Abstract In the paper, by a general and fundamental, but non-extensively circulated, formula for derivatives of a ratio of two differentiable functions and by a recursive relation of the Hessenberg determinant, the author finds a new determinantal expression and a new recursive relation of the Delannoy numbers. Consequently, the author derives a recursive relation for computing central Delannoy numbers in terms of related Delannoy numbers.
{"title":"A determinantal expression and a recursive relation of the Delannoy numbers","authors":"Feng Qi (祁锋)","doi":"10.2478/ausm-2021-0027","DOIUrl":"https://doi.org/10.2478/ausm-2021-0027","url":null,"abstract":"Abstract In the paper, by a general and fundamental, but non-extensively circulated, formula for derivatives of a ratio of two differentiable functions and by a recursive relation of the Hessenberg determinant, the author finds a new determinantal expression and a new recursive relation of the Delannoy numbers. Consequently, the author derives a recursive relation for computing central Delannoy numbers in terms of related Delannoy numbers.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85884715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We develop a group graded Morita theory over a G-graded G-acted algebra, where G is a finite group.
在G-梯度G-作用代数上，建立了G是有限群的群梯度Morita理论。
{"title":"Graded Morita theory over a G-graded G-acted algebra","authors":"Virgilius-Aurelian Minuță","doi":"10.2478/ausm-2020-0011","DOIUrl":"https://doi.org/10.2478/ausm-2020-0011","url":null,"abstract":"Abstract We develop a group graded Morita theory over a G-graded G-acted algebra, where G is a finite group.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74956625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We establish two Ostrowski type inequalities for double integrals of second order partial derivable functions which are bounded. Then, we deduce some inequalities of Hermite-Hadamard type for double integrals of functions whose partial derivatives in absolute value are convex on the co-ordinates on rectangle from the plane. Finally, some applications in Numerical Analysis in connection with cubature formula are given.
{"title":"Some inequalities for double integrals and applications for cubature formula","authors":"S. Erden, M. Sarıkaya","doi":"10.2478/ausm-2019-0021","DOIUrl":"https://doi.org/10.2478/ausm-2019-0021","url":null,"abstract":"Abstract We establish two Ostrowski type inequalities for double integrals of second order partial derivable functions which are bounded. Then, we deduce some inequalities of Hermite-Hadamard type for double integrals of functions whose partial derivatives in absolute value are convex on the co-ordinates on rectangle from the plane. Finally, some applications in Numerical Analysis in connection with cubature formula are given.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78707059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Let (pn) and (qn) be any two non-negative real sequences with Rn:=∑k=0npkqn-k≠0 (n∈) {{rm{R}}_{rm{n}}}: = sumlimits_{{rm{k}} = 0}^{rm{n}} {{{rm{p}}_{rm{k}}}{{rm{q}}_{{rm{n}} - {rm{k}}}}} ne 0,,,,left( {{rm{n}} in {rmmathbb{N}}} right) With En1 {rm{E}}_{rm{n}}^1 − we will denote the Euler summability method. Let (xn) be a sequence of real or complex numbers and set Np,qnEn1:=1Rn∑k=0npkqn-k12k∑v=0k(vk)xv {rm{N}}_{{rm{p}},{rm{q}}}^{rm{n}}{rm{E}}_{rm{n}}^1: = {1 over {{{rm{R}}_{rm{n}}}}}sumlimits_{{rm{k}} = 0}^{rm{n}} {{{rm{p}}_{rm{k}}}{{rm{q}}_{{rm{n - k}}}}{1 over {{2^{rm{k}}}}}sumlimits_{{rm{v}} = 0}^{rm{k}} {left( {_{rm{v}}^{rm{k}}} right){{rm{x}}_{rm{v}}}} } for n ∈ ℕ. In this paper, we present necessary and sufficient conditions under which the existence of the st− limit of (xn) follows from that of st-Np,qnE n1 {rm{st - N}}_{{rm{p}},q}^{rm{n}}{rm{E}}_{rm{n}}^1 − limit of (xn). These conditions are one-sided or two-sided if (xn) is a sequence of real or complex numbers, respectively.
{"title":"A Tauberian theorem for the statistical generalized Nörlund-Euler summability method","authors":"N. Braha","doi":"10.2478/ausm-2019-0019","DOIUrl":"https://doi.org/10.2478/ausm-2019-0019","url":null,"abstract":"Abstract Let (pn) and (qn) be any two non-negative real sequences with Rn:=∑k=0npkqn-k≠0 (n∈) {{rm{R}}_{rm{n}}}: = sumlimits_{{rm{k}} = 0}^{rm{n}} {{{rm{p}}_{rm{k}}}{{rm{q}}_{{rm{n}} - {rm{k}}}}} ne 0,,,,left( {{rm{n}} in {rmmathbb{N}}} right) With En1 {rm{E}}_{rm{n}}^1 − we will denote the Euler summability method. Let (xn) be a sequence of real or complex numbers and set Np,qnEn1:=1Rn∑k=0npkqn-k12k∑v=0k(vk)xv {rm{N}}_{{rm{p}},{rm{q}}}^{rm{n}}{rm{E}}_{rm{n}}^1: = {1 over {{{rm{R}}_{rm{n}}}}}sumlimits_{{rm{k}} = 0}^{rm{n}} {{{rm{p}}_{rm{k}}}{{rm{q}}_{{rm{n - k}}}}{1 over {{2^{rm{k}}}}}sumlimits_{{rm{v}} = 0}^{rm{k}} {left( {_{rm{v}}^{rm{k}}} right){{rm{x}}_{rm{v}}}} } for n ∈ ℕ. In this paper, we present necessary and sufficient conditions under which the existence of the st− limit of (xn) follows from that of st-Np,qnE n1 {rm{st - N}}_{{rm{p}},q}^{rm{n}}{rm{E}}_{rm{n}}^1 − limit of (xn). These conditions are one-sided or two-sided if (xn) is a sequence of real or complex numbers, respectively.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88790528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we define a class of analytic functions, ℱ(ℋ, α, δ, µ), satisfying the following condition (α[ zf′(z)f(z) ]δ+(1-α)[ zf′(z)f(z) ]μ[ 1+zf″(z)f′(z) ]1-μ)≺(z,t), left( {alpha {{left[ {{{{rm{zf'}}({rm{z}})} over {{rm{f}}(z)}}} right]}^delta } + (1 - alpha ){{left[ {{{{rm{zf'}}left( {rm{z}} right)} over {{rm{f}}(z)}}} right]}^mu }{{left[ {1 + {{{rm{zf''}}({rm{z}})} over {{rm{f'}}({rm{z}})}}} right]}^{1 - mu }}} right),, prec mathcal{H}({rm{z}},{rm{t}}), where α ∈ [0, 1], δ ∈ [1, 2] and µ ∈ [0, 1]. We give coefficient estimates and Fekete-Szegö inequality for this class.
摘要本文定义了一类解析函数，即满足以下条件(α[zf ' (z)f(z)]δ+(1-α)[zf ' (z)f(z)]μ[1+zf ' (z)]μ[1+zf ' (z)f ' (z)]1-μ)(z,t)， left ({alpha{{left[ {{{{rm{zf'}}({rm{z}})} over {{rm{f}}(z)}}} right]} ^ delta +(1-}alpha) {{left[ {{{{rm{zf'}}left( {rm{z}} right)} over {{rm{f}}(z)}}} right]} ^ mu}{{left[ {1 + {{{rm{zf''}}({rm{z}})} over {{rm{f'}}({rm{z}})}}} right]} ^{1 -mu}}}right)，， precmathcal{H}(，)，其中α∈[0,1]，δ∈[1,2]，µ∈[0,1]。我们给出了这类的系数估计和Fekete-Szegö不等式。{rm{z}}{rm{t}}
{"title":"Coefficient estimates and Fekete-Szegö inequality for a class of analytic functions satisfying subordinate condition associated with Chebyshev polynomials","authors":"Eszter Szatmari, Ş. Altınkaya","doi":"10.2478/ausm-2019-0031","DOIUrl":"https://doi.org/10.2478/ausm-2019-0031","url":null,"abstract":"Abstract In this paper, we define a class of analytic functions, ℱ(ℋ, α, δ, µ), satisfying the following condition (α[ zf′(z)f(z) ]δ+(1-α)[ zf′(z)f(z) ]μ[ 1+zf″(z)f′(z) ]1-μ)≺(z,t), left( {alpha {{left[ {{{{rm{zf'}}({rm{z}})} over {{rm{f}}(z)}}} right]}^delta } + (1 - alpha ){{left[ {{{{rm{zf'}}left( {rm{z}} right)} over {{rm{f}}(z)}}} right]}^mu }{{left[ {1 + {{{rm{zf''}}({rm{z}})} over {{rm{f'}}({rm{z}})}}} right]}^{1 - mu }}} right),, prec mathcal{H}({rm{z}},{rm{t}}), where α ∈ [0, 1], δ ∈ [1, 2] and µ ∈ [0, 1]. We give coefficient estimates and Fekete-Szegö inequality for this class.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90603320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract If A is a rectangular matrix of rank r, then A may be written as PSQ where P and Q are invertible matrices and s=(IrOOO) s = left( {matrix{ hfill {{{rm{I}}_{rm{r}}}} & hfill {rm{O}} cr hfill {rm{O}} & hfill {rm{O}} cr } } right) . This is the rank normal form of the matrix A. The purpose of this paper is to exhibit some consequences of this representation form.
{"title":"Some consequences of the rank normal form of a matrix","authors":"Sorin Radulescu, Marius Drăgan, M. Bencze","doi":"10.2478/ausm-2019-0028","DOIUrl":"https://doi.org/10.2478/ausm-2019-0028","url":null,"abstract":"Abstract If A is a rectangular matrix of rank r, then A may be written as PSQ where P and Q are invertible matrices and s=(IrOOO) s = left( {matrix{ hfill {{{rm{I}}_{rm{r}}}} & hfill {rm{O}} cr hfill {rm{O}} & hfill {rm{O}} cr } } right) . This is the rank normal form of the matrix A. The purpose of this paper is to exhibit some consequences of this representation form.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89008430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This article is devoted to study Elzaki transform and its applications in Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative. We derive formula of Elzaki transform for Hilfer–Prabhakar derivative and its regularized version. The solution of Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative of fractional order is presented in terms of Mittag-Leffler type function. Furthermore, we find the application of the generalized Hilfer-Prabhakar derivative in linear partial differential equation and some problems of Mathematical Physics.
{"title":"On the Elzaki transform and its applications in fractional free electron laser equation","authors":"Yudhveer Singh, Vinod Gill, Sunil Kundu, Devendra Kumar","doi":"10.2478/ausm-2019-0030","DOIUrl":"https://doi.org/10.2478/ausm-2019-0030","url":null,"abstract":"Abstract This article is devoted to study Elzaki transform and its applications in Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative. We derive formula of Elzaki transform for Hilfer–Prabhakar derivative and its regularized version. The solution of Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative of fractional order is presented in terms of Mittag-Leffler type function. Furthermore, we find the application of the generalized Hilfer-Prabhakar derivative in linear partial differential equation and some problems of Mathematical Physics.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91004588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The aim of this scientific note is first to present certain information associated with the Tremblay operator in the complex plane and then to determine several results constituted by the related operator for certain analytic functions and also to point some implications of them out.
{"title":"Some results concerning the Tremblay operator and some of its applications to certain analytic functions","authors":"H. Irmak, O. Engel","doi":"10.2478/ausm-2019-0022","DOIUrl":"https://doi.org/10.2478/ausm-2019-0022","url":null,"abstract":"Abstract The aim of this scientific note is first to present certain information associated with the Tremblay operator in the complex plane and then to determine several results constituted by the related operator for certain analytic functions and also to point some implications of them out.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88317610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we study the Γ-hyperrings via T-fuzzy hyperideals. By means of the use of a triangular norm T, we define, characterize and study the T-fuzzy left and right hyperideals, T-fuzzy quasi-hyperideal and bi-hyperideal in Γ-hyperrings and some related properties are investigated. Regular Γ-hyperrings are characterized in terms of T-fuzzy quasi-hyperideal and T-fuzzy bi-hyperideal. We also introduce the T-(λ, µ)-fuzzy bi-hyperideals in Γ-hyperrings and investigate some of their properties.
{"title":"Study of Γ-hyperrings by fuzzy hyperideals with respect to a t-norm","authors":"Krisanthi Naka, K. Hila, S. Onar, B. A. Ersoy","doi":"10.2478/ausm-2019-0023","DOIUrl":"https://doi.org/10.2478/ausm-2019-0023","url":null,"abstract":"Abstract In this paper, we study the Γ-hyperrings via T-fuzzy hyperideals. By means of the use of a triangular norm T, we define, characterize and study the T-fuzzy left and right hyperideals, T-fuzzy quasi-hyperideal and bi-hyperideal in Γ-hyperrings and some related properties are investigated. Regular Γ-hyperrings are characterized in terms of T-fuzzy quasi-hyperideal and T-fuzzy bi-hyperideal. We also introduce the T-(λ, µ)-fuzzy bi-hyperideals in Γ-hyperrings and investigate some of their properties.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73828309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we study generalized quasi-Einstein warped products with respect to quarter symmetric connection for dimension n ≥ 3 and Ricci-symmetric generalized quasi-Einstein manifold with quarter symmetric connection. We also investigate that in what conditions the generalized quasi-Einstein manifold to be nearly Einstein manifold with respect to quarter symmetric connection. Example of warped product on generalized quasi-Einstein manifold with respect to quarter symmetric connection are also discussed.
{"title":"On a non flat Riemannian warped product manifold with respect to quarter-symmetric connection","authors":"B. Pal, S. Dey, S. Pahan","doi":"10.2478/ausm-2019-0024","DOIUrl":"https://doi.org/10.2478/ausm-2019-0024","url":null,"abstract":"Abstract In this paper, we study generalized quasi-Einstein warped products with respect to quarter symmetric connection for dimension n ≥ 3 and Ricci-symmetric generalized quasi-Einstein manifold with quarter symmetric connection. We also investigate that in what conditions the generalized quasi-Einstein manifold to be nearly Einstein manifold with respect to quarter symmetric connection. Example of warped product on generalized quasi-Einstein manifold with respect to quarter symmetric connection are also discussed.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74249322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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