposed model is accurate, fast, and feasible. 相似文献