Pub Date : 2023-06-15DOI: 10.24193/mathcluj.2023.1.13
Mohamed Moumen, L. Taoufiq, A. Boua
Let A be a Banach algebra over R or C with center Z(A). In this paper, we show that, if a non-injective continuous derivation of A satisfies some local differential identities, then A must be commutative. We give several applications, and we provide examples to show that some hypotheses of our theorems are necessary.
{"title":"On prime Banach algebras with continuous derivations","authors":"Mohamed Moumen, L. Taoufiq, A. Boua","doi":"10.24193/mathcluj.2023.1.13","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.1.13","url":null,"abstract":"Let A be a Banach algebra over R or C with center Z(A). In this paper, we show that, if a non-injective continuous derivation of A satisfies some local differential identities, then A must be commutative. We give several applications, and we provide examples to show that some hypotheses of our theorems are necessary.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42097924","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 : 2023-06-15DOI: 10.24193/mathcluj.2023.1.12
Soufyane Mokhtari, Boualem Benseba
Let p be an odd prime number, and a be an integer divisible by p exactly once. We prove that the Galois group G of the trinomial X^{p^{2}}+aX+a over the field Q of rational number is either the full symmetric group S_{p^{2}} or G lies between AGL(1,p^{2}) and AGL(2,p)$. Furthermore, we establish conditions when G is S_{p^{2}}.
{"title":"The Galois group of X^{p^2}+aX+a","authors":"Soufyane Mokhtari, Boualem Benseba","doi":"10.24193/mathcluj.2023.1.12","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.1.12","url":null,"abstract":"Let p be an odd prime number, and a be an integer divisible by p exactly once. We prove that the Galois group G of the trinomial X^{p^{2}}+aX+a over the field Q of rational number is either the full symmetric group S_{p^{2}} or G lies between AGL(1,p^{2}) and AGL(2,p)$. Furthermore, we establish conditions when G is S_{p^{2}}.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42146858","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 : 2023-06-15DOI: 10.24193/mathcluj.2023.1.06
Orhan Dişkaya, H. Menken
In the present work, two new recurrences of the Jacobsthal sequence are defined. Some identities of these sequences which we call the Jacobsthal array is examined. Also, the generating and series functions of the Jacobsthal array are obtained.
{"title":"On the recurrences of the Jacobsthal sequence","authors":"Orhan Dişkaya, H. Menken","doi":"10.24193/mathcluj.2023.1.06","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.1.06","url":null,"abstract":"In the present work, two new recurrences of the Jacobsthal sequence are defined. Some identities of these sequences which we call the Jacobsthal array is examined. Also, the generating and series functions of the Jacobsthal array are obtained.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47681087","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 : 2023-06-15DOI: 10.24193/mathcluj.2023.1.08
Rachida Kaid, A. Matallah, Sofiane Messirdi
"In this paper, we use variational methods to study the existence and multiplicity of non negative solutions for a p-Kirchhoff equation involving critical Sobolev exponent."
{"title":"Multiple solutions to p-Kirchhoff type problems involving critical Sobolev exponent in R^N","authors":"Rachida Kaid, A. Matallah, Sofiane Messirdi","doi":"10.24193/mathcluj.2023.1.08","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.1.08","url":null,"abstract":"\"In this paper, we use variational methods to study the existence and multiplicity of non negative solutions for a p-Kirchhoff equation involving critical Sobolev exponent.\"","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44432151","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 : 2023-06-15DOI: 10.24193/mathcluj.2023.1.14
Parisa Seifizadeh, Amirali Farokhniaee
Let G be a finite non-abelian p-group, where p is a prime number, and Aut(G) be the group of all automorphisms of $G$. An automorphism alpha of $G$ is called absolute central automorphism if, x^{-1}alpha(x) lies in L(G), where L(G) is the absolute center of G. In addition, alpha is an absolute Frattini automorphism if x^{-1}alpha(x) is in Phi(L(G)), where Phi(L(G)) is the Frattini subgroup of the absolute center of G, and let LF(G) denote the group of all such automorphisms of G. Also, we denote by C_{LF(G)}(Z(G)) and C_{LA(G)}(Z(G)), respectively, the group of all absolute Frattini automorphisms and the group of all absolute central automorphisms of G, fixing elementwise the center Z(G) of G . We give necessary and sufficient conditions on a finite non-abelian p-group G of class two such that C_{LF(G)}(Z(G))=C_{LA(G)}(Z(G)). Moreover, we investigate the conditions under which LF(G) is a torsion-free abelian group.
{"title":"The absolute Frattini automorphisms","authors":"Parisa Seifizadeh, Amirali Farokhniaee","doi":"10.24193/mathcluj.2023.1.14","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.1.14","url":null,"abstract":"Let G be a finite non-abelian p-group, where p is a prime number, and Aut(G) be the group of all automorphisms of $G$. An automorphism alpha of $G$ is called absolute central automorphism if, x^{-1}alpha(x) lies in L(G), where L(G) is the absolute center of G. In addition, alpha is an absolute Frattini automorphism if x^{-1}alpha(x) is in Phi(L(G)), where Phi(L(G)) is the Frattini subgroup of the absolute center of G, and let LF(G) denote the group of all such automorphisms of G. Also, we denote by C_{LF(G)}(Z(G)) and C_{LA(G)}(Z(G)), respectively, the group of all absolute Frattini automorphisms and the group of all absolute central automorphisms of G, fixing elementwise the center Z(G) of G . We give necessary and sufficient conditions on a finite non-abelian p-group G of class two such that C_{LF(G)}(Z(G))=C_{LA(G)}(Z(G)). Moreover, we investigate the conditions under which LF(G) is a torsion-free abelian group.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41344045","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 : 2023-06-15DOI: 10.24193/mathcluj.2023.1.01
A. Acikgoz, T. Noiri, Busra Golpinar
In this research we introduce h-local functions by using h-open sets in an ideal topological space (X, tau, I). Some properties and characterizations of the h-local functions are studied. Also, we introduce and research the notions of I_{{s^*}g}-h-closed and I_{g}-h-closed sets in an ideal topological space. Additionally, Cl^*_h is defined and its properties are examined.
{"title":"On h-local functions in deal topological spaces","authors":"A. Acikgoz, T. Noiri, Busra Golpinar","doi":"10.24193/mathcluj.2023.1.01","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.1.01","url":null,"abstract":"In this research we introduce h-local functions by using h-open sets in an ideal topological space (X, tau, I). Some properties and characterizations of the h-local functions are studied. Also, we introduce and research the notions of I_{{s^*}g}-h-closed and I_{g}-h-closed sets in an ideal topological space. Additionally, Cl^*_h is defined and its properties are examined.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69192529","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 : 2023-06-15DOI: 10.24193/mathcluj.2023.1.02
Mokhtar Ahmadi, A. S. Janfada, K. Nabardi
In this article, first, using the elliptic curve method, it is proved that the quartic Diophantine equations x^4-y^4=k(t^lambda-u^4{+-} v^4) for positive even lambda and integers k and t has infinitely many non-trivial rational solutions. Then, by direct ways, parametric solutions for equations x^4-y^4=k(t^3{+-} u^4-v^4) are found.
{"title":"On the solutions of quartic Diophantine equations","authors":"Mokhtar Ahmadi, A. S. Janfada, K. Nabardi","doi":"10.24193/mathcluj.2023.1.02","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.1.02","url":null,"abstract":"In this article, first, using the elliptic curve method, it is proved that the quartic Diophantine equations x^4-y^4=k(t^lambda-u^4{+-} v^4) for positive even lambda and integers k and t has infinitely many non-trivial rational solutions. Then, by direct ways, parametric solutions for equations x^4-y^4=k(t^3{+-} u^4-v^4) are found.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41324498","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 : 2023-06-15DOI: 10.24193/mathcluj.2023.1.09
A. Lörinczi
We verify computationally a conjecture on the field independence of tree representations of Euclidean quivers, with dimension vector bounded by the minimal radical vector of the quiver. This includes a large class of exceptional representations, in particular all the regular non-homogeneous exceptionals. In addition we also present some thought-provoking findings, which further confirms the combinatorial nature of the category of representations of tame quivers.
{"title":"On the combinatorial nature of tree representations of Euclidean quivers","authors":"A. Lörinczi","doi":"10.24193/mathcluj.2023.1.09","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.1.09","url":null,"abstract":"We verify computationally a conjecture on the field independence of tree representations of Euclidean quivers, with dimension vector bounded by the minimal radical vector of the quiver. This includes a large class of exceptional representations, in particular all the regular non-homogeneous exceptionals. In addition we also present some thought-provoking findings, which further confirms the combinatorial nature of the category of representations of tame quivers.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48787029","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 : 2022-12-15DOI: 10.24193/mathcluj.2022.2.08
Sundas Khan, H. Budak, Yuming Chu
In this study, the Hermite-Hadamard inequality for q^{kappa_2}-integrals is demonstrated by a new method called the Green Function Technique. For this purpose, we first obtain certain identities. Then, by using these identities, we establish many new inequalities for functions whose second derivative is convex, monotone and concave in absolute value.
{"title":"New quantum inequalities of Hermite-Hadamard type via Green function","authors":"Sundas Khan, H. Budak, Yuming Chu","doi":"10.24193/mathcluj.2022.2.08","DOIUrl":"https://doi.org/10.24193/mathcluj.2022.2.08","url":null,"abstract":"In this study, the Hermite-Hadamard inequality for q^{kappa_2}-integrals is demonstrated by a new method called the Green Function Technique. For this purpose, we first obtain certain identities. Then, by using these identities, we establish many new inequalities for functions whose second derivative is convex, monotone and concave in absolute value.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48916087","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 : 2022-12-15DOI: 10.24193/mathcluj.2022.2.01
Meryem Ece Alkan, F. Nuray
This paper introduces the concepts of deferred almost convergence, strongly deferred almost convergence and deferred almost statistical convergence, and investigates the relationship between these concepts. Also, it gives the notions of asymptotical deferred almost equivalence and asymptotical deferred almost statistical equivalence.
{"title":"Strongly deferred almost convergence and deferred almost statistical convergence","authors":"Meryem Ece Alkan, F. Nuray","doi":"10.24193/mathcluj.2022.2.01","DOIUrl":"https://doi.org/10.24193/mathcluj.2022.2.01","url":null,"abstract":"This paper introduces the concepts of deferred almost convergence, strongly deferred almost convergence and deferred almost statistical convergence, and investigates the relationship between these concepts. Also, it gives the notions of asymptotical deferred almost equivalence and asymptotical deferred almost statistical equivalence.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44164116","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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