Pub Date : 2023-05-26DOI: 10.12697/acutm.2023.27.02
Nasir Sohail, Abdullahi Umar
A semigroup S is called left ample if it can be embedded in the symmetric inverse semigroup IX of partial bijections of a non-empty set X such that the image of S is closed under the unary operation α → αα⁻¹, where α⁻¹ is the inverse of α in IX. Right ample semigroups are defined dually. A semigroup is called ample if it is both left and right ample. A monoid is (left, right) ample if it is (left, right) ample as a semigroup. We observe that the dominion of an ample subsemigroup of IX coincides with the inverse subsemigroup of IX generated by it. We then determine the dominions of certain submonoids of In, the symmetric inverse semigroup over a finite chain 1<2<⋯
{"title":"On dominions of certain ample monoids","authors":"Nasir Sohail, Abdullahi Umar","doi":"10.12697/acutm.2023.27.02","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.02","url":null,"abstract":"A semigroup S is called left ample if it can be embedded in the symmetric inverse semigroup IX of partial bijections of a non-empty set X such that the image of S is closed under the unary operation α → αα⁻¹, where α⁻¹ is the inverse of α in IX. Right ample semigroups are defined dually. A semigroup is called ample if it is both left and right ample. A monoid is (left, right) ample if it is (left, right) ample as a semigroup. We observe that the dominion of an ample subsemigroup of IX coincides with the inverse subsemigroup of IX generated by it. We then determine the dominions of certain submonoids of In, the symmetric inverse semigroup over a finite chain 1<2<⋯<n.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134922590","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 : 2022-11-28DOI: 10.12697/acutm.2022.26.19
Heleen Saarse, K. Väljako
In this article we define the tensor product of partial acts over a semigroup and prove several properties of this tensor product. We also define the notion of a polite partial biact, which is needed to define partial actions on the tensor product of partial acts. Finally, we prove that a certain tensor functor of partial acts is left adjoint of a certain hom-functor of partial acts.
{"title":"Tensor product of partial acts","authors":"Heleen Saarse, K. Väljako","doi":"10.12697/acutm.2022.26.19","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.19","url":null,"abstract":"In this article we define the tensor product of partial acts over a semigroup and prove several properties of this tensor product. We also define the notion of a polite partial biact, which is needed to define partial actions on the tensor product of partial acts. Finally, we prove that a certain tensor functor of partial acts is left adjoint of a certain hom-functor of partial acts.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"70 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77867872","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 : 2022-11-28DOI: 10.12697/acutm.2022.26.21
A. Mürk, J. Lellep
The dynamic behaviour of clamped circular plates subjected to the concentrated blast loading is studied. The load is applied at a non-central point of the plate, non-axisymmetric deflections are taken into account. An approximate theoretical procedure developed earlier is applied for the evaluation of residual maximal deflections. The solution technique is based on the idea of equality of the power of the internal and external work, respectively. As it was shown earlier this concept leads to results which are close to exact ones in the case of axisymmetric loading of circular plates, also in the case of circular cylindrical shells.
{"title":"Asymmetric response of inelastic circular plates to blast loading","authors":"A. Mürk, J. Lellep","doi":"10.12697/acutm.2022.26.21","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.21","url":null,"abstract":"The dynamic behaviour of clamped circular plates subjected to the concentrated blast loading is studied. The load is applied at a non-central point of the plate, non-axisymmetric deflections are taken into account. An approximate theoretical procedure developed earlier is applied for the evaluation of residual maximal deflections. The solution technique is based on the idea of equality of the power of the internal and external work, respectively. As it was shown earlier this concept leads to results which are close to exact ones in the case of axisymmetric loading of circular plates, also in the case of circular cylindrical shells.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"50 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83994927","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 : 2022-11-28DOI: 10.12697/acutm.2022.26.18
Ö. Duran, N. Ömür, S. Koparal
In this paper, we give new identities involving degenerate q-Euler polynomials with weight α and q-Changhee polynomials of the second kind with weight α, using the Faà di Bruno formula and some identities of the Bell polynomials of the second kind.
{"title":"Applications of degenerate q-Euler and q-Changhee polynomials with weight α","authors":"Ö. Duran, N. Ömür, S. Koparal","doi":"10.12697/acutm.2022.26.18","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.18","url":null,"abstract":"In this paper, we give new identities involving degenerate q-Euler polynomials with weight α and q-Changhee polynomials of the second kind with weight α, using the Faà di Bruno formula and some identities of the Bell polynomials of the second kind.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"43 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90827057","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 : 2022-11-28DOI: 10.12697/acutm.2022.26.20
Laxmipriya Parida, T. Bulboacă, A. Sahoo
Using operator Lp(a, c) introduced by Saitoh (Math. Japon. 44 (1996), 31–38) we define the subclass Hp,nν,μ (a, c; ϕ) of the class A(p, n) and establish containment, subordination and coefficient inequalities of this subclass. We indicate the connections of our results with earlier results obtained by other researchers.
{"title":"On a generalized class of analytic functions related to Bazilevič functions","authors":"Laxmipriya Parida, T. Bulboacă, A. Sahoo","doi":"10.12697/acutm.2022.26.20","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.20","url":null,"abstract":"Using operator Lp(a, c) introduced by Saitoh (Math. Japon. 44 (1996), 31–38) we define the subclass Hp,nν,μ (a, c; ϕ) of the class A(p, n) and establish containment, subordination and coefficient inequalities of this subclass. We indicate the connections of our results with earlier results obtained by other researchers. \u0000","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"231 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76436488","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 : 2022-11-23DOI: 10.12697/acutm.2022.26.17
H. Bouhadjera
Fixed point theory is a crucial branch in mathematics with a colossal number of applications in countless subjects. It furnishes preeminent tools and resources for elucidating varied problems which at first glance do not look like a fixed point problem. Since and even before 1912 till now several authors launched the existence and uniqueness of common fixed points for pairs of single and set-valued maps satisfying certain compatibilities on different spaces. This paper proves existence and uniqueness of a common fixed point for pairs of occasionally weakly biased maps. This unique common fixed point is guaranteed under the concept of modified contractive modulus function. Our theorems improve some results existing in the fixed point literature.
{"title":"Unique common fixed points through a unified condition","authors":"H. Bouhadjera","doi":"10.12697/acutm.2022.26.17","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.17","url":null,"abstract":"Fixed point theory is a crucial branch in mathematics with a colossal number of applications in countless subjects. It furnishes preeminent tools and resources for elucidating varied problems which at first glance do not look like a fixed point problem. Since and even before 1912 till now several authors launched the existence and uniqueness of common fixed points for pairs of single and set-valued maps satisfying certain compatibilities on different spaces. This paper proves existence and uniqueness of a common fixed point for pairs of occasionally weakly biased maps. This unique common fixed point is guaranteed under the concept of modified contractive modulus function. Our theorems improve some results existing in the fixed point literature.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"85 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88509400","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 : 2022-11-23DOI: 10.12697/acutm.2022.26.16
H. Khachar, R. Vyas
In this article, extending the results of Fourier and conjugate Fourier series, the rates of convergence for rational and conjugate rational Fourier series for functions of generalized bounded variation are estimated.
推广傅里叶级数和共轭傅里叶级数的结果，估计了广义有界变分函数的有理和共轭有理傅里叶级数的收敛速率。
{"title":"Rate of convergence for rational and conjugate rational Fourier series of functions of generalized bounded variation","authors":"H. Khachar, R. Vyas","doi":"10.12697/acutm.2022.26.16","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.16","url":null,"abstract":"In this article, extending the results of Fourier and conjugate Fourier series, the rates of convergence for rational and conjugate rational Fourier series for functions of generalized bounded variation are estimated.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"8 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74885935","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 : 2022-11-23DOI: 10.12697/acutm.2022.26.15
L. Palacios, Pavel Ramos-Martinez, C. Signoret
Let X be a completely regular Hausdorff space and V a Nachbin familyon X. For a locally convex algebra A, let CV(0)(X, A) be the algebra ofall weighted vector-valued continuous functions with the topology givenby the uniform seminorms induced by V . In this paper we study someproperties of A that are inherited by CV(0)(X, A). These properties arerelated to the unit element, spectral seminorms and uniformly A-convexproperty
{"title":"On some properties of CV_{(0)}(X, A)","authors":"L. Palacios, Pavel Ramos-Martinez, C. Signoret","doi":"10.12697/acutm.2022.26.15","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.15","url":null,"abstract":"Let X be a completely regular Hausdorff space and V a Nachbin familyon X. For a locally convex algebra A, let CV(0)(X, A) be the algebra ofall weighted vector-valued continuous functions with the topology givenby the uniform seminorms induced by V . In this paper we study someproperties of A that are inherited by CV(0)(X, A). These properties arerelated to the unit element, spectral seminorms and uniformly A-convexproperty","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"41 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76358194","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 : 2022-11-22DOI: 10.12697/acutm.2022.26.13
A. Al-Omari, T. Noiri
Let (X,m, H) be a hereditary m-space. A subset A of X is said to be θ-H-compact relative to X if for every cover U of A by m(θ)-open sets of X, there exists a finite subset U0 of U such that A ∪ U0 ∈ H. We obtain several properties of these sets. Also, we define and investigate two kinds of strong forms of “θ-H-compact relative to X”.
设(X,m, H)是一个遗传的m空间。如果对于每一个覆盖U (A) × m(θ)-开集X，存在U的一个有限子集U0使得A ∪U0∈h，则X的子集A相对于X是θ- h紧致的。我们得到了这些集合的几个性质。此外，我们还定义并研究了两种“θ- h -相对于X紧”的强形式。
{"title":"Properties of theta-H-compact sets in hereditary m-spaces","authors":"A. Al-Omari, T. Noiri","doi":"10.12697/acutm.2022.26.13","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.13","url":null,"abstract":"Let (X,m, H) be a hereditary m-space. A subset A of X is said to be θ-H-compact relative to X if for every cover U of A by m(θ)-open sets of X, there exists a finite subset U0 of U such that A ∪ U0 ∈ H. We obtain several properties of these sets. Also, we define and investigate two kinds of strong forms of “θ-H-compact relative to X”. \u0000 ","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"59 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73838289","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 : 2022-11-22DOI: 10.12697/acutm.2022.26.14
A. Ipek
In this paper, we first give the Pascal’s identity for Pellnomial coefficients and then we show that the Pellnomial coefficients are integers. We obtain that the product of r consecutive Pell numbers is divisible by the Pell analog of r!. Also, we introduce the divisibility theorems between Pell numbers and Pellnomial coefficients. Furthermore, we first define Pell–Catalan numbers and then we derive two formulas for presenting Pell–Catalan numbers.
{"title":"On Pellnomial coefficients and Pell-Catalan numbers","authors":"A. Ipek","doi":"10.12697/acutm.2022.26.14","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.14","url":null,"abstract":"In this paper, we first give the Pascal’s identity for Pellnomial coefficients and then we show that the Pellnomial coefficients are integers. We obtain that the product of r consecutive Pell numbers is divisible by the Pell analog of r!. Also, we introduce the divisibility theorems between Pell numbers and Pellnomial coefficients. Furthermore, we first define Pell–Catalan numbers and then we derive two formulas for presenting Pell–Catalan numbers.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"144 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88654127","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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