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On the Diophantine Equation (p+n)^x+p^y=z^2 where p and p+n are Prime Numbers 关于丢番图方程(p+n)^x+p^y=z^2其中p和p+n是素数
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4822
Wachirarak Orosram
{"title":"On the Diophantine Equation (p+n)^x+p^y=z^2 where p and p+n are Prime Numbers","authors":"Wachirarak Orosram","doi":"10.29020/nybg.ejpam.v16i4.4822","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4822","url":null,"abstract":"In this paper, we study the Diophantine equation (p+n)^x+p^y=z^2, where p, p+n are prime numbers and n is a positive integer such that n equiv mod 4. In case p=3 and n=4, Rao{7} showed that the non-negative integer solutions are (x,y,z)=(0,1,2) and (1,2,4) In case p>3 and pequiv 3pmod4, if n-1 is a prime number and 2n-1 is not prime number, then the non-negative integer solution (x, y, z) is (0, 1,sqrt {p+1}) or ( 1, 0, sqrt{p+n+1}). In case pequiv 1pmod4, the non-negative integer solution (x,y,z) is also (0, 1,sqrt {p+1}) or ( 1,0, sqrt{p+n+1}).","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":"136068994","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}
引用次数: 1
$J^2$-Hop Domination in Graphs: Properties and Connections with Other Parameters 图中的$J^2$-Hop支配:与其他参数的性质和联系
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4905
Javier Hassan, Alcyn R. Bakkang, Amil-Shab S. Sappari
{"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":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":"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}
引用次数: 0
The Linear Algebra of (r, β)-Stirling Matrices (r， β)-Stirling矩阵的线性代数
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4854
Genevieve B. Engalan, Mary Joy Latayada
{"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":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":"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}
引用次数: 0
Solutions of Some Quadratic Diophantine Equations 若干二次丢番图方程的解
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4940
Alanoud Sibihi
{"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":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":"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}
引用次数: 0
Crystal Reduced Motif via the Vectors Exchange Theorem I: Impact of Swapping on two Orthogonalization Processes and the AE Algorithm 基于向量交换定理的晶体约简基元I:交换对两个正交化过程的影响及AE算法
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4941
Seddik Abdelalim, Ilias Elmouki
{"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":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":"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}
引用次数: 0
A Comparative Study of Numerical Solution of Second-order Singular Differential Equations Using Bernoulli Wavelet Techniques 使用伯努利小波技术数值求解二阶奇异微分方程的比较研究
IF 0.7
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4916
Kailash Yadav, Ateq Alsaadi
{"title":"A Comparative Study of Numerical Solution of Second-order Singular Differential Equations Using Bernoulli Wavelet Techniques","authors":"Kailash Yadav, Ateq Alsaadi","doi":"10.29020/nybg.ejpam.v16i4.4916","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4916","url":null,"abstract":"The main objective of this article is to discuss a numerical method for solving singular differential equations based on wavelets. Singular differential equations are first transformed into a system of linear algebraic equations, and then the linear system’s solution produces the unknown coefficients. Along with its estimated error, the convergence of the approximative solution is alsodetermined. Some numerical examples are thought to show that Bernoulli wavelet is better than Chebyshev and Legendre wavelet and other existing techniques.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139310106","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}
引用次数: 0
Certified Perfect Domination in Graphs 证明完美支配图
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4894
Jamil Hamja
{"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":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":"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}
引用次数: 0
S-invariant Termwise Addition of Reactions Via Reaction Vector Multiples (STAR-RVM) Transformation 通过反应向量倍数(STAR-RVM)变换的s不变逐项加法
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4859
Daryl Magpantay
{"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":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":"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}
引用次数: 0
Ideals of BCK-algebras and BCI-algebras Based on a New Form of Fuzzy Set 基于模糊集新形式的bck -代数和bci -代数理想
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4933
Eun Hwan Roh, Eunsuk Yang, Young Bae Jun
{"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":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":"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}
引用次数: 0
On controlling, Vibration Performance and Energy Transfer of an Offshore Wind Turbine Tower System via PPF Controller 基于PPF控制器的海上风电塔架系统控制、振动性能及能量传递研究
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4929
Ateq Alsaadi, Yasser Salah Hamed
{"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":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":"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}
引用次数: 0
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