Pub Date : 2023-12-01DOI: 10.12697/acutm.2023.27.22
K. Kaarli, S´ándor Radeleczki
Given a lattice L, we denote by Res(L) the lattice of all residuated maps on L. The main objective of the paper is to study the atoms of Res(L) where L is a complete lattice. Note that the description of dual atoms of Res(L) easily follows from earlier results of Shmuely (1974). We first consider lattices L for which all atoms of Res(L) are mappings with 2-element range and give a sufficient condition for this. Extending this result, we characterize these atoms of Res(L) which are weakly regular residuated maps in the sense of Blyth and Janowitz (Residuation Theory, 1972). In the rest of the paper we investigate the atoms of Res(M) where M is the lattice of a finite projective plane, in particular, we describe the atoms of Res(F), where F is the lattice of the Fano plane.
{"title":"Atoms of the lattices of residuated mappings","authors":"K. Kaarli, S´ándor Radeleczki","doi":"10.12697/acutm.2023.27.22","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.22","url":null,"abstract":"Given a lattice L, we denote by Res(L) the lattice of all residuated maps on L. The main objective of the paper is to study the atoms of Res(L) where L is a complete lattice. Note that the description of dual atoms of Res(L) easily follows from earlier results of Shmuely (1974). We first consider lattices L for which all atoms of Res(L) are mappings with 2-element range and give a sufficient condition for this. Extending this result, we characterize these atoms of Res(L) which are weakly regular residuated maps in the sense of Blyth and Janowitz (Residuation Theory, 1972). In the rest of the paper we investigate the atoms of Res(M) where M is the lattice of a finite projective plane, in particular, we describe the atoms of Res(F), where F is the lattice of the Fano plane.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138617201","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}
Pub Date : 2023-12-01DOI: 10.12697/acutm.2023.27.14
Kiran N. Darji
In this paper, we provide sufficient conditions for the generalized β-absolute convergence of multiple Fourier series of a function of p-(Λ1, ... ,ΛN)-bounded variation.
本文给出了p-(Λ1，…)函数的多重傅里叶级数广义β-绝对收敛的充分条件。ΛN)的变化。
{"title":"On the generalized β-absolute convergence of single and multiple Fourier series","authors":"Kiran N. Darji","doi":"10.12697/acutm.2023.27.14","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.14","url":null,"abstract":"In this paper, we provide sufficient conditions for the generalized β-absolute convergence of multiple Fourier series of a function of p-(Λ1, ... ,ΛN)-bounded variation. \u0000 ","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138618795","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}
Pub Date : 2023-12-01DOI: 10.12697/acutm.2023.27.12
Ahmad Al-Omari, T. Noiri
In this paper, we introduce the notion of mgH-closed sets in a hereditary m-space (X, m, H) and obtain a further generalization of mg-closed sets. We investigate basic properties, characterizations and preservation properties of mgH-closed sets.
本文在遗传m空间(X, m, H)中引入了mgh -闭集的概念，得到了mgh -闭集的进一步推广。研究了mgh闭集的基本性质、刻画和保存性质。
{"title":"A Generalization of mg-closed sets in Hereditary m-spaces","authors":"Ahmad Al-Omari, T. Noiri","doi":"10.12697/acutm.2023.27.12","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.12","url":null,"abstract":"In this paper, we introduce the notion of mgH-closed sets in a hereditary m-space (X, m, H) and obtain a further generalization of mg-closed sets. We investigate basic properties, characterizations and preservation properties of mgH-closed sets.\u0000 ","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138619470","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}
Pub Date : 2023-12-01DOI: 10.12697/acutm.2023.27.19
N. Saadaoui
In this paper, we introduce and study the low dimensional cohomology of metric Hom-Jacobi–Jordan algebras. We establish one-to-one correspondence between the equivalence classes of abelian quadraticextensions of a Hom-Jacobi–Jordan algebra and its second cohomology group.
{"title":"Second cohomology group and quadratic extensions of metric Hom-Jacobi–Jordan algebras","authors":"N. Saadaoui","doi":"10.12697/acutm.2023.27.19","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.19","url":null,"abstract":"In this paper, we introduce and study the low dimensional cohomology of metric Hom-Jacobi–Jordan algebras. We establish one-to-one correspondence between the equivalence classes of abelian quadraticextensions of a Hom-Jacobi–Jordan algebra and its second cohomology group.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138615252","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}
Pub Date : 2023-12-01DOI: 10.12697/acutm.2023.27.18
David Robbns, Terje Hill
Let {Ax : x ∈ X} be a collection of complex Banach algebras indexed by the compact Hausdorff space X. We investigate the character amenability of certain algebras of Ax-valued functions in relation to the character amenability of the Ax.
{"title":"Character amenability of vector-valued algebras","authors":"David Robbns, Terje Hill","doi":"10.12697/acutm.2023.27.18","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.18","url":null,"abstract":"Let {Ax : x ∈ X} be a collection of complex Banach algebras indexed by the compact Hausdorff space X. We investigate the character amenability of certain algebras of Ax-valued functions in relation to the character amenability of the Ax.\u0000 ","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138617388","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}
Pub Date : 2023-12-01DOI: 10.12697/acutm.2023.27.16
Taoufik Chtioui, Karima Benali, A. Hajjaji, S. Mabrouk
The aim of this paper is to introduce the notion of a mock-Lie bialgebra which is equivalent to a Manin triple of mock-Lie algebras. The study of a special case called coboundary mock-Lie bialgebra leads to introducing the mock-Lie Yang–Baxter equation on a mock-Lie algebra which is an analogue of the classical Yang–Baxter equation on a Lie algebra. Note that a skew-symmetric solution of mock-Lie Yang–Baxter equation gives a mock-Lie bialgebra. Finally, O-operators are studied to construct a skew-symmetric solution of a mock-Lie Yang–Baxter equation.
{"title":"Bialgebras, the Yang–Baxter equation and Manin triples for mock-Lie algebras","authors":"Taoufik Chtioui, Karima Benali, A. Hajjaji, S. Mabrouk","doi":"10.12697/acutm.2023.27.16","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.16","url":null,"abstract":"The aim of this paper is to introduce the notion of a mock-Lie bialgebra which is equivalent to a Manin triple of mock-Lie algebras. The study of a special case called coboundary mock-Lie bialgebra leads to introducing the mock-Lie Yang–Baxter equation on a mock-Lie algebra which is an analogue of the classical Yang–Baxter equation on a Lie algebra. Note that a skew-symmetric solution of mock-Lie Yang–Baxter equation gives a mock-Lie bialgebra. Finally, O-operators are studied to construct a skew-symmetric solution of a mock-Lie Yang–Baxter equation.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138618913","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}
Pub Date : 2023-12-01DOI: 10.12697/acutm.2023.27.21
P. Tiebekabe, K. R. Kakanou, Hamid Ben Yakkou
In this paper, we show that there are only finitely many Narayana's numbers which can be written as a product of three repdigits in base g with g >= 2. Moreover, for 2 <= g <= 10, we determine all these numbers.
在本文中，我们证明了只有有限多个Narayana数可以写成以g为底且g >= 2的三个数字的乘积。此外，对于2 <= g <= 10，我们确定了所有这些数。
{"title":"Narayana numbers as products of three repdigits in base g","authors":"P. Tiebekabe, K. R. Kakanou, Hamid Ben Yakkou","doi":"10.12697/acutm.2023.27.21","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.21","url":null,"abstract":"In this paper, we show that there are only finitely many Narayana's numbers which can be written as a product of three repdigits in base g with g >= 2. Moreover, for 2 <= g <= 10, we determine all these numbers.\u0000 \u0000 ","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138620503","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}
Pub Date : 2023-12-01DOI: 10.12697/acutm.2023.27.15
H. Srivastava, Biswajit Rath, Sanjay Kumar Karri, V. D.
The objective of this paper is to estimate the sharp bound of the third Hankel determinant for the kth-root transformation to the class of functions whose derivative has a positive real part satisfying the normalized conditions f(0) = 0 and f′(0) = 1 in the open unit disk D := {z ∈ C : |z| < 1}.
{"title":"The sharp bound of the third Hankel determinant of the kth-root transformation for bounded turning functions","authors":"H. Srivastava, Biswajit Rath, Sanjay Kumar Karri, V. D.","doi":"10.12697/acutm.2023.27.15","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.15","url":null,"abstract":"The objective of this paper is to estimate the sharp bound of the third Hankel determinant for the kth-root transformation to the class of functions whose derivative has a positive real part satisfying the normalized conditions f(0) = 0 and f′(0) = 1 in the open unit disk D := {z ∈ C : |z| < 1}.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138611741","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}
Pub Date : 2023-12-01DOI: 10.12697/acutm.2023.27.17
Zehra İşbilir, N. Gürses
This manuscript deals with introducing and discussing of a new type dual quaternions which are named generalized Tribonacci dual quaternions (GTDQ, for short). For this purpose, several new properties, such as Binet formula, generating function, exponential generating function, matrix formula, and determinant equations, are established. In addition to these, some numerical algorithms are constructed. In the last part, some special cases of the family of the GTDQ are examined regarding r, s, t values and initial values considering concluded results.
{"title":"Examination of generalized Tribonacci dual quaternions","authors":"Zehra İşbilir, N. Gürses","doi":"10.12697/acutm.2023.27.17","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.17","url":null,"abstract":"This manuscript deals with introducing and discussing of a new type dual quaternions which are named generalized Tribonacci dual quaternions (GTDQ, for short). For this purpose, several new properties, such as Binet formula, generating function, exponential generating function, matrix formula, and determinant equations, are established. In addition to these, some numerical algorithms are constructed. In the last part, some special cases of the family of the GTDQ are examined regarding r, s, t values and initial values considering concluded results.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138623689","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}
Pub Date : 2023-08-07DOI: 10.12697/acutm.2023.27.20
Shahid Mubasshar, J. Lellep
The free vibrations of elastic circular arches made of a nano-material are considered. A method of determination of eigenfrequencies of nanoarches weakened with stable cracks is developed making use of the concept of the massless spring and Eringen's nonlocal theory of elasticity. The aim of the paper is to evaluate the sensitivity of eigenfrequencies on the geometrical and physical parameters of the nanoarch.
{"title":"Natural vibrations of circular nanoarches of piecewise constant thickness","authors":"Shahid Mubasshar, J. Lellep","doi":"10.12697/acutm.2023.27.20","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.20","url":null,"abstract":"The free vibrations of elastic circular arches made of a nano-material are considered. A method of determination of eigenfrequencies of nanoarches weakened with stable cracks is developed making use of the concept of the massless spring and Eringen's nonlocal theory of elasticity. The aim of the paper is to evaluate the sensitivity of eigenfrequencies on the geometrical and physical parameters of the nanoarch.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139351453","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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