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Eulerian fractions and Stirling, Bernoulli and Euler functions with complex order parameters and their impact on the polylogarithm function 欧拉分数与复阶参数斯特林、伯努利和欧拉函数及其对多对数函数的影响
IF 0.9 4区 数学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm220506002b
P. Butzer, T. He, C. Markett
We first study some generalizations of Eulerian fractions with complex order parameter and investigate their interrelationship with likewise generalized Eulerian functions as well as Stirling functions. We apply the new approach to polylogarithms of non-integral order, for which only a few values are known in closed form. In particular, we present a structural solution of the counterpart of an old conjecture of Mengoli and Euler in the polylogarithm case with the aid of Riemann?s zeta function and the Dirichlet eta and beta functions.
本文首先研究了复阶参数欧拉分数的一些推广,并研究了它们与类似的推广欧拉函数和斯特林函数的相互关系。我们将新方法应用于非整阶的多对数,其中只有少数值以封闭形式已知。特别地,我们提出了一个结构解的对应物的旧猜想孟格里和欧拉在多对数情况下黎曼?s函数和狄利克雷函数和函数。
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引用次数: 1
New family of Jacobi-Stirling numbers 新的Jacobi-Stirling数族
IF 0.9 4区 数学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm210829013c
N. Cakic, B. El-Desouky, R. Gomaa
The Jacobi-Stirling numbers of the first and second kind were introduced in 2007 by Everitt et al. In this article we find new explicit formulas for Jacobi Stirling numbers. Furthermore, we derive and study new class of the Jacobi Stirling numbers so-called generalized Jacobi-Stirling numbers. Some special cases such as Legendre-Stirling numbers are given. Some interesting combinatorial identities are obtained.
第一类和第二类Jacobi-Stirling数是由Everitt等人在2007年引入的。本文给出了新的雅可比斯特林数的显式公式。在此基础上,导出并研究了一类新的Jacobi-Stirling数,即广义Jacobi-Stirling数。给出了一些特殊情况,如legende - stirling数。得到了一些有趣的组合恒等式。
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引用次数: 0
Applications of the generalized function-to-sequence transform 广义函数到序列变换的应用
IF 0.9 4区 数学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm210917004t
Slobodan Trickovic, M. Stankovic
We deal with applications of the transform T? we introduced in our paper On a generalized function-to-sequence transform, Appl. Anal. Disc. Math. Vol. 14 No 2 (2020) 300-316. Taking different sequences {?n}n?N0 linked to a generalized linear difference operator D? gives rise to a family of transforms T? that enables the mapping of a differential equation and its solutions to a difference equation and its solutions. It can map a differential operator to a difference one as well.
我们处理变换T的应用?本文介绍了一种广义的函数到序列变换。分析的阀瓣。数学。14卷第2期(2020)300-316。取不同的序列{?n}n?N0与广义线性差分算子D?得到一系列变换T?这使得微分方程及其解与差分方程及其解之间的映射成为可能。它也可以把一个微分算子映射成一个差分算子。
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引用次数: 0
Inverse problem for Dirac operators with a constant delay less than half the length of the interval 具有小于一半区间长度的常数延迟的狄拉克算子的反问题
IF 0.9 4区 数学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm221211009d
Nebojša Djurić, B. Vojvodić
We study inverse spectral problems for Dirac-type functional-differential operators with a constant delay a ? [?/3, ?/2).We consider the asymptotic behavior of eigenvalues and research the inverse problem of recovering operators from two spectra. The main result of the paper refers to the proof that the operator could be recovered uniquely from two spectra in the case a ? [2?/5, ?/2), as well as the proof that it is not possible in the case a ? [?/3, 2?/5).
研究具有常数时滞a ?的dirac型泛函微分算子的逆谱问题。[?/ 3, ? / 2)。考虑特征值的渐近性,研究了从两个谱中恢复算子的逆问题。本文的主要结果是证明了在a ?[2 ?/5, ?/2),以及证明在a ?[?/ 3, 2 ? / 5)。
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引用次数: 4
Application of the fink identity to Jensen-type inequalities for higher order convex functions fink恒等式在高阶凸函数jensen型不等式中的应用
4区 数学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm230210018b
Marija Bosnjak, Mario Krnic, Josip Pecaric
The focus of this paper is the application of the Fink identity in obtaining Jensen-type inequalities for higher order convex functions. In addition to the basic form, we establish superadditivity and monotonicity relations that correspond to the Jensen inequality in this setting. We also obtain the corresponding Lah-Ribaric inequality. The obtained results are valid for functions of even degree of convexity. With this method, we derive some new bounds for the differences of power means, as well as some new H?lder-type inequalities
本文重点讨论了Fink恒等式在求解高阶凸函数jensen型不等式中的应用。除了基本形式外,我们还建立了与詹森不等式对应的超加性和单调性关系。我们也得到了相应的la - ribaric不等式。所得结果对偶凸度函数是有效的。利用这种方法,我们得到了幂均值之差的一些新的界,以及一些新的H?lder-type不平等
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引用次数: 0
Determinant evaluation of banded Toeplitz matrices via bivariate polynomial families 基于二元多项式族的带状Toeplitz矩阵的行列式计算
IF 0.9 4区 数学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm210927014a
Abdullah Alazemi, E. Kılıç
We define three kinds banded Toeplitz matrices via with the upper and lower bandwidths ??x? and ??y?. The determinant evaluation is explicitly given for three kinds banded Toeplitz matrices via bivariate Tribonacci and Delannoy polynomials by using generating function approach and recurrence relations. Moreover perturbed versions of each kinds of the banded Toeplitz matrices by a 2 ? 2 general square matrix at the upper right corner will be explicitly computed.
我们定义了三种带状Toeplitz矩阵via,其上下带宽分别为x?y和? ? ?。利用生成函数法和递归关系,通过二元Tribonacci和Delannoy多项式,给出了三种带状Toeplitz矩阵的行列式求值。此外,每种带状Toeplitz矩阵的扰动版本被一个2 ?2 .将右上角的一般方阵显式计算。
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引用次数: 0
Some new results related to the constant e and function (1+1/x)x 一些关于常数e和函数(1+1/x)x的新结果
4区 数学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm230219019h
Xue-Feng Han, Chao-Ping Chen, H.M. Srivastava
It is known that the constant e has the following series representations: e = ?? k=0 1/k! and e = ?? k=0 9k2+1/(3k)!. The second series is extremely rapidly convergent. In this paper, we present asymptotic expansions and two-sided inequalities for the remainders Rn and Rn, where Rn = e ? ?n k=0 1/k! and Rn=e??n k=0 9k2+1/(3k)!. Also, we present some inequalities and completely monotonic functions involving (1 + 1/x)x. We also consider a number of related developments on the subject of this paper.
已知常数e有以下级数表示:e = ??k = 0 1 / k !e = ??k = 0 9 k2 + 1 / (3 k) !。第二个级数的收敛速度非常快。本文给出了余数Rn和Rn的渐近展开式和双边不等式,其中Rn = e ?n k=0 1/k!和Rn = e ? ?N k= 9k2+1/(3k)!同时,我们也给出了涉及(1 + 1/x)x的一些不等式和完全单调函数。我们还审议了关于本文主题的若干相关发展。
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引用次数: 0
The constructor-blocker game 构建者-拦阻者游戏
4区 数学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm220723022p
Balázs Patkós, Milos Stojakovic, Máté Vizer
Given two graphs F and H, Constructor and Blocker alternately claim unclaimed edges of the complete graph Kn. Constructor?s graph must remain F-free, while Blocker claims edges without restrictions. The game ends when Constructor cannot claim further edges or when all edges have been claimed. The score of the game is the number of H?s in Constructor?s graph. Constructor?s aim is to maximize the score, while Blocker tries to minimize it. We study this game for several choices of F and H.
给定两个图F和H, Constructor和Blocker轮流声明完全图Kn的未声明边。构造函数?s的图形必须保持无f,而Blocker则不受限制地声明边缘。当构造函数不能声明进一步的边或所有边都已被声明时,游戏结束。本场比赛的比分是H?s在构造函数?年代图。构造函数?他的目标是使分数最大化,而布洛克则试图使分数最小化。我们研究了F和H的几种选择。
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引用次数: 1
Existence and multiplicity for fractional Dirichlet problem with γ(ξ)-Laplacian equation and Nehari manifold 具有γ(ξ)-拉普拉斯方程和Nehari流形的分数阶Dirichlet问题的存在性和多重性
4区 数学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm220903017s
Vanterler da C. Sousa, D.S. Oliveira, Ravi Agarwal
This paper is divided in two parts. In the first part, we prove coercivity results and minimization of the Euler energy functional. In the second part, we focus on the existence and multiplicity of a positive solution of fractional Dirichlet problem involving the ?(?)-Laplacian equation with non-negative weight functions in H?,?;? ?(?) (?,R) using some variational techniques and Nehari manifold.
本文分为两部分。在第一部分中,我们证明了欧拉能量泛函的矫顽力结果和最小化。在第二部分中,我们重点讨论了在H?,?;;;;(?) (?,R)利用一些变分技术和Nehari流形。
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引用次数: 0
Series expansions for powers of sinc function and closed-form expressions for specific partial bell polynomials sinc函数幂的级数展开式和特定部分钟多项式的封闭表达式
4区 数学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm230902020q
Feng Qi, Peter Taylor
In the paper, with the aid of the Fa? di Bruno formula, in terms of the central factorial numbers and the Stirling numbers of the second kinds, the authors derive several series expansions for any positive integer powers of the sinc and sinhc functions, discover several closed-form expressions for partial Bell polynomials of all derivatives of the sinc function, establish several series expansions for any real powers of the sinc and sinhc functions, and present several identities for central factorial numbers of the second kind and for the Stirling numbers of the second kind.
在报纸上,借助于法?利用中心阶乘数和第二类Stirling数,导出了sinc和sinhc函数任意正整数幂的级数展开式,发现了sinc函数所有导数的部分Bell多项式的几个封闭表达式,建立了sinc和sinhc函数任意实幂的级数展开式,得到了sinc和sinhc函数任意实幂的级数展开式。并给出了第二类中心阶乘数和第二类斯特林数的几个恒等式。
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引用次数: 4
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