In this manuscript, we are concerned with the problem of locating the zeros of some special quaternionic polynomials and regular functions with restricted coefficients; namely quaternionic coefficients whose real components or their moduli satisfy suitable inequalities. The obtained results for this subclass of quaternionic polynomials and regular functions produce extensions of the classical Enestr?m-Kakeya theorem and its various variants from complex to the quaternionic setting.
{"title":"On the zero bounds of polynomials and regular functions of a quaternionic variable","authors":"G. Milovanović, A. Mir","doi":"10.2298/aadm220905033m","DOIUrl":"https://doi.org/10.2298/aadm220905033m","url":null,"abstract":"In this manuscript, we are concerned with the problem of locating the zeros of some special quaternionic polynomials and regular functions with restricted coefficients; namely quaternionic coefficients whose real components or their moduli satisfy suitable inequalities. The obtained results for this subclass of quaternionic polynomials and regular functions produce extensions of the classical Enestr?m-Kakeya theorem and its various variants from complex to the quaternionic setting.","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":"68354417","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 the present paper we investigate (p,q)-directed complete bipartite graphs ?K p,q, n-directed paths ?Pn and n-directed cycles ?C n from the perspective of Granular Computing. For each model, we establish the general form of all possible indiscernibility relations, analyze the classical rough approximation functions of rough set theory and provide a close formula for the global accuracy average. Finally, we completely determine the attribute dependency function and the global dependency average for both ?C n and ?Kp,q.
{"title":"Granular computing on basic digraphs","authors":"G. Chiaselotti, T. Gentile, F. Infusino","doi":"10.2298/aadm180615001c","DOIUrl":"https://doi.org/10.2298/aadm180615001c","url":null,"abstract":"In the present paper we investigate (p,q)-directed complete bipartite graphs ?K p,q, n-directed paths ?Pn and n-directed cycles ?C n from the perspective of Granular Computing. For each model, we establish the general form of all possible indiscernibility relations, analyze the classical rough approximation functions of rough set theory and provide a close formula for the global accuracy average. Finally, we completely determine the attribute dependency function and the global dependency average for both ?C n and ?Kp,q.","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":"68352069","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}
J. Baric, Ljiljanka Kvesić, J. Pečarić, Mihaela Ribicic-Penava
In this article new estimates on some quadrature rules are given using weighted Hermite-Hadamard inequality for higher order convex functions and weighted version of the integral identity expressed by w-harmonic sequences of functions. Obtained results are applied to weighted one-point formula for numerical integration in order to derive new estimates of the definite integral values.
{"title":"Estimates on some quadrature rules via weighted Hermite-Hadamard inequality","authors":"J. Baric, Ljiljanka Kvesić, J. Pečarić, Mihaela Ribicic-Penava","doi":"10.2298/aadm201127013b","DOIUrl":"https://doi.org/10.2298/aadm201127013b","url":null,"abstract":"In this article new estimates on some quadrature rules are given using weighted Hermite-Hadamard inequality for higher order convex functions and weighted version of the integral identity expressed by w-harmonic sequences of functions. Obtained results are applied to weighted one-point formula for numerical integration in order to derive new estimates of the definite integral values.","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":"68353860","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}
Numerous series representations for various special functions and mathematical constants have been developed by many authors. The aim of this article is to establish two parameterized series representations for the digamma function that seem interesting due to their independence from the given parameters. Among many particular cases of our two main findings, some are covered in the examples.
{"title":"Two parameterized series representations for the digamma function","authors":"H. Alzer, Junesang Choi","doi":"10.2298/aadm211208022a","DOIUrl":"https://doi.org/10.2298/aadm211208022a","url":null,"abstract":"Numerous series representations for various special functions and mathematical constants have been developed by many authors. The aim of this article is to establish two parameterized series representations for the digamma function that seem interesting due to their independence from the given parameters. Among many particular cases of our two main findings, some are covered in the examples.","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":"68354110","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}
New sufficient conditions for the oscillation of all solutions to a class of oddorder differential equations with a nonpositive sublinear neutral term and distributed deviating arguments are established. Example are included to illustrate the results.
{"title":"Oscillation of odd-order differential equations with a nonpositive sublinear neutral term and distributed deviating arguments","authors":"J. Graef, I. Jadlovská, E. Tunç","doi":"10.2298/aadm200918012g","DOIUrl":"https://doi.org/10.2298/aadm200918012g","url":null,"abstract":"New sufficient conditions for the oscillation of all solutions to a class of oddorder differential equations with a nonpositive sublinear neutral term and distributed deviating arguments are established. Example are included to illustrate the results.","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":"68353226","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 subset P of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from P. The cardinality of a minimum k-path vertex cover is called the k-path vertex cover number of G, and is denoted by ?k(G). It is known that the problem of finding a minimum 3-path vertex cover is NP-hard for planar graphs. In this paper we establish an upper bound for ?3(G), where G is from an important family of planar graphs, called hexagonal graphs, arising from real world applications.
{"title":"3-path vertex cover and dissociation number of hexagonal graphs","authors":"Rija Erveš, Aleksandra Tepeh","doi":"10.2298/aadm201009007e","DOIUrl":"https://doi.org/10.2298/aadm201009007e","url":null,"abstract":"A subset P of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from P. The cardinality of a minimum k-path vertex cover is called the k-path vertex cover number of G, and is denoted by ?k(G). It is known that the problem of finding a minimum 3-path vertex cover is NP-hard for planar graphs. In this paper we establish an upper bound for ?3(G), where G is from an important family of planar graphs, called hexagonal graphs, arising from real world applications.","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":"68353688","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 article, we introduce the extended Eulerian numbers for a large class of zeta functions, which includes the zeta functions associated to function fields, and to schemes over finite fields. This construction generalizes the extended Eulerian numbers defined by Carlitz. We give an asymptotic expansion for the summatory function associated to these numbers. Our main result generalizes the well known result on the asymptotic behavior of the extended Eulerian numbers associated to the Riemann zeta function.
{"title":"The extended Eulerian numbers over function fields","authors":"A. Bayad, Mounir Hajli","doi":"10.2298/aadm210930019b","DOIUrl":"https://doi.org/10.2298/aadm210930019b","url":null,"abstract":"In this article, we introduce the extended Eulerian numbers for a large class of zeta functions, which includes the zeta functions associated to function fields, and to schemes over finite fields. This construction generalizes the extended Eulerian numbers defined by Carlitz. We give an asymptotic expansion for the summatory function associated to these numbers. Our main result generalizes the well known result on the asymptotic behavior of the extended Eulerian numbers associated to the Riemann zeta function.","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":"68354060","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 establish a new identity between derangement numbers and Bell numbers. Two known identities can be recovered. We provide a combinatorial interpretation for the new identity and a representation of the derangement numbers in terms of the determinants of Hessenberg matrices.
{"title":"An identity involving derangement numbers and bell numbers","authors":"Z. Du, Fonseca da","doi":"10.2298/aadm200705010d","DOIUrl":"https://doi.org/10.2298/aadm200705010d","url":null,"abstract":"The aim of this paper is to establish a new identity between derangement numbers and Bell numbers. Two known identities can be recovered. We provide a combinatorial interpretation for the new identity and a representation of the derangement numbers in terms of the determinants of Hessenberg matrices.","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":"68353264","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}
Several notions of abstract Volterra operators on spaces of functions of one variable are well known. In this paper, we introduce various notions of abstract Volterra operators in spaces of functions of several variables. Some fixed point equations with such abstract Volterra operators are also studied. The basic ingredient in the theory of step by step contraction is the notion of G-contraction. The relevance of step by step contraction principle is illustrated by applications in the theory of Darboux-Ionescu problem.
{"title":"Fixed point equations with abstract Volterra operators on spaces of functions of several variables","authors":"A. Petruşel, I. Rus","doi":"10.2298/aadm180615016p","DOIUrl":"https://doi.org/10.2298/aadm180615016p","url":null,"abstract":"Several notions of abstract Volterra operators on spaces of functions of one variable are well known. In this paper, we introduce various notions of abstract Volterra operators in spaces of functions of several variables. Some fixed point equations with such abstract Volterra operators are also studied. The basic ingredient in the theory of step by step contraction is the notion of G-contraction. The relevance of step by step contraction principle is illustrated by applications in the theory of Darboux-Ionescu problem.","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":"68352088","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 asymptotic and numerical behavior of the so-called generalized Marcum function of the second kind is considered. By using some known expansions on the modified Bessel function of the second kind, we deduce the asymptotic expansions for the generalized Marcum function of the second kind for large parameters, and all the expansions are obtained when exactly one parameter is large and others are fixed. We also show numerically that the asymptotic formulas obtained in this paper are good approximations.
{"title":"Asymptotic and numerical aspects of the generalized Marcum function of the second kind","authors":"Á. Baricz, Nitin Bisht, Sanjeev Singh, Antony Vijesh","doi":"10.2298/aadm201001008b","DOIUrl":"https://doi.org/10.2298/aadm201001008b","url":null,"abstract":"The asymptotic and numerical behavior of the so-called generalized Marcum function of the second kind is considered. By using some known expansions on the modified Bessel function of the second kind, we deduce the asymptotic expansions for the generalized Marcum function of the second kind for large parameters, and all the expansions are obtained when exactly one parameter is large and others are fixed. We also show numerically that the asymptotic formulas obtained in this paper are good approximations.","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":"68353637","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：