In this study, we propose a non-negative integer-valued model based on the sum of Poisson-Lindley and geometric distributions. We show that it corresponds to the weighted geometric distribution and also a special mixture of two negative binomial distributions with certain parameters. The main statistical properties of the new distribution are studied comprehensively, including estimation of the model parameter. A new count regression analysis is introduced by using the new distribution. Finally, we provide some applications on practical data sets.
{"title":"A non-negative integer-valued model: Estimation, count regression and practical examples","authors":"H. Bakouch, K. Karakaya, C. Chesneau, Y. Akdoğan","doi":"10.2298/aadm210114029b","DOIUrl":"https://doi.org/10.2298/aadm210114029b","url":null,"abstract":"In this study, we propose a non-negative integer-valued model based on the sum of Poisson-Lindley and geometric distributions. We show that it corresponds to the weighted geometric distribution and also a special mixture of two negative binomial distributions with certain parameters. The main statistical properties of the new distribution are studied comprehensively, including estimation of the model parameter. A new count regression analysis is introduced by using the new distribution. Finally, we provide some applications on practical data sets.","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":"68354077","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 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.
{"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":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":"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}
O. Bodroža-Pantić, Harris Kwong, Jelena Djokic, R. Doroslovački, M. Pantić
Here, in Part II, we proceeded further with the enumeration of Hamiltonian cycles (HC's) on the grid cylinder graphs of the form Pm+1?Cn, where n is allowed to grow and m is fixed. We proposed two novel characterisations of the contractible HC's. Finally, we made a conjecture concerning the dependency of the asymptotically dominant type of HC's on the parity of m.
{"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":null,"pages":null},"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}
We study hidden geometry of Bier spheres Bier(K) = K * ? K? by describing their natural geometric realizations, compute their volume, describe an effective criterion for their polytopality, and associate to Bier(K) a natural coarsening Fan(K) of the Braid fan. We also establish a connection of Bier spheres of maximal volume with recent generalizations of the classical Van Kampen-Flores theorem and clarify the role of Bier spheres in the theory of generalized permutohedra.
我们研究了Bier球的隐几何Bier(K) = K * ?K ?通过描述它们的自然几何实现，计算它们的体积，描述它们的多面性的有效准则，并将Bier(K)与Braid扇的自然粗化扇(K)联系起来。我们还建立了最大体积Bier球与经典Van Kampen-Flores定理的最新推广之间的联系，并阐明了Bier球在广义复面体理论中的作用。
{"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":null,"pages":null},"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}
We prove a general alternate circular summation formula of theta functions, which implies a great deal of theta-function identities. In particular, we recover several identities in Ramanujan's Notebook from this identity. We also obtain two formulaes for (q; q)2n∞.
{"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":null,"pages":null},"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}
We evaluate in closed form several series involving products of Cauchy numbers with other special numbers (harmonic, skew-harmonic, hyperharmonic, and central binomial). Similar results are obtained with series involving Stirling numbers of the first kind. We focus on several particular cases which give new closed forms for Euler sums of hyperharmonic numbers and products of hyperharmonic and harmonic numbers.
{"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":null,"pages":null},"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}
The homology group of a tiling introduced by M. Reid is studied for certain topological tilings. As in the planar case, for finite square grids on topological surfaces, the method of homology groups, namely the non-triviality of some specific element in the group allows a ?coloring proof? of impossibility of a tiling. Several results about the non-existence of polyomino tilings on certain square-tiled surfaces are proved in the paper.
{"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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
A. Kashuri, Muhammad Uzair, Sadia Talib, Muhammad Noor Aslam, K. Inayat
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.
{"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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
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