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Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants Wallis序列的渐近展开式及与Glaisher-Kinkelin和Choi-Srivastava常数相关的一些新的数学常数
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2022-01-01 DOI: 10.2298/aadm220414024h
Xue Han, Chao-Ping Chen, H. Srivastava
{"title":"Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants","authors":"Xue Han, Chao-Ping Chen, H. Srivastava","doi":"10.2298/aadm220414024h","DOIUrl":"https://doi.org/10.2298/aadm220414024h","url":null,"abstract":"The celebrated Wallis sequence Wn, which is defined by Wn := ?nk=1 4k2/4k2?1, is known to have the limit ? 2 as n ? ?. Without using the Bernoulli numbers Bn, the authors present several asymptotic expansions and a recurrence relation for determining the coefficients of each asymptotic expansion related to the Wallis sequence Wn and the newly-introduced constants D and E, which are analogous to the Glaisher-Kinkelin constant A and the Choi-Srivastava constants B and C.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68354205","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
Complete asymptotic expansions related to the probability density function of the χ2-distribution 与χ2分布的概率密度函数相关的完全渐近展开式
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2022-01-01 DOI: 10.2298/aadm210720015c
Chao Chen, H. Srivastava
{"title":"Complete asymptotic expansions related to the probability density function of the χ2-distribution","authors":"Chao Chen, H. Srivastava","doi":"10.2298/aadm210720015c","DOIUrl":"https://doi.org/10.2298/aadm210720015c","url":null,"abstract":"In this paper, we consider the function fp(t) = ? 2p?2(?2pt + p;p), where ?2(x;n) defined by ?2(x;p) = 2?p/2/?(p/2) e?x/2xp/2?1, is the density function of a ?2-distribution with n degrees of freedom. The asymptotic expansion of fp(t) for p ? ?, where p is not necessarily an integer, is obtained by an application of the standard asymptotics of ln ?(x). Two different methods of obtaining the coefficients in the asymptotic expansion are presented, which involve the use of the Bell polynomials.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353943","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
Enumeration of Hamiltonian cycles on a thick grid cylinder - Part II: Contractible Hamiltonian cycles 厚网格圆柱体上哈密顿环的枚举。第二部分:可缩哈密顿环
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-09-16 DOI: 10.2298/AADM200629027B
O. Bodroža-Pantić, Harris Kwong, Jelena Djokic, R. Doroslovački, M. Pantić
{"title":"Enumeration of Hamiltonian cycles on a thick grid cylinder - Part II: Contractible Hamiltonian cycles","authors":"O. Bodroža-Pantić, Harris Kwong, Jelena Djokic, R. Doroslovački, M. Pantić","doi":"10.2298/AADM200629027B","DOIUrl":"https://doi.org/10.2298/AADM200629027B","url":null,"abstract":"Here, in Part II, we proceeded further with the enumeration of Hamiltonian\u0000 cycles (HC's) on the grid cylinder graphs of the form Pm+1?Cn, where n is\u0000 allowed to grow and m is fixed. We proposed two novel characterisations of\u0000 the contractible HC's. Finally, we made a conjecture concerning the\u0000 dependency of the asymptotically dominant type of HC's on the parity of m.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41765960","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: 2
Bier spheres of extremal volume and generalized permutohedra 极值体积的Bier球与广义置换面体
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-08-02 DOI: 10.2298/aadm211010026j
Filip D. Jevti'c, Rade T. vZivaljevi'c
{"title":"Bier spheres of extremal volume and generalized permutohedra","authors":"Filip D. Jevti'c, Rade T. vZivaljevi'c","doi":"10.2298/aadm211010026j","DOIUrl":"https://doi.org/10.2298/aadm211010026j","url":null,"abstract":"We study hidden geometry of Bier spheres Bier(K) = K * ? K? by describing\u0000 their natural geometric realizations, compute their volume, describe an\u0000 effective criterion for their polytopality, and associate to Bier(K) a\u0000 natural coarsening Fan(K) of the Braid fan. We also establish a connection\u0000 of Bier spheres of maximal volume with recent generalizations of the\u0000 classical Van Kampen-Flores theorem and clarify the role of Bier spheres in\u0000 the theory of generalized permutohedra.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45833657","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: 2
AN ALTERNATE CIRCULAR SUMMATION FORMULA OF THETA FUNCTIONS AND ITS APPLICATIONS θ函数的交替循环求和公式及其应用
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-06-26 DOI: 10.2298/AADM120204004Z
Jun-Ming Zhu
{"title":"AN ALTERNATE CIRCULAR SUMMATION FORMULA OF THETA FUNCTIONS AND ITS APPLICATIONS","authors":"Jun-Ming Zhu","doi":"10.2298/AADM120204004Z","DOIUrl":"https://doi.org/10.2298/AADM120204004Z","url":null,"abstract":"We prove a general alternate circular summation formula of theta functions, \u0000 which implies a great deal of theta-function identities. In particular, we \u0000 recover several identities in Ramanujan's Notebook from this identity. We \u0000 also obtain two formulaes for (q; q)2n∞.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"6 1","pages":"114-125"},"PeriodicalIF":0.9,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2298/AADM120204004Z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49634785","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: 7
New series with Cauchy and Stirling numbers, Part 2 柯西数和斯特林数的新级数，第二部分
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-03-17 DOI: 10.2298/aadm210112001b
K. Boyadzhiev, L. Kargin
{"title":"New series with Cauchy and Stirling numbers, Part 2","authors":"K. Boyadzhiev, L. Kargin","doi":"10.2298/aadm210112001b","DOIUrl":"https://doi.org/10.2298/aadm210112001b","url":null,"abstract":"We evaluate in closed form several series involving products of Cauchy\u0000 numbers with other special numbers (harmonic, skew-harmonic, hyperharmonic,\u0000 and central binomial). Similar results are obtained with series involving\u0000 Stirling numbers of the first kind. We focus on several particular cases\u0000 which give new closed forms for Euler sums of hyperharmonic numbers and\u0000 products of hyperharmonic and harmonic numbers.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42866148","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: 3
Homology of polyomino tilings on flat surfaces 平面上的多边形平铺的同构性
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-03-07 DOI: 10.2298/aadm210307031l
Edin Lidjan, Ðordje Baralic
{"title":"Homology of polyomino tilings on flat surfaces","authors":"Edin Lidjan, Ðordje Baralic","doi":"10.2298/aadm210307031l","DOIUrl":"https://doi.org/10.2298/aadm210307031l","url":null,"abstract":"The homology group of a tiling introduced by M. Reid is studied for certain\u0000 topological tilings. As in the planar case, for finite square grids on\u0000 topological surfaces, the method of homology groups, namely the\u0000 non-triviality of some specific element in the group allows a ?coloring\u0000 proof? of impossibility of a tiling. Several results about the non-existence\u0000 of polyomino tilings on certain square-tiled surfaces are proved in the\u0000 paper.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44724073","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
Integral cayley graphs over semi-dihedral groups 半二面体群上的积分cayley图
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/AADM190330001C
Tao Cheng, Lihua Feng, Guihai Yu, Chi Zhang
{"title":"Integral cayley graphs over semi-dihedral groups","authors":"Tao Cheng, Lihua Feng, Guihai Yu, Chi Zhang","doi":"10.2298/AADM190330001C","DOIUrl":"https://doi.org/10.2298/AADM190330001C","url":null,"abstract":"Classifying integral graphs is a hard problem that initiated by Harary and Schwenk in 1974. In this paper, with the help of character table, we treat the corresponding problem for Cayley graphs over the semi-dihedral group SD8n = ?a,b | a4n = b2 = 1; bab = a2n-1?, n ? 2. We present several necessary and sufficient conditions for the integrality of Cayley graphs over SD8n, we also obtain some simple sufficient conditions for the integrality of Cayley graphs over SD8n in terms of the Boolean algebra of hai. In particular, we give the sufficient conditions for the integrality of Cayley graphs over semi-dihedral groups SD2n (n?4) and SD8p for a prime p, from which we determine several infinite classes of integral Cayley graphs over SD2n and SD8p.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68352458","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: 3
On exponentially ϱ-preinvex functions and associated trapezium like inequalities 关于指数ϱ-preinvex函数和相关的梯形不等式
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/aadm200220025k
A. Kashuri, Muhammad Uzair, Sadia Talib, Muhammad Noor Aslam, K. Inayat
{"title":"On exponentially ϱ-preinvex functions and associated trapezium like inequalities","authors":"A. Kashuri, Muhammad Uzair, Sadia Talib, Muhammad Noor Aslam, K. Inayat","doi":"10.2298/aadm200220025k","DOIUrl":"https://doi.org/10.2298/aadm200220025k","url":null,"abstract":"In this paper, authors introduce a new extension of ?-convexity called ?- preinvexity and generalize the discussed results by Wu et al. in ?On a new class of convex functions and integral inequalities?. Some special cases are deduced from main results. At the end, a briefly conclusion is given.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353431","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
New classes of recurrence relations involving hyperbolic functions, special numbers and polynomials 涉及双曲函数、特殊数和多项式的递归关系的新类别
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/aadm201020015s
Y. Simsek
{"title":"New classes of recurrence relations involving hyperbolic functions, special numbers and polynomials","authors":"Y. Simsek","doi":"10.2298/aadm201020015s","DOIUrl":"https://doi.org/10.2298/aadm201020015s","url":null,"abstract":"By using the calculus of finite differences methods and the umbral calculus, we construct recurrence relations for a new class of special numbers. Using this recurrence relation, we define generating functions for this class of special numbers and also new classes of special polynomials. We investigate some properties of these generating functions. By using these generating functions with their functional equations, we obtain many new and interesting identities and relations related to these classes of special numbers and polynomials, the Bernoulli numbers and polynomials, the Euler numbers and polynomials, the Stirling numbers. Finally, some derivative formulas and integral formulas for these classes of special numbers and polynomials are given. In general, this article includes results that have the potential to be used in areas such as discrete mathematics, combinatorics analysis and their applications.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353754","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: 2
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