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On the Diophantine Equations $a^x+b^y+c^z=w^2$ 丢番图方程a^x+b^y+c^z=w^2
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4936
Kittipong Laipaporn, Saowapak Kaewchay, Adisak Karnbanjong
{"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":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":"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}
引用次数: 0
Oscillatory Properties Test for Even-Order Di§erential Equations of Neutral type 中性型偶阶Di§迭代方程的振荡性质检验
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4945
Alanoud Almutairi
{"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":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":"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}
引用次数: 0
Integral Resonant Controller for Suppressing Car’s Oscillations and Eliminating its Inherent Jump Phenomenon 抑制汽车振动和消除汽车固有跳变现象的积分谐振控制器
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4930
Ali Kandil, Y. S. Hamed
{"title":"Integral Resonant Controller for Suppressing Car’s Oscillations and Eliminating its Inherent Jump Phenomenon","authors":"Ali Kandil, Y. S. Hamed","doi":"10.29020/nybg.ejpam.v16i4.4930","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4930","url":null,"abstract":"This work deals with modeling and controlling the oscillations of a horizontally-supported car under the effect of a nonlinear spring, a damper, and a harmonic excitation external force. The proposed controller is the integral resonant controller (IRC) which is a first order oscillator coupled the car via a linear variable differential transformer (LVDT) and a servo-controlled linear actuator(SCLA). The multiple scales perturbation method is used to obtain an approximate solution and stability analyses are carried out. Based on the stability analysis, the optimum values of the controller parameters are recommended in this work for a better control operation. Several response curves are plotted for clarifying the concept of the proposed integral resonant control algorithm.A numerical simulation of the car’s motion is achieved by numerically integrating the model equations with the 4th order Rung-Kutta algorithm. The applied controller can treat the severe jumps in the oscillation amplitude where it is suppressed at different conditions of forward and backward sweeping of the amplitude and frequency of the external excitation force.","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":"136068698","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
Analytical Solution of Vertically Integrated Equations of a Confined Aquifer in two-dimension using Finite Volume method 用有限体积法解析求解二维承压含水层垂直积分方程
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4922
Cordy Jourvel Itoua-Tsele, Antoine Filankembo Ouassissou
{"title":"Analytical Solution of Vertically Integrated Equations of a Confined Aquifer in two-dimension using Finite Volume method","authors":"Cordy Jourvel Itoua-Tsele, Antoine Filankembo Ouassissou","doi":"10.29020/nybg.ejpam.v16i4.4922","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4922","url":null,"abstract":"Groundwater plays an important role in feeding many families and societies whose access to water is a huge problem for several reasons, then the mathematical model is an essential part of a hydrologist’s daily life to understand the physical phenomena. In this paper, we used Dupuit’s assumption to reduce the groundwater flow equation and integrated vertically it to obtainthe diffusivity equation in terms of the hydraulic head, further, the introduction of fundamental ideas in groundwater research, including vocabulary and mathematics will give readers the basis knowledge. Numerous numerical techniques can be recognized, the unstructured finite volume method was used to solve a transient diffusivity equation through a coastal confined aquifer. Theconstructed finite volume schemes are used to study the distribution of hydraulic heads in the model domain, to determine water table fluctuations, and to predict the drawdown phenomena.","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":"136068828","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
Upper and Lower weak $sbeta(star)$-continuity 上下弱$sbeta(star)$-连续性
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4734
Chawalit Boonpok, Jeeranunt Khampakdee
{"title":"Upper and Lower weak $sbeta(star)$-continuity","authors":"Chawalit Boonpok, Jeeranunt Khampakdee","doi":"10.29020/nybg.ejpam.v16i4.4734","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4734","url":null,"abstract":"This paper is concerned with the concepts of upper and lower weakly sβ(⋆)-continuous multifunctions. Moreover, some characterizations of upper and lower weakly sβ(⋆)-continuous multifunctions are investigated.","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":"136068852","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
Grundy Total Hop Dominating Sequences in Graphs 图中的Grundy全跳支配序列
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4877
Javier Hassan, Sergio R. Canoy, Jr.
{"title":"Grundy Total Hop Dominating Sequences in Graphs","authors":"Javier Hassan, Sergio R. Canoy, Jr.","doi":"10.29020/nybg.ejpam.v16i4.4877","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4877","url":null,"abstract":"Let G = (V (G), E(G)) be an undirected graph with γ(C) ̸= 1 for each component C of G. Let S = (v1, v2, · · · , vk) be a sequence of distint vertices of a graph G, and let Sˆ ={v1, v2, . . . , vk}. Then S is a legal open hop neighborhood sequence if N2G(vi) Si−1j=1 N2G(vj ) ̸= ∅for every i ∈ {2, . . . , k}. If, in addition, Sˆ is a total hop dominating set of G, then S is a Grundy total hop dominating sequence. The maximum length of a Grundy total hop dominating sequence in a graph G, denoted by γth gr(G), is the Grundy total hop domination number of G. In this paper, we show that the Grundy total hop domination number of a graph G is between the total hop domination number and twice the Grundy hop domination number of G. Moreover, determine values or bounds of the Grundy total hop domination number of some 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":"136068990","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 the Number of Restricted One-to-One and Onto Functons Having Integral Coordinates 关于具有积分坐标的受限1 - 1和映上函数的个数
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4901
Mary Joy R. Latayada
{"title":"On the Number of Restricted One-to-One and Onto Functons Having Integral Coordinates","authors":"Mary Joy R. Latayada","doi":"10.29020/nybg.ejpam.v16i4.4901","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4901","url":null,"abstract":"Let $N_m$ be the set of positive integers $1, 2, cdots, m$ and $S subseteq N_m$. In 2000, J. Caumeran and R. Corcino made a thorough investigation on counting restricted functions $f_{|S}$ under each of the following conditions:begin{itemize}item[(textit{a})]$f(a) leq a$, $forall a in S$;item[(textit{b})] $f(a) leq g(a)$, $forall a in S$ where $g$ is any nonnegative real-valued continuous functions;item[(textit{c})] $g_1(a) leq f(a) leq g_2(a)$, $forall a in S$, where $g_1$ and $g_2$ are any nonnegative real-valued continuous functions.end{itemize}Several formulae and identities were also obtained by Caumeran using basic concepts in combinatorics.In this paper, we count those restricted functions under condition $f(a) leq a$, $forall a in S$, which is one-to-one and onto, and establish some formulas and identities parallel to those obtained by J. Caumeran and R. Corcino.","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":"136068996","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
Global Existence of Weak Solutions to 3D Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosity 具有退化黏度的大气动力学三维可压缩原始方程弱解的整体存在性
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4931
Jules Ouya, Arouna Ouedraogo
{"title":"Global Existence of Weak Solutions to 3D Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosity","authors":"Jules Ouya, Arouna Ouedraogo","doi":"10.29020/nybg.ejpam.v16i4.4931","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4931","url":null,"abstract":"In this work, we show the existence of global weak solutions to the three-dimensional compressible primitive equations of atmospheric dynamics with degenerate viscosity density-dependent for large initial data. With a pressure law of the form ρ2, we represent the vertical velocity as a function of the density and the horizontal one which will be important in using Faedo-Galerkin method to obtain the global existence of the approximate solutions. In analogy with the cases in [28] and [26, 27], we prove that the weak solutions satisfy the basic energy inequality and the Bresch-Desjardins entropy inequality. Based on these estimates and using compactness arguments, we prove the global existence of weak solutions of (1.1) by vanishing the parameters in our approximate system step by step.","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":"136069127","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
Numerical Solutions of Some Classes of Partial Differential Equations of Fractional Order 几类分数阶偏微分方程的数值解
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4928
Iman ALdarawi, Banan Maayah, Eman Aldabbas, Eman Abuteen
{"title":"Numerical Solutions of Some Classes of Partial Differential Equations of Fractional Order","authors":"Iman ALdarawi, Banan Maayah, Eman Aldabbas, Eman Abuteen","doi":"10.29020/nybg.ejpam.v16i4.4928","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4928","url":null,"abstract":"This paper explores the solutions of certain fractional partial differential equations using two methods; the first method involves separation of variables, which is a common technique for solving partial differential equations. However, since many equations cannot be separated in this way, the tensor product of Banach spaces method is applied to find the atomic solutions. To solve the resulting ordinary differential equations, the reproducing Kernel Hilbert space method is used to find numerical solutions, which are then used to find the numerical solution of the partial differential equation. The residual errors indicate that this method is effective and powerful. In summary, this paper presents a study on the solutions of certain fractional partial differential equations using two methods and demonstrates the effectiveness of these methods in finding numerical solutions.","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":"136069146","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 General Family of Fifth-order Iterative Methods for Solving Nonlinear Equations 一类求解非线性方程的五阶迭代法
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4949
Ali Zein
{"title":"A General Family of Fifth-order Iterative Methods for Solving Nonlinear Equations","authors":"Ali Zein","doi":"10.29020/nybg.ejpam.v16i4.4949","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4949","url":null,"abstract":"A family of fifth-order iterative methods is proposed for solving nonlinear equations using the weight function technique. This family offers flexibility through its structure and the choice of weight functions, resulting in a wide range of new specific schemes. It is demonstrated that this proposed family includes several well-known and recent methods as special cases. In addition, several new particular methods are designed to achieve better results than existing methods of the same type. Convergence analysis is conducted, and numerical examples in both real and complex domains are provided for several specific schemes within the proposed family. Comparisons between the existing methods within this family and the newly introduced methods generally indicate improved performance among the new members. Notably, the study of complex dynamics and basins of attraction reveals that our new specific schemes have broader sets of initial points that lead to convergence.","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":"136069611","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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