Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4918
Eltiyeb Ali
Let $R$ be a ring and $M$ be a monoid with a twisting map $f : M times M rightarrow U(R)$ and an action map $omega : M rightarrow Aut(R)$. The objective of our work is to extend the reflexive properties of rings by focusing on the crossed product $R ast M$ over $R$. In order to achieve this, we introduce and examine the concept of strongly $CM$-reflexive rings. Although a monoid $M$ and any ring $R$ with an idempotent are not strongly $CM$-reflexive in general, we prove that $R$ is strongly $CM$-reflexive under some additional conditions. Moreover, we prove that if $R$ is a left $p.q.$-Baer (semiprime, left $APP$-ring, respectively), then $R$ is strongly $CM$-reflexive. Additionally, for a right Ore ring $R$ with a classical right quotient ring $Q$, we prove $R$ is strongly $CM$-reflexive if and only if $Q$ is strongly $CM$-reflexive. Finally, we discuss some relevant results on crossed products.
假设$R$是一个环，$M$是一个具有扭曲图$f : M times M rightarrow U(R)$和动作图$omega : M rightarrow Aut(R)$的单oid。我们工作的目标是通过关注$R ast M$ / $R$的交叉积来扩展环的自反性。为了达到这个目的，我们引入并检验了强$CM$ -自反环的概念。虽然一般情况下一元群$M$和任何幂等环$R$都不是强$CM$自反的，但我们证明了$R$在一些附加条件下是强$CM$自反的。此外，我们证明了如果$R$是左$p.q.$ -Baer(半素数，左$APP$ -环)，则$R$是强$CM$ -自反的。此外，对于具有经典右商环$Q$的右矿环$R$，我们证明了$R$是强$CM$ -自反的当且仅当$Q$是强$CM$ -自反的。最后讨论了交叉产物的一些相关结果。
{"title":"Generalized Reflexive Structures Properties of Crossed Products Type","authors":"Eltiyeb Ali","doi":"10.29020/nybg.ejpam.v16i4.4918","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4918","url":null,"abstract":"Let $R$ be a ring and $M$ be a monoid with a twisting map $f : M times M rightarrow U(R)$ and an action map $omega : M rightarrow Aut(R)$. The objective of our work is to extend the reflexive properties of rings by focusing on the crossed product $R ast M$ over $R$. In order to achieve this, we introduce and examine the concept of strongly $CM$-reflexive rings. Although a monoid $M$ and any ring $R$ with an idempotent are not strongly $CM$-reflexive in general, we prove that $R$ is strongly $CM$-reflexive under some additional conditions. Moreover, we prove that if $R$ is a left $p.q.$-Baer (semiprime, left $APP$-ring, respectively), then $R$ is strongly $CM$-reflexive. Additionally, for a right Ore ring $R$ with a classical right quotient ring $Q$, we prove $R$ is strongly $CM$-reflexive if and only if $Q$ is strongly $CM$-reflexive. Finally, we discuss some relevant results on crossed products.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068832","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4911
Farhat Yasser, Vadakasi Subramanian
In this article, in a bigeneralized topological space, we introduce an interesting tool namely, $(s, v)$-dense set, and examine the significance of this set. Also, we give the relations between nowhere-dense sets defined in generalized and bigeneralized topological space and give some of their properties by using functions. Finally, we give some applications for $(s, v)$-dense and $(s, v)$-nowhere dense sets in a soft set theory.
{"title":"Generalized Dense set in Bigeneralized Topological Spaces","authors":"Farhat Yasser, Vadakasi Subramanian","doi":"10.29020/nybg.ejpam.v16i4.4911","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4911","url":null,"abstract":"In this article, in a bigeneralized topological space, we introduce an interesting tool namely, $(s, v)$-dense set, and examine the significance of this set. Also, we give the relations between nowhere-dense sets defined in generalized and bigeneralized topological space and give some of their properties by using functions. Finally, we give some applications for $(s, v)$-dense and $(s, v)$-nowhere dense sets in a soft set theory.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069126","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4912
Javier Hassan, Jahiri Manditong, Alcyn Bakkang, Sisteta U. Kamdon, Jeffrey Imer Salim
Let G be a graph with no isolated vertex. A subset M ⊆ V (G) is called a J-open set if NG(a)NG(b) ̸= ∅ and NG(b)NG(a) ̸= ∅ ∀ a, b ∈ M, where a ̸= b. If in addition, M is a total dominating in G, then we call M a J-total dominating set in G. The maximum cardinality amongall J-total dominating set in G, denoted by γJt(G), is called the J-total domination number of G. In this paper, we characterize J-total dominating sets in some special graphs and join of two graphs, and we use these results to obtain formulas for the parameters of these graphs. Moreover, we determine its relationships with other known parameters in graph theory. Finally, we derive the lower bound of the parameter for the corona of two graphs.
{"title":"Characterizations of $J$-Total Dominating Sets in Some Special Graphs and Graphs under Some Operations","authors":"Javier Hassan, Jahiri Manditong, Alcyn Bakkang, Sisteta U. Kamdon, Jeffrey Imer Salim","doi":"10.29020/nybg.ejpam.v16i4.4912","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4912","url":null,"abstract":"Let G be a graph with no isolated vertex. A subset M ⊆ V (G) is called a J-open set if NG(a)NG(b) ̸= ∅ and NG(b)NG(a) ̸= ∅ ∀ a, b ∈ M, where a ̸= b. If in addition, M is a total dominating in G, then we call M a J-total dominating set in G. The maximum cardinality amongall J-total dominating set in G, denoted by γJt(G), is called the J-total domination number of G. In this paper, we characterize J-total dominating sets in some special graphs and join of two graphs, and we use these results to obtain formulas for the parameters of these graphs. Moreover, we determine its relationships with other known parameters in graph theory. Finally, we derive the lower bound of the parameter for the corona of two graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069136","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4914
Sergio Canoy Jr, Ferdinand Jamil, Sheila Menchavez
Given a simple graph $G=(V(G),E(G))$, a function $f:V(G)to {0,1,2}$ is a hop Italian dominating function if for every vertex $v$ with $f(v)=0$ there exists a vertex $u$ with $f(u)=2$ for which $u$ and $v$ are of distance $2$ from each other or there exist two vertices $w$ and $z$ for which $f(w)=1=f(z)$ and each of $w$ and $z$ is of distance $2$ from $v$. The minimum weight $sum_{vin V(G)}f(v)$ of a hop Italian dominating function is the hop Italian domination number of $G$, and is denoted by $gamma_{hI}(G)$. In this paper, we initiate the study of the hop Italian domination. In particular, we establish some properties of the the hop Italian dominating function and explore the relationships of the hop Italian domination number with the hop Roman domination number cite{Rad2,Natarajan} and with the $2$-hop domination number cite{Canoy}. We study the concept under some binary graph operations. We establish tight bounds and determine exact values for their respective hop Italian domination numbers.
{"title":"Hop Italian Domination in Graphs","authors":"Sergio Canoy Jr, Ferdinand Jamil, Sheila Menchavez","doi":"10.29020/nybg.ejpam.v16i4.4914","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4914","url":null,"abstract":"Given a simple graph $G=(V(G),E(G))$, a function $f:V(G)to {0,1,2}$ is a hop Italian dominating function if for every vertex $v$ with $f(v)=0$ there exists a vertex $u$ with $f(u)=2$ for which $u$ and $v$ are of distance $2$ from each other or there exist two vertices $w$ and $z$ for which $f(w)=1=f(z)$ and each of $w$ and $z$ is of distance $2$ from $v$. The minimum weight $sum_{vin V(G)}f(v)$ of a hop Italian dominating function is the hop Italian domination number of $G$, and is denoted by $gamma_{hI}(G)$. In this paper, we initiate the study of the hop Italian domination. In particular, we establish some properties of the the hop Italian dominating function and explore the relationships of the hop Italian domination number with the hop Roman domination number cite{Rad2,Natarajan} and with the $2$-hop domination number cite{Canoy}. We study the concept under some binary graph operations. We establish tight bounds and determine exact values for their respective hop Italian domination numbers.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069138","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4924
Hamed Ouédraogo, Abdoulaye Dembega, André Conseibo
In this paper we study a class of commutative non associative algebras satisfying a polynomial identity of degree five. We show that under the assumption of the existence of a non-zero idempotent, any commutative algebra verifying such an identity admits a Peirce decomposition. Using this decomposition we proceeded to the study of the derivations and representations of algebras of this class.
{"title":"Derivations and Representations of Commutative Algebras Verifying a Polynomial Identity of Degree Five","authors":"Hamed Ouédraogo, Abdoulaye Dembega, André Conseibo","doi":"10.29020/nybg.ejpam.v16i4.4924","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4924","url":null,"abstract":"In this paper we study a class of commutative non associative algebras satisfying a polynomial identity of degree five. We show that under the assumption of the existence of a non-zero idempotent, any commutative algebra verifying such an identity admits a Peirce decomposition. Using this decomposition we proceeded to the study of the derivations and representations of algebras of this class.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069307","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}
In this paper, we introduce one interesting mathematical tool namely, (s, v)*-dense, and analyze its nature in a bigeneralized topological space. Further, we prove some properties of this set and give the relationship between (s, v)-dense and (s, v)*-dense sets. Finally, we give some applications for various sets defined in a bigeneralized topological space.
{"title":"On Dense Sets","authors":"None Diaa Elgezouli, None Mutaz Omer, Yasser Farhat, None Elmhadi Afif, Vadakasi Subramanian","doi":"10.29020/nybg.ejpam.v16i4.4944","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4944","url":null,"abstract":"In this paper, we introduce one interesting mathematical tool namely, (s, v)*-dense, and analyze its nature in a bigeneralized topological space. Further, we prove some properties of this set and give the relationship between (s, v)-dense and (s, v)*-dense sets. Finally, we give some applications for various sets defined in a bigeneralized topological space.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068825","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4883
Javier Hassan, Jeffrey Imer Salim
Let G be a graph. A subset D = {d1, d2, · · · , dm} of vertices of G is called a J-set ifNG[di] NG[dj ] ̸= ∅ for every i ̸= j, where i, j ∈ {1, 2, . . . , m}. A J-set is called a J-dominatingset of G if D = {d1, d2, . . . , dm} is a dominating set of G. The J-domination number of G, denotedby γJ (G), is the maximum cardinality of a J-dominating set of G. In this paper, we introducethis new concept and we establish formulas and properties on some classes of graphs and in joinof two graphs. Upper and lower bounds of J-domination parameter with respect to the order of agraph and other parameters in graph theory are obtained. In addition, we present realization resultinvolving this parameter and the standard domination. Moreover, we characterize J-dominatingsets in some classes of graphs and join of two graphs and finally determine the exact value of theparameter of each of these graphs.
{"title":"J-Domination in Graphs","authors":"Javier Hassan, Jeffrey Imer Salim","doi":"10.29020/nybg.ejpam.v16i4.4883","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4883","url":null,"abstract":"Let G be a graph. A subset D = {d1, d2, · · · , dm} of vertices of G is called a J-set ifNG[di] NG[dj ] ̸= ∅ for every i ̸= j, where i, j ∈ {1, 2, . . . , m}. A J-set is called a J-dominatingset of G if D = {d1, d2, . . . , dm} is a dominating set of G. The J-domination number of G, denotedby γJ (G), is the maximum cardinality of a J-dominating set of G. In this paper, we introducethis new concept and we establish formulas and properties on some classes of graphs and in joinof two graphs. Upper and lower bounds of J-domination parameter with respect to the order of agraph and other parameters in graph theory are obtained. In addition, we present realization resultinvolving this parameter and the standard domination. Moreover, we characterize J-dominatingsets in some classes of graphs and join of two graphs and finally determine the exact value of theparameter of each of these graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068992","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4972
Ahlam Ahmed Alharbi, Adem Kilicman
The principle objective of this research is to present generalised functions ideas which are: fuzzy generalised continuous, generalized strongly continuous, generalized irresolute, generalized open and closed mapping, and the last part is the homomorphism in fuzzy bitopological spaces. We also study the relationships between them, their characteristics, their composition, and some important theories and counterexamples.
{"title":"Generalized Different Types of Mappings in Fuzzy Bitopological Spaces","authors":"Ahlam Ahmed Alharbi, Adem Kilicman","doi":"10.29020/nybg.ejpam.v16i4.4972","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4972","url":null,"abstract":"The principle objective of this research is to present generalised functions ideas which are: fuzzy generalised continuous, generalized strongly continuous, generalized irresolute, generalized open and closed mapping, and the last part is the homomorphism in fuzzy bitopological spaces. We also study the relationships between them, their characteristics, their composition, and some important theories and counterexamples.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069703","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4829
Ayesha Alorini, Aymen Ben Amira, Mohammad Alzohairi, Moncef Bouaziz
A graph G consists of a finite set V (G) of vertices with a collection E(G) of unordered pairs of distinct vertices called edge set of G. Let G be a graph. A set M of vertices is a module of G if, for vertices x and y in M and each vertex z outside M, {z, x} ∈ E(G) ⇐⇒ {z, y} ∈ E(G). Thus, a module of G is a set M of vertices indistinguishable by the vertices outside M. The empty set, the singleton sets and the full set of vertices represent the trivial modules. A graph is indecomposable if all its modules are trivial, otherwise it is decomposable. Indecomposable graphs with at least four vertices are prime graphs. The introduction and the study of the construction of prime graphs obtained from a given decomposable graph by adding one edge constitue the central points of this paper.
{"title":"Prime Graph Generation through Single Edge Addition: Characterizing a Class of Graphs","authors":"Ayesha Alorini, Aymen Ben Amira, Mohammad Alzohairi, Moncef Bouaziz","doi":"10.29020/nybg.ejpam.v16i4.4829","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4829","url":null,"abstract":"A graph G consists of a finite set V (G) of vertices with a collection E(G) of unordered pairs of distinct vertices called edge set of G. Let G be a graph. A set M of vertices is a module of G if, for vertices x and y in M and each vertex z outside M, {z, x} ∈ E(G) ⇐⇒ {z, y} ∈ E(G). Thus, a module of G is a set M of vertices indistinguishable by the vertices outside M. The empty set, the singleton sets and the full set of vertices represent the trivial modules. A graph is indecomposable if all its modules are trivial, otherwise it is decomposable. Indecomposable graphs with at least four vertices are prime graphs. The introduction and the study of the construction of prime graphs obtained from a given decomposable graph by adding one edge constitue the central points of this paper.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136107072","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}
This article presents a mathematical model of the COVID-19 transmission mechanism, considering therapeutic interventions like immunization and recovery or treatment. The model shows that the disease-free and endemic equilibriums are globally asymptotically stable when effective reproduction numbers are less than or larger than unity. The critical vaccination thresholddepends on the vaccine’s ability to prevent or cure the illness. The model predicts the effectiveness of vaccination based on factors like vaccination efficiency, scheduling, and relaxation of social measures. The subsiding of the epidemic as vaccination is implemented depends on the scale of relaxation of social measures.
{"title":"A simulation Model of COVID-19 Epidemic Based on Vaccination and Treatment","authors":"Fahdah Alshammari, Alaa Mustafa, Ehssan Omer, Fatima Omer","doi":"10.29020/nybg.ejpam.v16i4.4805","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4805","url":null,"abstract":"This article presents a mathematical model of the COVID-19 transmission mechanism, considering therapeutic interventions like immunization and recovery or treatment. The model shows that the disease-free and endemic equilibriums are globally asymptotically stable when effective reproduction numbers are less than or larger than unity. The critical vaccination thresholddepends on the vaccine’s ability to prevent or cure the illness. The model predicts the effectiveness of vaccination based on factors like vaccination efficiency, scheduling, and relaxation of social measures. The subsiding of the epidemic as vaccination is implemented depends on the scale of relaxation of social measures.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069134","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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