In this paper, we consider the degenerate multi-poly-Bernoulli numbers and polynomials which are defined by means of the multiple polylogarithms and degenerate versions of the multi-poly-Bernoulli numbers and polynomials. We investigate some properties for those numbers and polynomials. In addition, we give some identities and relations for the degenerate multi-poly- Bernoulli numbers and polynomials.
{"title":"A note on degenerate multi-poly-Bernoulli numbers and polynomials","authors":"Taekyun Kim, Dae San Kim","doi":"10.2298/aadm200510005k","DOIUrl":"https://doi.org/10.2298/aadm200510005k","url":null,"abstract":"In this paper, we consider the degenerate multi-poly-Bernoulli numbers and\u0000 polynomials which are defined by means of the multiple polylogarithms and\u0000 degenerate versions of the multi-poly-Bernoulli numbers and polynomials. We\u0000 investigate some properties for those numbers and polynomials. In addition,\u0000 we give some identities and relations for the degenerate multi-poly-\u0000 Bernoulli numbers and polynomials.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42563479","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}
In this paper, we give a generalization of the Pascal triangle called the quasi s-Pascal triangle. For this, consider a set of lattice path, which is a dual approach to the definition of Ramirez and Sirvent: A Generalization of the k-bonacci Sequence from Riordan Arrays. The electronic journal of combinatorics, 22(1) (2015), 1-38. We give the recurrence relation for the sum of elements lying over finite ray of the quasi s-Pascal triangle, then, we establish a q-analogue of the coefficient of this triangle. Some identities are also given.
{"title":"Asymmetric extension of Pascal-Delannoy triangles","authors":"Said Amrouche, H. Belbachir","doi":"10.2298/aadm200411028a","DOIUrl":"https://doi.org/10.2298/aadm200411028a","url":null,"abstract":"In this paper, we give a generalization of the Pascal triangle called the\u0000 quasi s-Pascal triangle. For this, consider a set of lattice path, which is\u0000 a dual approach to the definition of Ramirez and Sirvent: A Generalization\u0000 of the k-bonacci Sequence from Riordan Arrays. The electronic journal of\u0000 combinatorics, 22(1) (2015), 1-38. We give the recurrence relation for the\u0000 sum of elements lying over finite ray of the quasi s-Pascal triangle, then,\u0000 we establish a q-analogue of the coefficient of this triangle. Some\u0000 identities are also given.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47574403","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}
Ángeles Carmona Mejías, Margarida Mitjana Riera, Enrique P.J. Monsó Burgués
In this paper we consider a subdivision of a given network and we show how the group inverse matrix of the normalized laplacian of the subdivision network is related to the group inverse matrix of the normalized laplacian of the initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both structures and takes advantage on the properties of the group inverse matrix. As a consequence we get formulae for effective resistances and the Kirchhoff Index of the subdivision network expressed in terms of its corresponding in the base network. Finally, we study two examples where the base network are the star and the wheel, respectively.
{"title":"Group inverse matrix of the normalized Laplacian on subdivision networks","authors":"Ángeles Carmona Mejías, Margarida Mitjana Riera, Enrique P.J. Monsó Burgués","doi":"10.2298/aadm180420023c","DOIUrl":"https://doi.org/10.2298/aadm180420023c","url":null,"abstract":"In this paper we consider a subdivision of a given network and we show how the group inverse matrix of the normalized laplacian of the subdivision network is related to the group inverse matrix of the normalized laplacian of the initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both structures and takes advantage on the properties of the group inverse matrix. As a consequence we get formulae for effective resistances and the Kirchhoff Index of the subdivision network expressed in terms of its corresponding in the base network. Finally, we study two examples where the base network are the star and the wheel, respectively.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68352060","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}
The aim of this paper is to define new families of combinatorial numbers and polynomials associated with Peters polynomials. These families are also a modification of the special numbers and polynomials in [11]. Some fundamental properties of these polynomials and numbers are given. Moreover, a combinatorial identity, which calculates the Fibonacci numbers with the aid of binomial coefficients and which was proved by Lucas in 1876, is proved by different method with the help of these combinatorial numbers. Consequently, by using the same method, we give a new recurrence formula for the Fibonacci numbers and Lucas numbers. Finally, relations between these combinatorial numbers and polynomials with their generating functions and other well-known special polynomials and numbers are given.
{"title":"A new family of combinatorial numbers and polynomials associated with peters numbers and polynomials","authors":"Y. Simsek","doi":"10.2298/aadm190220042s","DOIUrl":"https://doi.org/10.2298/aadm190220042s","url":null,"abstract":"The aim of this paper is to define new families of combinatorial numbers and polynomials associated with Peters polynomials. These families are also a modification of the special numbers and polynomials in [11]. Some fundamental properties of these polynomials and numbers are given. Moreover, a combinatorial identity, which calculates the Fibonacci numbers with the aid of binomial coefficients and which was proved by Lucas in 1876, is proved by different method with the help of these combinatorial numbers. Consequently, by using the same method, we give a new recurrence formula for the Fibonacci numbers and Lucas numbers. Finally, relations between these combinatorial numbers and polynomials with their generating functions and other well-known special polynomials and numbers are given.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68352365","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}
In this paper, we firstly introduce the polylogarithms and incomplete gamma function. Then, we claim that there is a relation between polylogarithms and a generalization of incomplete gamma function. Secondly, we give a formula related to polylogarithms. Also, we obtain a relation between incomplete gamma function and the derivatives of polylogarithms. Finally, we find a generating function for the values of incomplete gamma function.
{"title":"A note on polylogarithms and incomplete gamma function","authors":"A. Ahmet","doi":"10.2298/aadm190221047a","DOIUrl":"https://doi.org/10.2298/aadm190221047a","url":null,"abstract":"In this paper, we firstly introduce the polylogarithms and incomplete gamma function. Then, we claim that there is a relation between polylogarithms and a generalization of incomplete gamma function. Secondly, we give a formula related to polylogarithms. Also, we obtain a relation between incomplete gamma function and the derivatives of polylogarithms. Finally, we find a generating function for the values of incomplete gamma function.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68352425","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}
Let k be a non-negative integer. We define the M?bius-Bernoulli numbers which is denoted by Mk(n) and double M?bius-Bernoulli numbers Mk(n, n') for some n, n' ? N. In this article, we find formula of Mk(n, n') and examples.
设k为非负整数。我们定义M?比乌斯-伯努利数用Mk(n)和双M?比乌斯-伯努利数Mk(n, n')对于某些n, n' ?在本文中，我们找到了Mk(n, n')的公式和例子。
{"title":"A study of Möbius-Bernoulli numbers","authors":"Daeyeoul Kim, A. Bayad, Hyungyu Ahn","doi":"10.2298/aadm190223049k","DOIUrl":"https://doi.org/10.2298/aadm190223049k","url":null,"abstract":"Let k be a non-negative integer. We define the M?bius-Bernoulli numbers which is denoted by Mk(n) and double M?bius-Bernoulli numbers Mk(n, n') for some n, n' ? N. In this article, we find formula of Mk(n, n') and examples.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68352550","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}
In this paper we establish several Jensen-type operator inequalities for a class of superquadratic functions and self-adjoint operators. Our results are given in the so-called external form. As an application, we give improvements of the H?lder-McCarthy inequality and the classical discrete and integral Jensen inequality in the corresponding external forms. In addition, the established Jensen-type inequalities are compared with the previously known results and we show that our results provide more accurate estimates in some general settings.
{"title":"External Jensen-type operator inequalities via superquadraticity","authors":"M. Kian, M. Krnic, M. Rostamian","doi":"10.2298/aadm191010031k","DOIUrl":"https://doi.org/10.2298/aadm191010031k","url":null,"abstract":"In this paper we establish several Jensen-type operator inequalities for a class of superquadratic functions and self-adjoint operators. Our results are given in the so-called external form. As an application, we give improvements of the H?lder-McCarthy inequality and the classical discrete and integral Jensen inequality in the corresponding external forms. In addition, the established Jensen-type inequalities are compared with the previously known results and we show that our results provide more accurate estimates in some general settings.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68352649","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}
In this paper we consider total reduction of the nonhomogeneous linear system of operator equations with constant coefficients and commuting operators. The totally reduced system obtained in this manner is completely decoupled. All equations of the system differ only in the variables and in the nonhomogeneous terms. The homogeneous parts are obtained using the generalized characteristic polynomial of the system matrix. We also indicate how this technique may be used to examine differential transcendence of the solution of the linear system of the differential equations with constant coefficients over the complex field and meromorphic free terms.
{"title":"Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system","authors":"I. Jovović","doi":"10.2298/aadm190627024j","DOIUrl":"https://doi.org/10.2298/aadm190627024j","url":null,"abstract":"In this paper we consider total reduction of the nonhomogeneous linear system of operator equations with constant coefficients and commuting operators. The totally reduced system obtained in this manner is completely decoupled. All equations of the system differ only in the variables and in the nonhomogeneous terms. The homogeneous parts are obtained using the generalized characteristic polynomial of the system matrix. We also indicate how this technique may be used to examine differential transcendence of the solution of the linear system of the differential equations with constant coefficients over the complex field and meromorphic free terms.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68352911","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}
The purpose of this work is to give a positive answer to two questions asked by professor Yilmaz Simsek in a recent paper [6] concerning special numbers B(n,k) for computing negative order Euler numbers.
{"title":"An affirmative answer to two questions concerning special case of Simsek numbers and open problems","authors":"M. Goubi","doi":"10.2298/aadm190116012g","DOIUrl":"https://doi.org/10.2298/aadm190116012g","url":null,"abstract":"The purpose of this work is to give a positive answer to two questions asked by professor Yilmaz Simsek in a recent paper [6] concerning special numbers B(n,k) for computing negative order Euler numbers.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68352208","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}
Marija S. Najdanovic, L. Velimirović, Svetozar R. Rancic
In this paper we consider infinitesimal bending of the second order of curves and knots. The total torsion of the knot during the second order infinitesimal bending is discussed and expressions for the first and the second variation of the total torsion are given. Some examples aimed to illustrate infinitesimal bending of knots are shown using figures. Colors are used to illustrate torsion values at different points of bent knots and the total torsion is numerically calculated.
{"title":"The total torsion of knots under second order infinitesimal bending","authors":"Marija S. Najdanovic, L. Velimirović, Svetozar R. Rancic","doi":"10.2298/aadm200206035n","DOIUrl":"https://doi.org/10.2298/aadm200206035n","url":null,"abstract":"In this paper we consider infinitesimal bending of the second order of curves and knots. The total torsion of the knot during the second order infinitesimal bending is discussed and expressions for the first and the second variation of the total torsion are given. Some examples aimed to illustrate infinitesimal bending of knots are shown using figures. Colors are used to illustrate torsion values at different points of bent knots and the total torsion is numerically calculated.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353418","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：