The aim of this paper is to give many new and elegant formulas for a new class of generalized Fubini polynomials with the aid of generating functions and their functional equations. By using these formulas, some computational algorithms involving a new class of generalized Fubini polynomials and special polynomials and numbers are constructed. Using these algorithms, some values of these numbers and polynomials are computed. Finally, some remarks and observations on the results of this paper are presented.
{"title":"A new class of generalized Fubini polynomials and their computational algorithms","authors":"Neslihan Kilar","doi":"10.2298/aadm210708023k","DOIUrl":"https://doi.org/10.2298/aadm210708023k","url":null,"abstract":"The aim of this paper is to give many new and elegant formulas for a new class of generalized Fubini polynomials with the aid of generating functions and their functional equations. By using these formulas, some computational algorithms involving a new class of generalized Fubini polynomials and special polynomials and numbers are constructed. Using these algorithms, some values of these numbers and polynomials are computed. Finally, some remarks and observations on the results of this paper are presented.","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":"136304061","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}
Jelena DJoki'c, Ksenija Doroslovački, O. Bodroža-Pantić
In this paper, we prove that all but one of the components of the transfer digraph D? m needed for the enumeration of 2-factors in the rectangular, thick cylinder and Moebius strip grid graphs of the fixed width m (m ? N) are bipartite digraphs and that their orders could be expressed in term of binomial coefficients. In addition, we prove that the set of vertices of each component consists of all the binary m-words for which the difference of numbers of zeros in odd and even positions is constant.
{"title":"The structure of the 2-factor transfer digraph common for rectangular, thick cylinder and Moebius strip grid graphs","authors":"Jelena DJoki'c, Ksenija Doroslovački, O. Bodroža-Pantić","doi":"10.2298/aadm211211006d","DOIUrl":"https://doi.org/10.2298/aadm211211006d","url":null,"abstract":"In this paper, we prove that all but one of the components of the transfer\u0000 digraph D? m needed for the enumeration of 2-factors in the rectangular,\u0000 thick cylinder and Moebius strip grid graphs of the fixed width m (m ? N)\u0000 are bipartite digraphs and that their orders could be expressed in term of\u0000 binomial coefficients. In addition, we prove that the set of vertices of\u0000 each component consists of all the binary m-words for which the difference\u0000 of numbers of zeros in odd and even positions is constant.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47438756","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 H?gelsch?ffer cubic curves which are generated using appropriate geometric constructions. The main result of this work is the mode of explicitly calculating the area of the egg-shaped part of the cubic curve using elliptic integrals. In this paper, we also analyze the H?gelsch?ffer surface of cubic curves for which we provide new forms of formulae for the volume and surface area of the egg-shaped part. Curves and surfaces of ovoid shape have wide applicability in aero-engineering and construction, and are also of biologic importance. With respect to this, in the final section, we consider some examples of the real applicability of this H?gelsch?ffer model.
{"title":"Hügelschäffer egg curve and surface","authors":"Maja M. Petrović, Branko J. Malesevic","doi":"10.2298/AADM220526027P","DOIUrl":"https://doi.org/10.2298/AADM220526027P","url":null,"abstract":"In this paper we consider H?gelsch?ffer cubic curves which are generated\u0000 using appropriate geometric constructions. The main result of this work is\u0000 the mode of explicitly calculating the area of the egg-shaped part of the\u0000 cubic curve using elliptic integrals. In this paper, we also analyze the\u0000 H?gelsch?ffer surface of cubic curves for which we provide new forms of\u0000 formulae for the volume and surface area of the egg-shaped part. Curves and\u0000 surfaces of ovoid shape have wide applicability in aero-engineering and\u0000 construction, and are also of biologic importance. With respect to this, in\u0000 the final section, we consider some examples of the real applicability of\u0000 this H?gelsch?ffer model.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42377097","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 further study some properties and identities on the degenerate Fubini and the degenerate Bell polynomials which are degenerate versions of the Fubini and the Bell polynomials, respectively. Especially, we find several expressions for the generating function of the sum of the values of the generalized falling factorials at positive consecutive integers.
{"title":"Some results on degenerate Fubini and degenerate bell polynomials","authors":"Taekyun Kim, Dae San Kim","doi":"10.2298/aadm200310035k","DOIUrl":"https://doi.org/10.2298/aadm200310035k","url":null,"abstract":"The aim of this paper is to further study some properties and identities on\u0000 the degenerate Fubini and the degenerate Bell polynomials which are\u0000 degenerate versions of the Fubini and the Bell polynomials, respectively.\u0000 Especially, we find several expressions for the generating function of the\u0000 sum of the values of the generalized falling factorials at positive\u0000 consecutive integers.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49084623","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 integral circulant graph ICGn(D) has the vertex set Zn = {0, 1, 2, . . . , n? 1} and vertices a and b are adjacent if gcd(a ? b, n) ? D, where D ? Dn, Dn = {d : d | n, 1 ? d < n}. Motivated by the incorrect proof of a previously published result, in this paper we characterize the class of integral circulant graphs that are strongly regular. More precisely, connected ICGn(D) is strongly regular if and only if n is composite and D = {d ? Dn | m ? d} for some m | n and n ? 1 ? m ? 2.
积分循环图ICGn(D)的顶点集Zn ={0,1,2，…n ?如果gcd(a ?B, n) ?D，哪里D ?Dn, Dn = {d: d | n, 1 ?D < n}。基于先前发表的一个结果的错误证明，本文刻画了一类强正则的积分循环图。更准确地说，连通ICGn(D)是强正则的当且仅当n是复合且D = {D ?不是bbbbm吗?D}对于某个m b| n和n ?1 ？ m ?2.
{"title":"Characterization of strongly regular integral circulant graphs by spectral approach","authors":"Milan Basic","doi":"10.2298/aadm180713023b","DOIUrl":"https://doi.org/10.2298/aadm180713023b","url":null,"abstract":"The integral circulant graph ICGn(D) has the vertex set Zn = {0, 1, 2, . . . , n? 1} and vertices a and b are adjacent if gcd(a ? b, n) ? D, where D ? Dn, Dn = {d : d | n, 1 ? d < n}. Motivated by the incorrect proof of a previously published result, in this paper we characterize the class of integral circulant graphs that are strongly regular. More precisely, connected ICGn(D) is strongly regular if and only if n is composite and D = {d ? Dn | m ? d} for some m | n and n ? 1 ? m ? 2.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68351716","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 investigate certain connections between the class Rs,? of rapidly varying sequences (in the sense of de Haan) and the rapid equivalence, selection principles and game theory.
{"title":"On rapidly varying sequences","authors":"Valentina Timotic, D. Djurcic, L. Kočinac","doi":"10.2298/aadm181107003t","DOIUrl":"https://doi.org/10.2298/aadm181107003t","url":null,"abstract":"In this paper we investigate certain connections between the class Rs,? of rapidly varying sequences (in the sense of de Haan) and the rapid equivalence, selection principles and game theory.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68352025","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}
By studying the monotonicity properties of K(r), E(r) and some combinations of elementary functions and special functions, some new inequalities for the complete elliptic integrals of the first and second kinds are established. where K(r) =f0 ?/2
{"title":"Sharp inequalities for the complete elliptic integrals of the first and second kinds","authors":"Weidong Jiang","doi":"10.2298/aadm200613020j","DOIUrl":"https://doi.org/10.2298/aadm200613020j","url":null,"abstract":"By studying the monotonicity properties of K(r), E(r) and some combinations of elementary functions and special functions, some new inequalities for the complete elliptic integrals of the first and second kinds are established. where K(r) =f0 ?/2","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353210","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}
We present some asymptotic expansions and inequalities for ?(x+1)1/x ?(x+2)1/(x+1) and ?(x+1)1/x.
给出了?(x+1)1/x ?(x+2)1/(x+1)和?(x+1)1/x的渐近展开式和不等式。
{"title":"Asymptotic expansions and inequalities relating to the gamma function","authors":"Chao-Ping Chen, C. Mortici","doi":"10.2298/aadm200710034c","DOIUrl":"https://doi.org/10.2298/aadm200710034c","url":null,"abstract":"We present some asymptotic expansions and inequalities for ?(x+1)1/x ?(x+2)1/(x+1) and ?(x+1)1/x.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353279","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 discuss holomorphic mappings f of the unit disc U and corresponding index defined as If (z) = zf?(z) f(z). We are interested in finding bounds on the growth of functions f and related issues, if there are known some properties of If on U. Our main tool in accomplishing this connection is Jack?s lemma. As a special case, we got estimates on the growth of some classes of ?-starlike functions as well as some interesting generalisations.
{"title":"Note on some classes of holomorphic functions related to Jack’s and Schwarz’s lemma","authors":"M. Mateljevic, N. Mutavdzic, B. Örnek","doi":"10.2298/aadm200319006m","DOIUrl":"https://doi.org/10.2298/aadm200319006m","url":null,"abstract":"In this paper we discuss holomorphic mappings f of the unit disc U and corresponding index defined as If (z) = zf?(z) f(z). We are interested in finding bounds on the growth of functions f and related issues, if there are known some properties of If on U. Our main tool in accomplishing this connection is Jack?s lemma. As a special case, we got estimates on the growth of some classes of ?-starlike functions as well as some interesting generalisations.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353480","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}
For a ? (0,1/2] and r ? (0,1), let Ka(r) (K (r)) denote the generalized elliptic integral (complete elliptic integral, respectively) of the first kind. In this article, we mainly present a sufficient and necessary condition under which the function a ? [K(r)-Ka(r)]=(1-2a)?(?? R) is monotone on (0,1/2) for each fixed r ? (0,1). The obtained result leads to the conclusion that inequality K (r)- (1-2a)? [K(r)- ?/2] ? Ka(r) ? K (r)-(1-2a)? [K(r)-?/2] holds for all a ? (0,1/2] and r ? (0,1) with the best possible constants ? = ?/2 and ? = 2.
{"title":"A monotonicity theorem for the generalized elliptic integral of the first kind","authors":"Qi Bao, Xue-Jing Ren, Miao-Kun Wang","doi":"10.2298/aadm201005031b","DOIUrl":"https://doi.org/10.2298/aadm201005031b","url":null,"abstract":"For a ? (0,1/2] and r ? (0,1), let Ka(r) (K (r)) denote the generalized elliptic integral (complete elliptic integral, respectively) of the first kind. In this article, we mainly present a sufficient and necessary condition under which the function a ? [K(r)-Ka(r)]=(1-2a)?(?? R) is monotone on (0,1/2) for each fixed r ? (0,1). The obtained result leads to the conclusion that inequality K (r)- (1-2a)? [K(r)- ?/2] ? Ka(r) ? K (r)-(1-2a)? [K(r)-?/2] holds for all a ? (0,1/2] and r ? (0,1) with the best possible constants ? = ?/2 and ? = 2.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353655","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}
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