Pub Date : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4780
Sara Zeidani, B. Asady, Mohsen Rostamy Malkhalifeh, T. Lotfi
The artificial bee colony algorithm is one of the population-based optimization methods inspired by the evolutionary principles of the social behavior of bees. On the other hand, one of the sub-fields of operations research science is data envelopment analysis. There are some difficulties in DEA models for selecting the appropriate numerical value for an infinitesimal non-Archimedean epsilon. So far, various methods have been proposed to solve this problem and choose the suitable non-Archimedean epsilon. In order to solve the problem, the artificial bee colony algorithm (ABC), and modification of the original ABC algorithm (MABC) are adopted and proposed in this paper. The impacts of our proposed algorithms on the suitable non-Archimedean epsilon by solving only one linear programming (LP), instead of n LP are investigated. Finally, the performance of the proposed algorithms is evaluated by comparing the solutions obtained from GAMS software based on the presented examples.
{"title":"Using the Modified Artificial Bee Colony Algorithm to Find the Non-Archimedean Epsilon for Evaluating the Efficiency in DEA","authors":"Sara Zeidani, B. Asady, Mohsen Rostamy Malkhalifeh, T. Lotfi","doi":"10.29020/nybg.ejpam.v16i3.4780","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4780","url":null,"abstract":"The artificial bee colony algorithm is one of the population-based optimization methods inspired by the evolutionary principles of the social behavior of bees. On the other hand, one of the sub-fields of operations research science is data envelopment analysis. There are some difficulties in DEA models for selecting the appropriate numerical value for an infinitesimal non-Archimedean epsilon. So far, various methods have been proposed to solve this problem and choose the suitable non-Archimedean epsilon. In order to solve the problem, the artificial bee colony algorithm (ABC), and modification of the original ABC algorithm (MABC) are adopted and proposed in this paper. The impacts of our proposed algorithms on the suitable non-Archimedean epsilon by solving only one linear programming (LP), instead of n LP are investigated. Finally, the performance of the proposed algorithms is evaluated by comparing the solutions obtained from GAMS software based on the presented examples.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41367886","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4815
Devendra Kumar
Let $F$ be a real valued generalized biaxisymmetric potential (GBASP) in $L^{beta}$ on $S_{R}$, the open sphere of radius $R$ about the origin. In this paper we have obtained the necessary and sufficient conditions on the rate of decrease of a sequence of best harmonic polynomial approximates to $F$ such that $F$ is harmonically continues as an entire function GBASP and determine their $(p,q)$-order and generalized $(p,q)$-type with respect to proximate order $rho(r)$.
{"title":"Approximation of Generalized Biaxisymmetric Potentials in $L^{beta}$-norm","authors":"Devendra Kumar","doi":"10.29020/nybg.ejpam.v16i3.4815","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4815","url":null,"abstract":"Let $F$ be a real valued generalized biaxisymmetric potential (GBASP) in $L^{beta}$ on $S_{R}$, the open sphere of radius $R$ about the origin. In this paper we have obtained the necessary and sufficient conditions on the rate of decrease of a sequence of best harmonic polynomial approximates to $F$ such that $F$ is harmonically continues as an entire function GBASP and determine their $(p,q)$-order and generalized $(p,q)$-type with respect to proximate order $rho(r)$.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42263473","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4848
Farene Loida Alfeche, Victor Barraza, Sergio R. Canoy
In this paper, we revisit the concept of (normalized) closeness centrality of a vertex in a graph and investigate it in some graphs under some operations. Specifically, we derive formulas that compute the closeness centrality of vertices in the shadow graph, complementary prism, edge corona, and disjunction of graphs.
{"title":"Closeness Centrality of Vertices in Graphs Under Some Operations","authors":"Farene Loida Alfeche, Victor Barraza, Sergio R. Canoy","doi":"10.29020/nybg.ejpam.v16i3.4848","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4848","url":null,"abstract":"In this paper, we revisit the concept of (normalized) closeness centrality of a vertex in a graph and investigate it in some graphs under some operations. Specifically, we derive formulas that compute the closeness centrality of vertices in the shadow graph, complementary prism, edge corona, and disjunction of graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46149309","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4737
Chawalit Boonpok, Montri Thongmoon
This paper is concerned with the concepts of some topological spaces. Firstly, we introduce the notions of δs(Λ, p)-open sets. Some properties concerning δs(Λ, p)-open sets are discussed. Secondly, the concept of s(Λ, p)-connected spaces is introduced. Moreover, we give several characterizations of s(Λ, p)-connected spaces by utilizing δs(Λ, p)-open sets. Thirdly, we apply the notion of s(Λ, p)-open sets to present and study new classes of spaces called s(Λ, p)-regular spaces and s(Λ, p)-normal spaces. Especially, some characterizations of s(Λ, p)-regular spaces and s(Λ, p)-normal spaces are established. Fourthly, we introduce and investigate the concepts of s(Λ, p)-T2 spaces and s(Λ, p)-Urysohn spaces. Finally, the notion of S(Λ, p)-closed spaces is studied. Basic properties and characterizations of S(Λ, p)-closed spaces are considered.
{"title":"Characterizations of Some Topological Spaces","authors":"Chawalit Boonpok, Montri Thongmoon","doi":"10.29020/nybg.ejpam.v16i3.4737","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4737","url":null,"abstract":"This paper is concerned with the concepts of some topological spaces. Firstly, we introduce the notions of δs(Λ, p)-open sets. Some properties concerning δs(Λ, p)-open sets are discussed. Secondly, the concept of s(Λ, p)-connected spaces is introduced. Moreover, we give several characterizations of s(Λ, p)-connected spaces by utilizing δs(Λ, p)-open sets. Thirdly, we apply the notion of s(Λ, p)-open sets to present and study new classes of spaces called s(Λ, p)-regular spaces and s(Λ, p)-normal spaces. Especially, some characterizations of s(Λ, p)-regular spaces and s(Λ, p)-normal spaces are established. Fourthly, we introduce and investigate the concepts of s(Λ, p)-T2 spaces and s(Λ, p)-Urysohn spaces. Finally, the notion of S(Λ, p)-closed spaces is studied. Basic properties and characterizations of S(Λ, p)-closed spaces are considered.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135359754","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4841
Joel G. Adanza
In this paper, we investigate some properties of B-commutators of B-algebras. We also characterize solvable B-algebras via B-commutators.
本文研究了b -代数的b对易子的一些性质。我们还通过b -对易子描述了可解b代数。
{"title":"On B-commutators of B-algebras","authors":"Joel G. Adanza","doi":"10.29020/nybg.ejpam.v16i3.4841","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4841","url":null,"abstract":"In this paper, we investigate some properties of B-commutators of B-algebras. We also characterize solvable B-algebras via B-commutators.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43885831","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4684
Javier Hassan, Abdurajan B. Lintasan, N. H. M. Mohammad
In this paper, we construct a realization problems involving connected outer-hop independent hop domination and we determine its connections with other known parameters in graph theory. In particular, given two positive integers a and b with 2 ≤ a ≤ b are realizable as the connected hop domination, connected outer-hop independent hop domination, and connected outer-independent hop domination numbers, respectively, of a connected graph. In addition, we characterize the connected outer-hop independent hop dominating sets in some families of graphs, join and corona of two graphs, and we use these results to derive formulas for the parameters of these graphs.
{"title":"Some Properties and Realization Problems Involving Connected Outer-hop Independent Hop Domination in Graphs","authors":"Javier Hassan, Abdurajan B. Lintasan, N. H. M. Mohammad","doi":"10.29020/nybg.ejpam.v16i3.4684","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4684","url":null,"abstract":"In this paper, we construct a realization problems involving connected outer-hop independent hop domination and we determine its connections with other known parameters in graph theory. In particular, given two positive integers a and b with 2 ≤ a ≤ b are realizable as the connected hop domination, connected outer-hop independent hop domination, and connected outer-independent hop domination numbers, respectively, of a connected graph. In addition, we characterize the connected outer-hop independent hop dominating sets in some families of graphs, join and corona of two graphs, and we use these results to derive formulas for the parameters of these graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45431444","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4857
Maysoon M. Aziz, Ghassan. E. Arif, Ahmad T. Ahmad
In this paper a new Rabinovitch-Fabrikant (R-F) four dimensional (4D) continuous time dynamical system was generated from three dimensional (3D) Rabinovitch-Fabrikant dynamical system using the state augmentation technique by adding new state variables u. The system employs thirteen terms includes five cross-product terms and one irreversible function. The dynamical behaviors of the system were investigated which include equilibrium points, stability analysis, wave form analysis, phase space analysis, multistability, Hopf-bifurcation, the Lyapunov exponent and Lyapunov dimension. The values of Lyapunov exponents are:L1 = 14.025946, L2 = 0.295151, L3 = −2.854401, L4 = −13.736833. and Lyapunov dimension is (3.83474), so the system is unstable and hyperchaotic with coexistence attractors. Chaos was handled in two ways: adaptive control and adaptive synchronization, it was found that the new system is stable and achieved good results.
{"title":"Analysis of Novel 4D Rabinovich-Fabrikant Continuous Dynamical System with Coexistence Attractors","authors":"Maysoon M. Aziz, Ghassan. E. Arif, Ahmad T. Ahmad","doi":"10.29020/nybg.ejpam.v16i3.4857","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4857","url":null,"abstract":"In this paper a new Rabinovitch-Fabrikant (R-F) four dimensional (4D) continuous time dynamical system was generated from three dimensional (3D) Rabinovitch-Fabrikant dynamical system using the state augmentation technique by adding new state variables u. The system employs thirteen terms includes five cross-product terms and one irreversible function. The dynamical behaviors of the system were investigated which include equilibrium points, stability analysis, wave form analysis, phase space analysis, multistability, Hopf-bifurcation, the Lyapunov exponent and Lyapunov dimension. The values of Lyapunov exponents are:L1 = 14.025946, L2 = 0.295151, L3 = −2.854401, L4 = −13.736833. and Lyapunov dimension is (3.83474), so the system is unstable and hyperchaotic with coexistence attractors. Chaos was handled in two ways: adaptive control and adaptive synchronization, it was found that the new system is stable and achieved good results.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44426217","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4821
Gymaima Canete, Helen M. Rara, Angelica Mae Mahistrado
Let $G$ be an undirected graph with vertex-set $V(G)$ and edge-set $E(G)$, respectively. A set $Ssubseteq V(G)$ is a $2$-locating set of $G$ if $big|[big(N_G(x)backslash N_G(y)big)cap S] cup [big(N_G(y)backslash N_G(x)big)cap S]big|geq 2$, for all linebreak $x,yin V(G)backslash S$ with $xneq y$, and for all $vin S$ and $win V(G)backslash S$, $big(N_G(v)backslash N_G(w)big)cap S neq varnothing$ or $big(N_G(w)backslash N_G[v]big) cap Sneq varnothing$. In this paper, we investigate the concept and study 2-locating sets in graphs resulting from some binary operations. Specifically, we characterize the 2-locating sets in the join, corona, edge corona and lexicographic product of graphs, and determine bounds or exact values of the 2-locating number of each of these graphs.
{"title":"2-Locating Sets in a Graph","authors":"Gymaima Canete, Helen M. Rara, Angelica Mae Mahistrado","doi":"10.29020/nybg.ejpam.v16i3.4821","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4821","url":null,"abstract":"Let $G$ be an undirected graph with vertex-set $V(G)$ and edge-set $E(G)$, respectively. A set $Ssubseteq V(G)$ is a $2$-locating set of $G$ if $big|[big(N_G(x)backslash N_G(y)big)cap S] cup [big(N_G(y)backslash N_G(x)big)cap S]big|geq 2$, for all linebreak $x,yin V(G)backslash S$ with $xneq y$, and for all $vin S$ and $win V(G)backslash S$, $big(N_G(v)backslash N_G(w)big)cap S neq varnothing$ or $big(N_G(w)backslash N_G[v]big) cap Sneq varnothing$. In this paper, we investigate the concept and study 2-locating sets in graphs resulting from some binary operations. Specifically, we characterize the 2-locating sets in the join, corona, edge corona and lexicographic product of graphs, and determine bounds or exact values of the 2-locating number of each of these graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49170314","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4794
W. Al-Hayani, Mahasin Thabet Younis
To obtain approximate-exact solutions to nonlocal initial-boundary value problems (IBVPs) of linear and nonlinear parabolic and hyperbolic partial differential equations (PDEs) subject to initial and nonlocal boundary conditions of integral type, the homotopy perturbation method (HPM) is utilized in this study. The HPM is used to solve the specified nonlocal IBVPs, which are then transformed into local Dirichlet IBVPs. Some examples demonstrate how accurate and efficient the HPM.
{"title":"The Homotopy Perturbation Method for Solving Nonlocal Initial-Boundary Value Problems for Parabolic and Hyperbolic Partial Differential Equations","authors":"W. Al-Hayani, Mahasin Thabet Younis","doi":"10.29020/nybg.ejpam.v16i3.4794","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4794","url":null,"abstract":"To obtain approximate-exact solutions to nonlocal initial-boundary value problems (IBVPs) of linear and nonlinear parabolic and hyperbolic partial differential equations (PDEs) subject to initial and nonlocal boundary conditions of integral type, the homotopy perturbation method (HPM) is utilized in this study. The HPM is used to solve the specified nonlocal IBVPs, which are then transformed into local Dirichlet IBVPs. Some examples demonstrate how accurate and efficient the HPM. \u0000 ","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43033286","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4863
Teresa L. Tacbobo
This paper presents a way to represent a group using a graph, which involves the concept of a generator element of a group. The graph representing a group is called the generator graph. In the generator graph, the vertices correspond to the elements of the group, and two vertices, x and y, are connected by an edge if either x or y serves as a generator for the group. The paper investigates some properties of these generator graphs and obtains the generator graphs for specific groups. Additionally, it explores the relationship between the generator graph of a group and the generating graph introduced by Lucchini et al. in their work [7].
{"title":"The Generator Graph of a Group","authors":"Teresa L. Tacbobo","doi":"10.29020/nybg.ejpam.v16i3.4863","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4863","url":null,"abstract":"This paper presents a way to represent a group using a graph, which involves the concept of a generator element of a group. The graph representing a group is called the generator graph. In the generator graph, the vertices correspond to the elements of the group, and two vertices, x and y, are connected by an edge if either x or y serves as a generator for the group. The paper investigates some properties of these generator graphs and obtains the generator graphs for specific groups. Additionally, it explores the relationship between the generator graph of a group and the generating graph introduced by Lucchini et al. in their work [7].","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41870248","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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