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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
Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm220506002b
P. Butzer, T. He, C. Markett
{"title":"Eulerian fractions and Stirling, Bernoulli and Euler functions with complex order parameters and their impact on the polylogarithm function","authors":"P. Butzer, T. He, C. Markett","doi":"10.2298/aadm220506002b","DOIUrl":"https://doi.org/10.2298/aadm220506002b","url":null,"abstract":"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.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68354273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
New family of Jacobi-Stirling numbers 新的Jacobi-Stirling数族
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm210829013c
N. Cakic, B. El-Desouky, R. Gomaa
{"title":"New family of Jacobi-Stirling numbers","authors":"N. Cakic, B. El-Desouky, R. Gomaa","doi":"10.2298/aadm210829013c","DOIUrl":"https://doi.org/10.2298/aadm210829013c","url":null,"abstract":"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.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm210917004t
Slobodan Trickovic, M. Stankovic
{"title":"Applications of the generalized function-to-sequence transform","authors":"Slobodan Trickovic, M. Stankovic","doi":"10.2298/aadm210917004t","DOIUrl":"https://doi.org/10.2298/aadm210917004t","url":null,"abstract":"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.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68354010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm221211009d
Nebojša Djurić, B. Vojvodić
{"title":"Inverse problem for Dirac operators with a constant delay less than half the length of the interval","authors":"Nebojša Djurić, B. Vojvodić","doi":"10.2298/aadm221211009d","DOIUrl":"https://doi.org/10.2298/aadm221211009d","url":null,"abstract":"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).","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68354427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm230210018b
Marija Bosnjak, Mario Krnic, Josip Pecaric
{"title":"Application of the fink identity to Jensen-type inequalities for higher order convex functions","authors":"Marija Bosnjak, Mario Krnic, Josip Pecaric","doi":"10.2298/aadm230210018b","DOIUrl":"https://doi.org/10.2298/aadm230210018b","url":null,"abstract":"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","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm210927014a
Abdullah Alazemi, E. Kılıç
{"title":"Determinant evaluation of banded Toeplitz matrices via bivariate polynomial families","authors":"Abdullah Alazemi, E. Kılıç","doi":"10.2298/aadm210927014a","DOIUrl":"https://doi.org/10.2298/aadm210927014a","url":null,"abstract":"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.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68354023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm230219019h
Xue-Feng Han, Chao-Ping Chen, H.M. Srivastava
{"title":"Some new results related to the constant e and function (1+1/x)x","authors":"Xue-Feng Han, Chao-Ping Chen, H.M. Srivastava","doi":"10.2298/aadm230219019h","DOIUrl":"https://doi.org/10.2298/aadm230219019h","url":null,"abstract":"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.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136201907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The constructor-blocker game 构建者-拦阻者游戏
4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm220723022p
Balázs Patkós, Milos Stojakovic, Máté Vizer
{"title":"The constructor-blocker game","authors":"Balázs Patkós, Milos Stojakovic, Máté Vizer","doi":"10.2298/aadm220723022p","DOIUrl":"https://doi.org/10.2298/aadm220723022p","url":null,"abstract":"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.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136210047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm220903017s
Vanterler da C. Sousa, D.S. Oliveira, Ravi Agarwal
{"title":"Existence and multiplicity for fractional Dirichlet problem with γ(ξ)-Laplacian equation and Nehari manifold","authors":"Vanterler da C. Sousa, D.S. Oliveira, Ravi Agarwal","doi":"10.2298/aadm220903017s","DOIUrl":"https://doi.org/10.2298/aadm220903017s","url":null,"abstract":"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.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI: 10.2298/aadm230902020q
Feng Qi, Peter Taylor
{"title":"Series expansions for powers of sinc function and closed-form expressions for specific partial bell polynomials","authors":"Feng Qi, Peter Taylor","doi":"10.2298/aadm230902020q","DOIUrl":"https://doi.org/10.2298/aadm230902020q","url":null,"abstract":"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.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136201893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
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