Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4905
Javier Hassan, Alcyn R. Bakkang, Amil-Shab S. Sappari
A subset $T={v_1, v_2, cdots, v_m}$ of vertices of an undirected graph $G$ is called a $J^2$-set if$N_G^2[v_i]setminus N_G^2[v_j]neq varnothing$ for every $ineq j$, where $i,jin{1, 2, ldots, m}$.A $J^2$-set is called a $J^2$-hop dominating in $G$ if for every $ain V(G)s T$, there exists $bin T$ such that $d_G(a,b)=2$. The $J^2$-hop domination number of $G$, denoted by $gamma_{J^2h}(G)$, is the maximum cardinality among all $J^2$-hop dominating sets in $G$. In this paper, we introduce this new parameter and wedetermine its connections with other known parameters in graph theory. We derive its bounds with respect to the order of a graph and other known parameters on a generalized graph, join and corona of two graphs. Moreover,we obtain exact values of the parameter for some special graphs and shadow graphs using the characterization results that are formulated in this study.
{"title":"$J^2$-Hop Domination in Graphs: Properties and Connections with Other Parameters","authors":"Javier Hassan, Alcyn R. Bakkang, Amil-Shab S. Sappari","doi":"10.29020/nybg.ejpam.v16i4.4905","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4905","url":null,"abstract":"A subset $T={v_1, v_2, cdots, v_m}$ of vertices of an undirected graph $G$ is called a $J^2$-set if$N_G^2[v_i]setminus N_G^2[v_j]neq varnothing$ for every $ineq j$, where $i,jin{1, 2, ldots, m}$.A $J^2$-set is called a $J^2$-hop dominating in $G$ if for every $ain V(G)s T$, there exists $bin T$ such that $d_G(a,b)=2$. The $J^2$-hop domination number of $G$, denoted by $gamma_{J^2h}(G)$, is the maximum cardinality among all $J^2$-hop dominating sets in $G$. In this paper, we introduce this new parameter and wedetermine its connections with other known parameters in graph theory. We derive its bounds with respect to the order of a graph and other known parameters on a generalized graph, join and corona of two graphs. Moreover,we obtain exact values of the parameter for some special graphs and shadow graphs using the characterization results that are formulated in this study.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069139","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.v16i4.4854
Genevieve B. Engalan, Mary Joy Latayada
This paper establishes the linear algebra of the $(r, beta)$-Stirling matrix. Along the way, this paper derives various identities, such as its factorization and relationship to the Pascal matrix and the Stirling matrix of the second kind. Additionally, this paper develops a natural extension of the Vandermonde matrix, which can be used to study and evaluate successive power sums of arithmetic progressions.
{"title":"The Linear Algebra of (r, β)-Stirling Matrices","authors":"Genevieve B. Engalan, Mary Joy Latayada","doi":"10.29020/nybg.ejpam.v16i4.4854","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4854","url":null,"abstract":"This paper establishes the linear algebra of the $(r, beta)$-Stirling matrix. Along the way, this paper derives various identities, such as its factorization and relationship to the Pascal matrix and the Stirling matrix of the second kind. Additionally, this paper develops a natural extension of the Vandermonde matrix, which can be used to study and evaluate successive power sums of arithmetic progressions.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"195 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069160","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.v16i4.4940
Alanoud Sibihi
Let $P(t)_i^{pm}=t^{2k} pm i t^m$ be a non square polynomial and $Q(t)_i^{pm}=4k^2t^{4k-2}+i^2m^2t^{2m-2} pm 4imkt^{2k+m-2} -4t^{2k} mp 4it^m -1$ be a polynomial, such that $k geq 2m$ and $i in leftlbrace 1,2 rightrbrace $. In this paper, we consider the number of integer solutions of Diophantine equation $$E : x^2-P(t)_i^{pm}y^2-2P'(t)_i^{pm}x+4 P(t)_i^{pm} y +Q(t)_i^{pm}=0.$$ We extend a previous results given by A. Tekcan and A. Chandoul et al. . We also derive some recurrence relations on the integer solutions of a Pell equation.
设$P(t)_i^{pm}=t^{2k} pm i t^m$为非平方多项式$Q(t)_i^{pm}=4k^2t^{4k-2}+i^2m^2t^{2m-2} pm 4imkt^{2k+m-2} -4t^{2k} mp 4it^m -1$为多项式，使得$k geq 2m$和$i in leftlbrace 1,2 rightrbrace $。本文考虑Diophantine方程$$E : x^2-P(t)_i^{pm}y^2-2P'(t)_i^{pm}x+4 P(t)_i^{pm} y +Q(t)_i^{pm}=0.$$的整数解的个数，推广了a . Tekcan和a . Chandoul等人的结果。我们还推导了一类Pell方程整数解的递推关系。
{"title":"Solutions of Some Quadratic Diophantine Equations","authors":"Alanoud Sibihi","doi":"10.29020/nybg.ejpam.v16i4.4940","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4940","url":null,"abstract":"Let $P(t)_i^{pm}=t^{2k} pm i t^m$ be a non square polynomial and $Q(t)_i^{pm}=4k^2t^{4k-2}+i^2m^2t^{2m-2} pm 4imkt^{2k+m-2} -4t^{2k} mp 4it^m -1$ be a polynomial, such that $k geq 2m$ and $i in leftlbrace 1,2 rightrbrace $. In this paper, we consider the number of integer solutions of Diophantine equation $$E : x^2-P(t)_i^{pm}y^2-2P'(t)_i^{pm}x+4 P(t)_i^{pm} y +Q(t)_i^{pm}=0.$$ We extend a previous results given by A. Tekcan and A. Chandoul et al. . We also derive some recurrence relations on the integer solutions of a Pell equation.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"116 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069541","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.v16i4.4941
Seddik Abdelalim, Ilias Elmouki
Crystallographic literature is relying more on observational rules for the determination of the motif that could generate the whole representing Bravais lattice of a crystal. Here, we devise an algebraic method that can serve in this regard at least in cases when the associated unit cell is made of quasi-orthogonal vectors. To let our approach be applicable to other reduction problems, we introduce a concept which is about starting first from any 'bad' crystal cell, not necessarily the primitive elementary cell, in order to find a 'good' crystal cell and that means seeking a motif made of a basis whose vectors are close-to-orthogonal. The orthogonalization loss could happen any time of vectors swapping which represents a very important process in dealing with lattice reduction, but it has insufficiently been discussed in this subject. Thus, through our present version of vectors exchange theorem, and by using examples of two processes, namely the Gram-Schmidt (GS) procedure and its modified version (MGS), we provide formulations for the new reduced unit cell vectors and analyze the impact of the repeated exchange of vectors on the orthogonalization precision. Finally, we give a detailed explanation to our procedure named as AE algorithm. More interestingly, we show that MGS is not only better than GS because of the classical reason related to numerics, but also because its formulation for the new motif vectors in four conditions, has been preserved in three times rather than two for GS, and this may recommend more the introduction of MGS in a harder problem, namely when the crystal dimension is very big.
{"title":"Crystal Reduced Motif via the Vectors Exchange Theorem I: Impact of Swapping on two Orthogonalization Processes and the AE Algorithm","authors":"Seddik Abdelalim, Ilias Elmouki","doi":"10.29020/nybg.ejpam.v16i4.4941","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4941","url":null,"abstract":"Crystallographic literature is relying more on observational rules for the determination of the motif that could generate the whole representing Bravais lattice of a crystal. Here, we devise an algebraic method that can serve in this regard at least in cases when the associated unit cell is made of quasi-orthogonal vectors. To let our approach be applicable to other reduction problems, we introduce a concept which is about starting first from any 'bad' crystal cell, not necessarily the primitive elementary cell, in order to find a 'good' crystal cell and that means seeking a motif made of a basis whose vectors are close-to-orthogonal. The orthogonalization loss could happen any time of vectors swapping which represents a very important process in dealing with lattice reduction, but it has insufficiently been discussed in this subject. Thus, through our present version of vectors exchange theorem, and by using examples of two processes, namely the Gram-Schmidt (GS) procedure and its modified version (MGS), we provide formulations for the new reduced unit cell vectors and analyze the impact of the repeated exchange of vectors on the orthogonalization precision. Finally, we give a detailed explanation to our procedure named as AE algorithm. More interestingly, we show that MGS is not only better than GS because of the classical reason related to numerics, but also because its formulation for the new motif vectors in four conditions, has been preserved in three times rather than two for GS, and this may recommend more the introduction of MGS in a harder problem, namely when the crystal dimension is very big.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"117 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069704","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.v16i4.4894
Jamil Hamja
Let $ G = (V(G),E(G)) $ be a simple connected graph. A set $ S subseteq V(G) $ is called a certified perfect dominating set of $ G $ if every vertex $ v in V(G)setminus S $ is dominated by exactly one element $ u in S $, such that $ u $ has either zero or at least two neighbors in $ V(G)setminus S $. The minimum cardinality of a certified perfect dominating set of $ G $ is called the textit{certified perfect domination number} of $ G $ and denoted by $ gamma_{cerp}(G) $. A certified perfect dominating set $ S $ of $ G $ with $ lvert S rvert = gamma_{cerp}(G) $ is called a $ gamma_{cerp} $-set. In this paper, the author focuses on several key aspects: a characterization of the certified perfect dominating set, determining the exact values of the certified perfect domination number for specific graphs, and investigating the certified perfect domination number of graphs resulting from the join of two graphs. Furthermore, some relationships between the certified dominating set, the perfect dominating set, and the certified perfect dominating set of a graph $ G $ are established.
设$ G = (V(G),E(G)) $为简单连通图。如果每个顶点$ v in V(G)setminus S $只被一个元素$ u in S $支配，使得$ u $在$ V(G)setminus S $中有0个或至少两个邻居，则集合$ S subseteq V(G) $被称为$ G $的证明完全支配集。$ G $的证明完全支配集的最小基数称为$ G $的textit{证明完全支配数}，用$ gamma_{cerp}(G) $表示。具有$ lvert S rvert = gamma_{cerp}(G) $的$ G $的证明完全支配集$ S $称为$ gamma_{cerp} $ -集。在本文中，作者着重于几个关键方面:证明完美支配集的表征，确定特定图的证明完美支配数的确切值，以及研究由两个图的连接所产生的图的证明完美支配数。进一步，建立了图$ G $的认证完美控制集、认证完美控制集和认证完美控制集之间的关系。
{"title":"Certified Perfect Domination in Graphs","authors":"Jamil Hamja","doi":"10.29020/nybg.ejpam.v16i4.4894","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4894","url":null,"abstract":"Let $ G = (V(G),E(G)) $ be a simple connected graph. A set $ S subseteq V(G) $ is called a certified perfect dominating set of $ G $ if every vertex $ v in V(G)setminus S $ is dominated by exactly one element $ u in S $, such that $ u $ has either zero or at least two neighbors in $ V(G)setminus S $. The minimum cardinality of a certified perfect dominating set of $ G $ is called the textit{certified perfect domination number} of $ G $ and denoted by $ gamma_{cerp}(G) $. A certified perfect dominating set $ S $ of $ G $ with $ lvert S rvert = gamma_{cerp}(G) $ is called a $ gamma_{cerp} $-set. In this paper, the author focuses on several key aspects: a characterization of the certified perfect dominating set, determining the exact values of the certified perfect domination number for specific graphs, and investigating the certified perfect domination number of graphs resulting from the join of two graphs. Furthermore, some relationships between the certified dominating set, the perfect dominating set, and the certified perfect dominating set of a graph $ G $ are established.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068847","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.v16i4.4859
Daryl Magpantay
Interest in connecting Chemical Reactions Network Theory (CRNT) and evolutionary game theory (EGT) arise viewing the tools of network in the analysis of evolutionary games. Here, the evolution of population species is studied as a biological phenomenon and describing the rate of such changes through a replicator system becomes a focus. A set of polynomial kinetics (POK) may then be introduced for the realization of this replicator system and this is based on the polynomial payoff functions defined in the game. These polynomial kinetics result in polynomial dynamical systems of ordinary differential equations, which are used in analyzing strategies that prove beneficial under certain conditions. From the CRNT point of view, it now becomes interesting to study a superset of POK, which we call poly-PL kinetics (PYK). This set is formed by getting nonnegative linear combinations of power law functions. Thus, PYK contains the set PLK of power law kinetics as mono-PL kinetics with coefficient 1. Seeing this connection between CRNT and EGT and what are known about power law kinetics, we take an interest in studying PYK systems. This paper aims to analyze different ways of transforming PYK to PLK in order to explore some approaches for CRNT analysis of PYK systems. Specifically, we study a network structure-oriented transformations using the S-invariant term-wise addition of reactions (STAR) Via Reaction Vector Multiples (RVM) that transform PYK to PLK systems.
{"title":"S-invariant Termwise Addition of Reactions Via Reaction Vector Multiples (STAR-RVM) Transformation","authors":"Daryl Magpantay","doi":"10.29020/nybg.ejpam.v16i4.4859","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4859","url":null,"abstract":"Interest in connecting Chemical Reactions Network Theory (CRNT) and evolutionary game theory (EGT) arise viewing the tools of network in the analysis of evolutionary games. Here, the evolution of population species is studied as a biological phenomenon and describing the rate of such changes through a replicator system becomes a focus. A set of polynomial kinetics (POK) may then be introduced for the realization of this replicator system and this is based on the polynomial payoff functions defined in the game. These polynomial kinetics result in polynomial dynamical systems of ordinary differential equations, which are used in analyzing strategies that prove beneficial under certain conditions. From the CRNT point of view, it now becomes interesting to study a superset of POK, which we call poly-PL kinetics (PYK). This set is formed by getting nonnegative linear combinations of power law functions. Thus, PYK contains the set PLK of power law kinetics as mono-PL kinetics with coefficient 1. Seeing this connection between CRNT and EGT and what are known about power law kinetics, we take an interest in studying PYK systems. This paper aims to analyze different ways of transforming PYK to PLK in order to explore some approaches for CRNT analysis of PYK systems. Specifically, we study a network structure-oriented transformations using the S-invariant term-wise addition of reactions (STAR) Via Reaction Vector Multiples (RVM) that transform PYK to PLK systems.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069145","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.v16i4.4933
Eun Hwan Roh, Eunsuk Yang, Young Bae Jun
Ideals in BCK/BCI algebra based on $Y_J^{varepsilon}$-fuzzy sets are studied. The fundamental properties of the level set of $Y_J^{varepsilon}$-fuzzy sets are investigate first. The concept of (closed) $Y_J^{varepsilon}$-fuzzy ideals in BCK/BCI-algebras is introduces, and several properties are investigated. The relationship between $Y_J^{varepsilon}$-fuzzy ideal and $Y_J^{varepsilon}$-fuzzy subalgebra are discussed, and also the relationship between $Y_J^{varepsilon}$-fuzzy ideal and fuzzy ideal is identified. The characterization of (closed) $Y_J^{varepsilon}$-fuzzy ideal using the Y-level set is established. The necessary and sufficient conditions for $Y_J^{varepsilon}$-fuzzy ideal to be closed is explored, and conditions for $Y_J^{varepsilon}$-fuzzy subalgebra to be $Y_J^{varepsilon}$-fuzzy ideal are provided.
{"title":"Ideals of BCK-algebras and BCI-algebras Based on a New Form of Fuzzy Set","authors":"Eun Hwan Roh, Eunsuk Yang, Young Bae Jun","doi":"10.29020/nybg.ejpam.v16i4.4933","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4933","url":null,"abstract":"Ideals in BCK/BCI algebra based on $Y_J^{varepsilon}$-fuzzy sets are studied. The fundamental properties of the level set of $Y_J^{varepsilon}$-fuzzy sets are investigate first. The concept of (closed) $Y_J^{varepsilon}$-fuzzy ideals in BCK/BCI-algebras is introduces, and several properties are investigated. The relationship between $Y_J^{varepsilon}$-fuzzy ideal and $Y_J^{varepsilon}$-fuzzy subalgebra are discussed, and also the relationship between $Y_J^{varepsilon}$-fuzzy ideal and fuzzy ideal is identified. The characterization of (closed) $Y_J^{varepsilon}$-fuzzy ideal using the Y-level set is established. The necessary and sufficient conditions for $Y_J^{varepsilon}$-fuzzy ideal to be closed is explored, and conditions for $Y_J^{varepsilon}$-fuzzy subalgebra to be $Y_J^{varepsilon}$-fuzzy ideal are provided.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"41 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069446","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.v16i4.4929
Ateq Alsaadi, Yasser Salah Hamed
In this paper, we focus on the control, energy transfer, and vibration performance under multi mixed excitations for the offshore wind turbine tower (OWTT) system. For reducing the controlled system oscillations, the positive position feedback (PPF) controller is applied. The energy transfers occur in the system of wind turbine by adding the PPF controller to the system equations. With the help of the phase plane approach, frequency response equations, and Poincare maps, the bifurcation and stability at worst resonance cases are sought and investigated. The vibration behaviors are studied numerically at different parameters values for the wind turbine system. Additionally, the response and numerical outcomes are examined, also, the approach of multiple scales is used to establish the approximate solutions of the wind turbine-controlled system. Besides that, MAPLE and MATLAB algorithms are used to implement the numerical results and compare analytical solutions with numerical behavior. The results also be compared to previous research that has been published.
{"title":"On controlling, Vibration Performance and Energy Transfer of an Offshore Wind Turbine Tower System via PPF Controller","authors":"Ateq Alsaadi, Yasser Salah Hamed","doi":"10.29020/nybg.ejpam.v16i4.4929","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4929","url":null,"abstract":"In this paper, we focus on the control, energy transfer, and vibration performance under multi mixed excitations for the offshore wind turbine tower (OWTT) system. For reducing the controlled system oscillations, the positive position feedback (PPF) controller is applied. The energy transfers occur in the system of wind turbine by adding the PPF controller to the system equations. With the help of the phase plane approach, frequency response equations, and Poincare maps, the bifurcation and stability at worst resonance cases are sought and investigated. The vibration behaviors are studied numerically at different parameters values for the wind turbine system. Additionally, the response and numerical outcomes are examined, also, the approach of multiple scales is used to establish the approximate solutions of the wind turbine-controlled system. Besides that, MAPLE and MATLAB algorithms are used to implement the numerical results and compare analytical solutions with numerical behavior. The results also be compared to previous research that has been published.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"8 18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069694","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}
Over the past decade, exponential Diophantine equations of the form ax + by = wn have been studied as if they were a phenomenon. In particular, numerous articles have focused on the cases where n = 2 or n = 4 and 2 ≤ a, b ≤ 200. However, these articles are primarily concerned with determining whether the left-hand side of the equation needs to consist of more than twoexponentials. Therefore, in this article, we investigate the exponential Diophantine equation in the form ax + by + cz = w2, using only elementary tools related to modulo concepts. We present three theorems in which the variables a, b and c vary under certain conditions, and three additional theorems where the variable c is fixed at 7. Furthermore, if we restrict our parameters a, b and cto 2 ≤ a ≤ b ≤ c ≤ 20, then 1,330 equations have been considered. Our results confirm that 135 of these equations have been fully clarified.
在过去的十年里，人们研究了ax + by = wn形式的指数丢番图方程，好像它们是一种现象。特别是，许多文章都关注于n = 2或n = 4且2≤a, b≤200的情况。然而，这些文章主要关注的是确定方程的左边是否需要由两个以上的指数组成。因此，在本文中，我们只使用与模概念相关的基本工具，研究ax + by + cz = w2形式的指数丢芬图方程。我们给出了变量a, b和c在一定条件下变化的三个定理，以及变量c固定为7的另外三个定理。进一步，如果我们将参数a、b和c限制为2≤a≤b≤c≤20，则考虑了1330个方程。我们的结果证实，其中135个方程已经完全澄清。
{"title":"On the Diophantine Equations $a^x+b^y+c^z=w^2$","authors":"Kittipong Laipaporn, Saowapak Kaewchay, Adisak Karnbanjong","doi":"10.29020/nybg.ejpam.v16i4.4936","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4936","url":null,"abstract":"Over the past decade, exponential Diophantine equations of the form ax + by = wn have been studied as if they were a phenomenon. In particular, numerous articles have focused on the cases where n = 2 or n = 4 and 2 ≤ a, b ≤ 200. However, these articles are primarily concerned with determining whether the left-hand side of the equation needs to consist of more than twoexponentials. Therefore, in this article, we investigate the exponential Diophantine equation in the form ax + by + cz = w2, using only elementary tools related to modulo concepts. We present three theorems in which the variables a, b and c vary under certain conditions, and three additional theorems where the variable c is fixed at 7. Furthermore, if we restrict our parameters a, b and cto 2 ≤ a ≤ b ≤ c ≤ 20, then 1,330 equations have been considered. Our results confirm that 135 of these equations have been fully clarified.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"16 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068665","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.v16i4.4945
Alanoud Almutairi
This paper presents a study on the oscillatory behavior of solutions to even-order neutral differential equations involving p-Laplacian-like operator. We obtain oscillation criteria using techniques from first-order delay differential equations, Riccati technique and integral averages technique. The results of this work contribute to a deeper understanding of even-order differential equations and their connections to various branches of mathematics and practical sciences. The findings emphasize the importance of continued research in this area.
{"title":"Oscillatory Properties Test for Even-Order Di§erential Equations of Neutral type","authors":"Alanoud Almutairi","doi":"10.29020/nybg.ejpam.v16i4.4945","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4945","url":null,"abstract":"This paper presents a study on the oscillatory behavior of solutions to even-order neutral differential equations involving p-Laplacian-like operator. We obtain oscillation criteria using techniques from first-order delay differential equations, Riccati technique and integral averages technique. The results of this work contribute to a deeper understanding of even-order differential equations and their connections to various branches of mathematics and practical sciences. The findings emphasize the importance of continued research in this area.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068668","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：