In this work, we determined the general terms of all almost balancing numbers of first and second type in terms of balancing numbers and conversely we determined the general terms of all balancing numbers in terms of all almost balancing numbers of first and second type. We also set a correspondence between all almost balancing numbers of first and second type and Pell numbers.
{"title":"General Terms of All Almost Balancing Numbers of First and Second Type","authors":"A. Tekcan, Alper Erdem","doi":"10.46298/cm.10318","DOIUrl":"https://doi.org/10.46298/cm.10318","url":null,"abstract":"In this work, we determined the general terms of all almost balancing numbers\u0000of first and second type in terms of balancing numbers and conversely we\u0000determined the general terms of all balancing numbers in terms of all almost\u0000balancing numbers of first and second type. We also set a correspondence\u0000between all almost balancing numbers of first and second type and Pell numbers.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44976605","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}
Let $mathscr{R}$ be a prime ring of Char$(mathscr{R}) neq 2$ and $mneq 1$ be a positive integer. If $S$ is a nonzero skew derivation with an associated automorphism $mathscr{T}$ of $mathscr{R}$ such that $([S([a, b]), [a, b]])^{m} = [S([a, b]), [a, b]]$ for all $a, b in mathscr{R}$, then $mathscr{R}$ is commutative.
{"title":"On commutativity of prime rings with skew derivations","authors":"N. Rehman, Shuliang Huang","doi":"10.46298/cm.10319","DOIUrl":"https://doi.org/10.46298/cm.10319","url":null,"abstract":"Let $mathscr{R}$ be a prime ring of Char$(mathscr{R}) neq 2$ and $mneq 1$\u0000be a positive integer. If $S$ is a nonzero skew derivation with an associated\u0000automorphism $mathscr{T}$ of $mathscr{R}$ such that $([S([a, b]), [a,\u0000b]])^{m} = [S([a, b]), [a, b]]$ for all $a, b in mathscr{R}$, then\u0000$mathscr{R}$ is commutative.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49291994","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 paper, we define the Mus-Gradient metric on tangent bundle $TM$ by a deformation non-conform of Sasaki metric over an n-dimensional Riemannian manifold $(M, g)$. First we investigate the geometry of the Mus-Gradient metric and we characterize a new class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when all of the factors are Euclidean spaces.
{"title":"Proper biharmonic maps on tangent bundle","authors":"N. Djaa, F. Latti, A. Zagane","doi":"10.46298/cm.10305","DOIUrl":"https://doi.org/10.46298/cm.10305","url":null,"abstract":"This paper, we define the Mus-Gradient metric on tangent bundle $TM$ by a\u0000deformation non-conform of Sasaki metric over an n-dimensional Riemannian\u0000manifold $(M, g)$. First we investigate the geometry of the Mus-Gradient metric\u0000and we characterize a new class of proper biharmonic maps. Examples of proper\u0000biharmonic maps are constructed when all of the factors are Euclidean spaces.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44861275","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}
Legendre curves play a very important and special role in geometry and topology of almost contact manifolds.There are certain results known for Legendre curves in 3-dimensional normal almost contact manifolds. The aim of this paper is to study Legendre curves of three-dimensional $C_{12}$-manifolds which are non-normal almost contact manifolds and classifying all biharmonic Legendre curves in these manifolds.
{"title":"Legendre curves on 3-dimensional $C_{12}$-Manifolds","authors":"G. Beldjilali, Benaoumeur Bayour, Habib Bouzir","doi":"10.46298/cm.10390","DOIUrl":"https://doi.org/10.46298/cm.10390","url":null,"abstract":"Legendre curves play a very important and special role in geometry and\u0000topology of almost contact manifolds.There are certain results known for\u0000Legendre curves in 3-dimensional normal almost contact manifolds. The aim of\u0000this paper is to study Legendre curves of three-dimensional $C_{12}$-manifolds\u0000which are non-normal almost contact manifolds and classifying all biharmonic\u0000Legendre curves in these manifolds.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47617150","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 article, a continuous analogue of strictly non-Volterra quadratic dynamical systems with continuous time and points of equilibrium is investigated, a phase portrait of the system is constructed, numerical solutions are found, and a comparative analysis is carried out with a particular solution of the system.
{"title":"Qualitative analysis of strictly non-Volterra quadratic dynamical systems with continuous time","authors":"Rasulov Xaydar Raupovich","doi":"10.46298/cm.10528","DOIUrl":"https://doi.org/10.46298/cm.10528","url":null,"abstract":"In this article, a continuous analogue of strictly non-Volterra quadratic\u0000dynamical systems with continuous time and points of equilibrium is\u0000investigated, a phase portrait of the system is constructed, numerical\u0000solutions are found, and a comparative analysis is carried out with a\u0000particular solution of the system.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49006049","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}
We consider Complex Ginzburg-Landau equations with a polynomial nonlinearity in the real line. We use splitting-methods to prove well-posedness for a subset of almost periodic spaces. Specifically, we prove that if the initial condition has multiples of an irrational phase, then the solution of the equation maintains those same phases.
{"title":"Polynomial Complex Ginzburg-Landau equations in almost periodic spaces","authors":"A. Besteiro","doi":"10.46298/cm.10279","DOIUrl":"https://doi.org/10.46298/cm.10279","url":null,"abstract":"We consider Complex Ginzburg-Landau equations with a polynomial nonlinearity\u0000in the real line. We use splitting-methods to prove well-posedness for a subset\u0000of almost periodic spaces. Specifically, we prove that if the initial condition\u0000has multiples of an irrational phase, then the solution of the equation\u0000maintains those same phases.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45951847","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}
Recall that a ring R is called strongly pi-regular if, for every a in R, there is a positive integer n, depending on a, such that a^n belongs to the intersection of a^{n+1}R and Ra^{n+1}. In this paper we give a further study of the notion of a strongly pi-star-regular ring, which is the star-version of strongly pi-regular rings and which was originally introduced by Cui-Wang in J. Korean Math. Soc. (2015). We also establish various properties of these rings and give several new characterizations in terms of (strong) pi-regularity and involution. Our results also considerably extend recent ones in the subject due to Cui-Yin in Algebra Colloq. (2018) proved for pi-star-regular rings and due to Cui-Danchev in J. Algebra Appl. (2020) proved for star-periodic rings.
回想一下，环R被称为强π正则，如果R中的每个a都有一个正整数n，取决于a，使得a^n属于a^{n+1}R和Ra^{n+1｝的交集。本文进一步研究了强π星正则环的概念，它是强π星规则环的星型，最初由崔旺在《韩国数学》中提出。Soc.（2015）。我们还建立了这些环的各种性质，并根据（强）π正则性和演化给出了几个新的刻画。我们的结果也相当大地扩展了最近在主题dueto Cui Yin在Algebra Cololq.（2018）中的结果，证明了π星正则环和dueto崔丹切夫在J.Algebra-Appl中的结果。（2020）为恒星周期环证明。
{"title":"On Strongly pi-Regular Rings with Involution","authors":"Jian Cui, P. Danchev","doi":"10.46298/cm.10273","DOIUrl":"https://doi.org/10.46298/cm.10273","url":null,"abstract":"Recall that a ring R is called strongly pi-regular if, for every a in R,\u0000there is a positive integer n, depending on a, such that a^n belongs to the\u0000intersection of a^{n+1}R and Ra^{n+1}. In this paper we give a further study of\u0000the notion of a strongly pi-star-regular ring, which is the star-version of\u0000strongly pi-regular rings and which was originally introduced by Cui-Wang in J.\u0000Korean Math. Soc. (2015). We also establish various properties of these rings\u0000and give several new characterizations in terms of (strong) pi-regularity and\u0000involution. Our results also considerably extend recent ones in the subject due\u0000to Cui-Yin in Algebra Colloq. (2018) proved for pi-star-regular rings and due\u0000to Cui-Danchev in J. Algebra Appl. (2020) proved for star-periodic rings.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49222628","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 study regularity of weak solutions to the incompressible Navier-Stokes equations in $mathbb{R}^{3}times (0,T)$. The main goal is to establish the regularity criterion via the gradient of one velocity component in multiplier spaces.
{"title":"A regularity criterion in multiplier spaces to Navier-Stokes equations via the gradient of one velocity component","authors":"A. Alghamdi, S. Gala, M. Ragusa","doi":"10.46298/cm.10267","DOIUrl":"https://doi.org/10.46298/cm.10267","url":null,"abstract":"In this paper, we study regularity of weak solutions to the incompressible\u0000Navier-Stokes equations in $mathbb{R}^{3}times (0,T)$. The main goal is to\u0000establish the regularity criterion via the gradient of one velocity component\u0000in multiplier spaces.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42282372","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}
The main objective of the present paper is to introduce and study the function $_pR_q(A, B; z)$ with matrix parameters and investigate the convergence of this matrix function. The contiguous matrix function relations, differential formulas and the integral representation for the matrix function $_pR_q(A, B; z)$ are derived. Certain properties of the matrix function $_pR_q(A, B; z)$ have also been studied from fractional calculus point of view. Finally, we emphasize on the special cases namely the generalized matrix $M$-series, the Mittag-Leffler matrix function and its generalizations and some matrix polynomials.
{"title":"On the matrix function $_pR_q(A, B; z)$ and its fractional calculus properties","authors":"Ravi Dwivedi, Reshma Sanjhira","doi":"10.46298/cm.10205","DOIUrl":"https://doi.org/10.46298/cm.10205","url":null,"abstract":"The main objective of the present paper is to introduce and study the\u0000function $_pR_q(A, B; z)$ with matrix parameters and investigate the\u0000convergence of this matrix function. The contiguous matrix function relations,\u0000differential formulas and the integral representation for the matrix function\u0000$_pR_q(A, B; z)$ are derived. Certain properties of the matrix function\u0000$_pR_q(A, B; z)$ have also been studied from fractional calculus point of view.\u0000Finally, we emphasize on the special cases namely the generalized matrix\u0000$M$-series, the Mittag-Leffler matrix function and its generalizations and some\u0000matrix polynomials.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45706524","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 the present paper, seventh order Caudrey-Dodd-Gibbon (CDG) equation is solved by Lie symmetry analysis. All the geometry vector fields of seventh order KdV equations are presented. Using Lie transformation seventh order CDG equation is reduced into ordinary differential equations. These ODEs are solved by power series method to obtain exact solution. The convergence of the power series is also discussed.
{"title":"Lie Symmetry Analysis of Seventh Order Caudrey-Dodd- Gibbon Equation","authors":"Hariom Sharma, Rajan Arora","doi":"10.46298/cm.10102","DOIUrl":"https://doi.org/10.46298/cm.10102","url":null,"abstract":"In the present paper, seventh order Caudrey-Dodd-Gibbon (CDG) equation is solved by Lie symmetry analysis. All the geometry vector fields of seventh order KdV equations are presented. Using Lie transformation seventh order CDG equation is reduced into ordinary\u0000differential equations. These ODEs are solved by power series method to obtain exact solution. The convergence of the power series is also discussed.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47602677","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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