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Foundations of generalized Prabhakar-Hilfer fractional calculus with applications 广义Prabhakar-Hilfer分式微积分的基础及其应用
IF 0.5 Q3 MATHEMATICS Pub Date : 2021-12-01 DOI: 10.4067/s0719-06462021000300423
G. Anastassiou
Here we introduce the generalized Prabhakar fractional calculus and we also combine it with the generalized Hilfer calculus. We prove that the generalized left and right side Prabhakar fractional integrals preserve continuity and we find tight upper bounds for them. We present several left and right side generalized Prabhakar fractional inequalities of Hardy, Opial and Hilbert-Pachpatte types. We apply these in the setting of generalized Hilfer calculus.
这里我们介绍了广义Prabhakar分式微积分,并将其与广义Hilfer微积分相结合。我们证明了广义左、右侧Prabhakar分数积分保持连续性,并给出了它们的紧上界。我们给出了Hardy型、Opial型和Hilbert-Pachpatte型的几个左右侧广义Prabhakar分数不等式。我们将这些应用于广义希尔弗微积分的设置中。
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引用次数: 3
On the periodic solutions for some retarded partial differential equations by the use of semi-Fredholm operators 用半Fredholm算子研究一类时滞偏微分方程的周期解
IF 0.5 Q3 MATHEMATICS Pub Date : 2021-12-01 DOI: 10.4067/s0719-06462021000300469
A. Elazzouzi, K. Ezzinbi, Mohammed Kriche
The main goal of this work is to examine the periodic dynamic behavior of some retarded periodic partial differential equations (PDE). Taking into consideration that the linear part realizes the Hille-Yosida condition, we discuss the Massera’s problem to this class of equations. Especially, we use the perturbation theory of semi-Fredholm operators and the Chow and Hale’s fixed point theorem to study the relation between the boundedness and the periodicity of solutions for some inhomogeneous linear retarded PDE. An example is also given at the end of this work to show the applicability of our theoretical results.
本文的主要目的是研究一类时滞周期偏微分方程的周期动力学行为。考虑到线性部分满足Hille-Yosida条件,我们讨论了这类方程的Massera问题。特别地,我们利用半fredholm算子的摄动理论和Chow和Hale不动点定理研究了一类非齐次线性时滞偏微分方程解的有界性与周期性之间的关系。最后给出了一个算例,说明了理论结果的适用性。
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引用次数: 0
Extension of Exton’s hypergeometric function K16 Exton超几何函数K16的推广
IF 0.5 Q3 MATHEMATICS Pub Date : 2021-12-01 DOI: 10.4067/s0719-06462021000300489
Ahmed Ali Atash, Maisoon Ahmed Kulib
The purpose of this article is to introduce an extension of Exton’s hypergeometric function K 16 by using the extended beta function given by Özergin et al. [11]. Some integral representations, generating functions, recurrence relations, transformation formulas, derivative formula and summation formulas are obtained for this extended function. Some special cases of the main results of this paper are also considered.
本文的目的是通过使用Özergin等人给出的扩展beta函数来介绍Exton的超几何函数k16的扩展。得到了该扩展函数的积分表示、生成函数、递归关系、变换公式、导数公式和求和公式。文中还考虑了本文主要结果的一些特殊情况。
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引用次数: 0
Basic asymptotic estimates for powers of Wallis’ ratios Wallis比率幂的基本渐近估计
IF 0.5 Q3 MATHEMATICS Pub Date : 2021-12-01 DOI: 10.4067/s0719-06462021000300357
V. Lampret
For any a ∈ R , for every n ∈ N , and for n -th Wallis’ ratio w n := (cid:81) nk =1 2 k − 1 2 k , the relative error r 0 ( a, n ) := (cid:0) v 0 ( a, n ) − w an (cid:1) /w an of the approximation w an ≈ v 0 ( a, n ) := ( πn ) − a/ 2 is estimated as (cid:12)(cid:12) r 0 ( a, n ) (cid:12)(cid:12) < 14 n . The improvement w an ≈ v ( a, n ) := ( πn ) − a/ 2 (cid:16) 1 − a 8 n + a 2 128 n 2 (cid:17) is also studied.
为任何a∈R,因为每n∈n, and For -th沃利斯“ratio w n = (cid): 81) nk k = 1 2 k−1,亲戚错误R 0杂志》(a, n): = (cid) v 0 (a, n) w−an (cid》:1)/ w的类似w v≈0的(a, n): =(π)−a / 2是美国estimated (cid 12: 12) (cid) R 0 (a, n) (cid: 12 (cid): 12) < 14 n。安improvement w v≈杂志》(a, n): =(πa / 2 (n)−cid: 16) 1−a 8 n + 2 128 n (cid: 17)是也studied。
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引用次数: 0
Dirichlet series and series with Stirling numbers 狄利克雷级数和斯特林级数
IF 0.5 Q3 MATHEMATICS Pub Date : 2021-09-19 DOI: 10.56754/0719-0646.2501.103
K. Boyadzhiev
This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers, derangement numbers, binomial coefficients, central binomial coefficients, and Catalan numbers.
本文给出了狄利克雷级数和第一类斯特林数级数的一些恒等式。作为狄利克雷级数的系数,我们使用第一类和第二类柯西数、超调和数、无序数、二项式系数、中心二项式系数和加泰罗尼亚数。
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引用次数: 0
A new class of graceful graphs: k-enriched fan graphs and their characterisations 一类新的优美图:k-富集扇形图及其特征
IF 0.5 Q3 MATHEMATICS Pub Date : 2021-08-01 DOI: 10.4067/s0719-06462021000200313
M. Haviar, S. Kurtulík
The Graceful Tree Conjecture stated by Rosa in the mid 1960s says that every tree can be gracefully labelled. It is one of the best known open problems in Graph Theory. The conjecture has caused a great interest in the study of gracefulness of simple graphs and has led to many new contributions to the list of graceful graphs. However, it has to be acknowledged that not much is known about the structure of graceful graphs after 55 years. Our paper adds an infinite family of classes of graceful graphs to the list of known simple graceful graphs. We introduce classes of (k)-enriched fan graphs (kF_n) for all integers (k, nge 2) and we prove that these graphs are graceful. Moreover, we provide characterizations of the (k)-enriched fan graphs (kF_n) among all simple graphs via Sheppard's labelling sequences introduced in the 1970s, as well as via labelling relations and graph chessboards. These last approaches are new tools for the study of graceful graphs introduced by Haviar and Ivaska in 2015. The labelling relations are closely related to Sheppard's labelling sequences while the graph chessboards provide a nice visualization of graceful labellings. We close our paper with an open problem concerning another infinite family of extended fan graphs.
罗莎在20世纪60年代中期提出的优雅树猜想说,每棵树都可以被优雅地标记。它是图论中最著名的开放问题之一。该猜想引起了简单图优美性研究的极大兴趣,并为优美图列表做出了许多新的贡献。然而,必须承认的是,在55年后,人们对优美图的结构知之甚少。我们的论文在已知的简单优美图的列表中添加了一个无穷族的优美图类。我们引入了所有整数(k,nge2)的(k)-富集扇形图(kF_n)的类,并证明了这些图是优美的。此外,我们还通过20世纪70年代引入的Sheppard标记序列,以及标记关系和图棋盘,给出了所有简单图中的(k)富集扇形图(kF_n)的特征。最后这些方法是Haviar和Ivaska在2015年引入的研究优美图的新工具。标记关系与Sheppard的标记序列密切相关,而图棋盘提供了优美标记的良好可视化。我们用一个关于另一个无限族扩展扇图的开放问题来结束我们的论文。
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引用次数: 0
On Rellich's Lemma, the Poincaré inequality, and Friedrichs extension of an operator on complex spaces 复空间上算子的Rellich引理、poincar<s:1>不等式和Friedrichs推广
IF 0.5 Q3 MATHEMATICS Pub Date : 2021-08-01 DOI: 10.4067/s0719-06462021000200265
C. Tung, P. D. Lamberti
This paper is mainly concerned with: (i) a generalization of the Rellich’s Lemma to a Riemann subdomain of a complex space, (ii) the Poincare inequality, and (iii) Friedrichs extension of a Schrodinger type operator. Applications to the eigenfunction expansion problem associated to the modified Laplacian are also given.
本文主要研究:(i)复空间的黎曼子域上Rellich引理的推广,(ii)庞加莱不等式,(iii)薛定谔型算子的Friedrichs推广。并给出了在与修正拉普拉斯算子相关的特征函数展开问题上的应用。
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引用次数: 0
Approximate solution of Abel integral equation in Daubechies wavelet basis Daubechies小波基中Abel积分方程的近似解
IF 0.5 Q3 MATHEMATICS Pub Date : 2021-08-01 DOI: 10.4067/s0719-06462021000200245
Jyotirmoy Mouley, M. M. Panja, B. N. Mandal
This paper presents a new computational method for solving Abel integral equation (both first kind and second kind). The numerical scheme is based on approximations in Daubechies wavelet basis. The properties of Daubechies scale functions are employed to reduce an integral equation to the solution of a system of algebraic equations. The error analysis associated with the method is given. The method is illustrated with some examples and the present method works nicely for low resolution.
本文提出了求解Abel积分方程(第一类和第二类)的一种新的计算方法。该数值格式基于Daubechies小波基中的近似。利用Daubechies标度函数的性质将积分方程简化为代数方程组的解。给出了与该方法相关的误差分析。通过实例说明了该方法的有效性。
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引用次数: 0
Weakly strongly star-Menger spaces 弱强星门格尔空间
IF 0.5 Q3 MATHEMATICS Pub Date : 2021-08-01 DOI: 10.4067/s0719-06462021000200287
G. Kumar, B. Tyagi
A space (X) is called weakly strongly star-Menger space if for each sequence ((mathcal{U}_{n} : n in omega)) of open covers of (X), there is a sequence ((F_n : ninomega)) of finite subsets of (X) such that (overline{bigcup_{ninomega} St(F_n, mathcal{U}_n)}) is (X). In this paper, we investigate the relationship of weakly strongly star-Menger spaces with other related spaces. It is shown that a Hausdorff paracompact weakly star Menger (P)-space is star-Menger. We also study the images and preimages of weakly strongly star-Menger spaces under various type of maps.
空间(X)称为弱强星Menger空间,如果对于每个序列((mathcal{U}_{n} :ninomega))的开覆盖,存在(X)的有限子集的序列((F_n:ninomega)),使得(overline{bigcup_{ninomega}St(F_n,mathcal{U}_n)})是(X)。本文研究了弱强星Menger空间与其它相关空间的关系。证明了一个Hausdorff仿紧弱星Menger(P)-空间是星Menger。我们还研究了在各种类型的映射下,弱强恒星Menger空间的图像和前图像。
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引用次数: 1
Coincidence point results of nonlinear contractive mappings in partially ordered metric spaces 部分有序度量空间中非线性压缩映射的重合点结果
IF 0.5 Q3 MATHEMATICS Pub Date : 2021-08-01 DOI: 10.4067/s0719-06462021000200207
K. Kalyani, N. S. Rao
In this paper, we proved some coincidence point results for (f)- nondecreasing self-mapping satisfying certain rational type contractions in the context of a metric space endowed with a partial order. Moreover, some consequences of the main result are given by involving integral type contractions in the space. Some numerical examples are illustrated to support our results. As an application, we have discussed the existence of a unique solution of integral equation.
在给定偏序的度量空间中,证明了(f) -非递减自映射满足某些有理型压缩的一些重合点结果。此外,通过在空间中引入积分型收缩,给出了主要结果的一些结果。文中给出了一些数值算例来支持我们的结果。作为应用,我们讨论了积分方程唯一解的存在性。
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引用次数: 2
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