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Matrix representations for a certain class of combinatorial numbers associated with Bernstein basis functions and cyclic derangements and their probabilistic and asymptotic analyses 一类与Bernstein基函数和循环无序相关的组合数的矩阵表示及其概率和渐近分析
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/AADM201017009K
Irem Kucukoglu, Y. Simsek
{"title":"Matrix representations for a certain class of combinatorial numbers associated with Bernstein basis functions and cyclic derangements and their probabilistic and asymptotic analyses","authors":"Irem Kucukoglu, Y. Simsek","doi":"10.2298/AADM201017009K","DOIUrl":"https://doi.org/10.2298/AADM201017009K","url":null,"abstract":"In this paper, we mainly concerned with an alternate form of the generating functions for a certain class of combinatorial numbers and polynomials. We give matrix representations for these numbers and polynomials with their applications. We also derive various identities such as Rodrigues-type formula, recurrence relation and derivative formula for the aforementioned combinatorial numbers. Besides, we present some plots of the generating functions for these numbers. Furthermore, we give relationships of these combinatorial numbers and polynomials with not only Bernstein basis functions, but the two-variable Hermite polynomials and the number of cyclic derangements. We also present some applications of these relationships. By applying Laplace transform and Mellin transform respectively to the aforementioned functions, we give not only an infinite series representation, but also an interpolation function of these combinatorial numbers. We also provide a contour integral representation of these combinatorial numbers. In addition, we construct exponential generating functions for a new family of numbers arising from the linear combination of the numbers of cyclic derangements in the wreath product of the finite cyclic group and the symmetric group of permutations of a set. Finally, we analyse the aforementioned functions in probabilistic and asymptotic manners, and we give some of their relationships with not only the Laplace distribution, but also the standard normal distribution. Then, we provide an asymptotic power series representation of the aforementioned exponential generating functions.","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":"68353708","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
On spectral theory of a k-uniform directed hypergraph 关于k-一致有向超图的谱理论
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/AADM180213022S
G. Shirdel, A. Mortezaee, E. Golpar-Raboky
{"title":"On spectral theory of a k-uniform directed hypergraph","authors":"G. Shirdel, A. Mortezaee, E. Golpar-Raboky","doi":"10.2298/AADM180213022S","DOIUrl":"https://doi.org/10.2298/AADM180213022S","url":null,"abstract":"In this paper, we study a k-uniform directed hypergraph in general form and introduce its associated tensors. We present different spectral properties and show that some of them are generalization of the classical results for undirected hypergraphs. The notation of odd-bipartite directed hypergraph are presented and some spectral properties and characterizations of them comparing with ones in undirected hypergraphs are studied. We also introduce power directed hypergraph and cored directed hypergraph and investigate their spectral properties.","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":"68351651","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
Sine and cosine types of generating functions 正弦和余弦类型的生成函数
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/AADM200530002M
M. Masjed‐Jamei, Zahra Moalemi
{"title":"Sine and cosine types of generating functions","authors":"M. Masjed‐Jamei, Zahra Moalemi","doi":"10.2298/AADM200530002M","DOIUrl":"https://doi.org/10.2298/AADM200530002M","url":null,"abstract":"We introduce two sine and cosine types of generating functions in a general case and apply them to the generating functions of classical hypergeometric orthogonal polynomials as well as some widely investigated combinatorial numbers such as Bernoulli, Euler and Genocchi numbers. This approach can also be applied to other celebrated sequences.","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":"68353196","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
Comparison inequalities of Bernstein-type between polynomials with restricted zeros 具有限制零的多项式的bernstein型比较不等式
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/aadm200911029m
A. Mir
{"title":"Comparison inequalities of Bernstein-type between polynomials with restricted zeros","authors":"A. Mir","doi":"10.2298/aadm200911029m","DOIUrl":"https://doi.org/10.2298/aadm200911029m","url":null,"abstract":"In this paper, we establish certain comparison inequalities of Bernstein-type for a linear operator between complex polynomials under certain constraints on their zeros. A variety of interesting results follow as special cases from our results.","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":"68353403","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
A new chain of inequalities involving the Toader-Qi, logarithmic and exponential means 一个新的不等式链，涉及Toader-Qi，对数和指数均值
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/aadm201227028y
Zhen-Hang Yang, Jingfeng Tian
{"title":"A new chain of inequalities involving the Toader-Qi, logarithmic and exponential means","authors":"Zhen-Hang Yang, Jingfeng Tian","doi":"10.2298/aadm201227028y","DOIUrl":"https://doi.org/10.2298/aadm201227028y","url":null,"abstract":"In this paper, we establish an interesting chain of sharp inequalities involving Toader-Qi mean, exponential mean, logarithmic mean, arithmetic mean and geometric mean. This greatly improves some existing results.","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":"68354039","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
A characterisation of completeness of b-fuzzy metric spaces and nonlinear contractions b-模糊度量空间和非线性压缩的完备性刻画
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/aadm200911057r
B. Randjelovic, N. Ćirović, S. Jesic
{"title":"A characterisation of completeness of b-fuzzy metric spaces and nonlinear contractions","authors":"B. Randjelovic, N. Ćirović, S. Jesic","doi":"10.2298/aadm200911057r","DOIUrl":"https://doi.org/10.2298/aadm200911057r","url":null,"abstract":"The purpose of this paper is to present a common fixed point theorem for a pair of R-weakly commuting mappings defined on b-fuzzy metric spaces satisfying nonlinear contractive conditions of Boyd-Wong type, obtained in D. W. Boyd, J. S. W. Wong: On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464.","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":"68353587","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
Necessary and sufficient conditions for complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function 一个包含三角函数的函数的两个导数所定义的两个函数的完全单调性和单调性的充分必要条件
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/aadm191111014q
Feng Qi (祁锋)
{"title":"Necessary and sufficient conditions for complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function","authors":"Feng Qi (祁锋)","doi":"10.2298/aadm191111014q","DOIUrl":"https://doi.org/10.2298/aadm191111014q","url":null,"abstract":"In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein's theorem for completely monotonic functions, some properties of a function involving exponential function, and other analytic techniques, the author finds necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic. These results generalize corresponding known ones.","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":"68352723","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
Families of log Legendre Chi function integrals 对数勒让德函数积分的族
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/AADM200506021S
A. Sofo
{"title":"Families of log Legendre Chi function integrals","authors":"A. Sofo","doi":"10.2298/AADM200506021S","DOIUrl":"https://doi.org/10.2298/AADM200506021S","url":null,"abstract":"In this paper we investigate the representation of integrals involving the product of the Legendre Chi function, polylogarithm function and log function. We will show that in many cases these integrals take an explicit form involving the Riemann zeta function, the Dirichlet Eta function, Dirichlet lambda function and many other special functions. Some examples illustrating the theorems will be detailed.","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":"68353571","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
Accessible spectrum of graphs 图的可达谱
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/AADM180319007H
M. Hamidi, A. Borumand
{"title":"Accessible spectrum of graphs","authors":"M. Hamidi, A. Borumand","doi":"10.2298/AADM180319007H","DOIUrl":"https://doi.org/10.2298/AADM180319007H","url":null,"abstract":"This paper computes eigenvalues of discrete complete hypergraphs and partitioned hypergraphs. We define positive equivalence relation on hypergraphs that establishes a connection between hypergraphs and graphs. With this regards it makes a connection between spectrum of graphs and spectrum of quotient of any hypergraphs. Finally, this study tries to construct spectrum of path trees via quotient of partitioned hypergraphs.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":"7-7"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68351759","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: 1
Commutative von Neumann regular rings are 1-Gröbner 交换冯·诺伊曼正则环是1-Gröbner
IF 0.9 4区 数学
Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.2298/aadm210419030p
Z. Petrovic, Maja Roslavcev
{"title":"Commutative von Neumann regular rings are 1-Gröbner","authors":"Z. Petrovic, Maja Roslavcev","doi":"10.2298/aadm210419030p","DOIUrl":"https://doi.org/10.2298/aadm210419030p","url":null,"abstract":"Let R be a commutative von Neumann regular ring. We show that every finitely generated ideal I in the ring of polynomials R[X] has a strong Gr?bner basis. We prove this result using only the defining property of a von Neumann regular ring.","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":"68353726","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
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