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A Short Note on a Mus-Cheeger-Gromoll Type Metric 关于Mus-Cheeger-Gromoll型公制的简短注释
Journal of New Theory Pub Date : 2023-03-31 DOI: 10.53570/jnt.1167010
Murat Altunbaş
{"title":"A Short Note on a Mus-Cheeger-Gromoll Type Metric","authors":"Murat Altunbaş","doi":"10.53570/jnt.1167010","DOIUrl":"https://doi.org/10.53570/jnt.1167010","url":null,"abstract":"In this paper, we first show that the complete lift $U^{c}$ to $TM$ of a vector field $U$ on $M$ is an infinitesimal fiber-preserving conformal transformation if and only if $U$ is an infinitesimal homothetic transformation of $(M,g)$. Here, $(M, g)$ is a Riemannian manifold and $TM$ is its tangent bundle with a Mus-Cheeger-Gromoll type metric $tilde{g}$. Secondly, we search for some conditions under which $left(overset{h}{nabla},tilde{g}right)$ is a Codazzi pair on $TM$ when $(nabla, g)$ is a Codazzi pair on $M$ where $overset{h}{nabla}$ is the horizontal lift of a linear connection $nabla$ on $M$. We finally discuss the need for further research.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128372221","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
Multiplicity of Scator Roots and the Square Roots in $mathbb{S}^{1+2}$ $mathbb{S}^{1+2}$中分散子根和平方根的多重性
Journal of New Theory Pub Date : 2023-03-31 DOI: 10.53570/jnt.1188215
M. Fernandez-Guasti
{"title":"Multiplicity of Scator Roots and the Square Roots in $mathbb{S}^{1+2}$","authors":"M. Fernandez-Guasti","doi":"10.53570/jnt.1188215","DOIUrl":"https://doi.org/10.53570/jnt.1188215","url":null,"abstract":"This paper presents the roots of elliptic scator numbers in $mathbb{S}^{1+n}$, which includes both the fundamental $2pi$ symmetry and the $pi$-pair symmetry for $ngeq2$. Here, the scator set $mathbb{S}^{1+n}$ is a subset of $mathbb{R}^{1+n}$ with the scator product and the multiplicative representation. These roots are expressed in terms of both additive (rectangular) and multiplicative (polar) variables. Additionally, the paper provides a comprehensive description of square roots in $mathbb{S}^{1+2}$, which includes a geometrical representation in three-dimensional space that provides a clear visualization of the concept and makes it easier to understand and interpret. Finally, the paper handles whether the aspects should be further investigated.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129614983","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 Hyperbolic Leonardo and Hyperbolic Francois Quaternions 论双曲列奥纳多和双曲弗朗索瓦四元数
Journal of New Theory Pub Date : 2023-03-31 DOI: 10.53570/jnt.1199465
Orhan Dişkaya, H. Menken, Paula Maria Machado CRUZ CATARİNO
{"title":"On the Hyperbolic Leonardo and Hyperbolic Francois Quaternions","authors":"Orhan Dişkaya, H. Menken, Paula Maria Machado CRUZ CATARİNO","doi":"10.53570/jnt.1199465","DOIUrl":"https://doi.org/10.53570/jnt.1199465","url":null,"abstract":"In this paper, we present a new definition, referred to as the Francois sequence, related to the Lucas-like form of the Leonardo sequence. We also introduce the hyperbolic Leonardo and hyperbolic Francois quaternions. Afterward, we derive the Binet-like formulas and their generating functions. Moreover, we provide some binomial sums, Honsberger-like, d’Ocagne-like, Catalan-like, and Cassini-like identities of the hyperbolic Leonardo quaternions and hyperbolic Francois quaternions that allow an understanding of the quaternions' properties and their relation to the Francois sequence and Leonardo sequence. Finally, considering the results presented in this study, we discuss the need for further research in this field.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"179 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124483769","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: 2
A Note on 4-Dimensional 2-Crossed Modules 关于四维2交叉模的一个注记
Journal of New Theory Pub Date : 2023-03-31 DOI: 10.53570/jnt.1208633
Koray Yılmaz
{"title":"A Note on 4-Dimensional 2-Crossed Modules","authors":"Koray Yılmaz","doi":"10.53570/jnt.1208633","DOIUrl":"https://doi.org/10.53570/jnt.1208633","url":null,"abstract":"The study presents the direct product of two objects in the category of 4-dimensional 2-crossed modules. The structures of the domain, kernel, image, and codomain can be related using isomorphism theorems by defining the kernel and image of a morphism in a category. It then establishes the kernel and image of a morphism in the category of 4-dimensional 2-crossed modules to apply isomorphism theorems. These isomorphism theorems provide a powerful tool to understand the properties of this category. Moreover, isomorphism theorems in 4-dimensional 2-crossed modules allow us to establish connections between different algebraic structures and simplify complicated computations. Lastly, the present research inquires whether additional studies should be conducted.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"336 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131479820","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
Characterizations of Unit Darboux Ruled Surface with Quaternions 单位达布直纹曲面的四元数刻画
Journal of New Theory Pub Date : 2023-03-31 DOI: 10.53570/jnt.1194990
Abdussamet Çalışkan
{"title":"Characterizations of Unit Darboux Ruled Surface with Quaternions","authors":"Abdussamet Çalışkan","doi":"10.53570/jnt.1194990","DOIUrl":"https://doi.org/10.53570/jnt.1194990","url":null,"abstract":"This paper presents a quaternionic approach to generating and characterizing the ruled surface drawn by the unit Darboux vector. The study derives the Darboux frame of the surface and relates it to the Frenet frame of the base curve. Moreover, it obtains the quaternionic shape operator and its matrix representation using the normal and geodesic curvatures to provide a more detailed analysis. To illustrate the concepts discussed, the paper offers a clear example that will help readers better understand the concepts and showcases the quaternionic shape operator, Gauss curvature, mean curvature, and rotation matrix. Finally, it emphasizes the need for further research on this topic.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128590583","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 Characterization of Semiprime Rings with Homoderivations 一类具有同导的半素环的性质
Journal of New Theory Pub Date : 2023-03-31 DOI: 10.53570/jnt.1181895
Emine Koç Sögütcü
{"title":"A Characterization of Semiprime Rings with Homoderivations","authors":"Emine Koç Sögütcü","doi":"10.53570/jnt.1181895","DOIUrl":"https://doi.org/10.53570/jnt.1181895","url":null,"abstract":"This paper is focused on the commutativity of the laws of semiprime rings, which satisfy some algebraic identities involving homoderivations on ideals. It provides new and notable results that will interest researchers in this field, such as “R contains a nonzero central ideal if R admits a nonzero homoderivation δ on I such that δ(I)⊆Z where R is a semiprime ring with center Z and I a nonzero ideal of R”. Moreover, the research also generalizes some results previously published in the literature, including derivation on prime rings using homoderivation semiprime rings. It also demonstrates the necessity of hypotheses operationalized in theorems by an example. Finally, the paper discusses how the results herein can be further developed in future research.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132484296","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 Effect of the Additive Row Operation on the Permanent 加性行操作对永久性行的影响
Journal of New Theory Pub Date : 2023-03-31 DOI: 10.53570/jnt.1178990
A. Küçük, Abdullah Talha Sözer
{"title":"The Effect of the Additive Row Operation on the Permanent","authors":"A. Küçük, Abdullah Talha Sözer","doi":"10.53570/jnt.1178990","DOIUrl":"https://doi.org/10.53570/jnt.1178990","url":null,"abstract":"The permanent function is not as stable as the determinant function under the elementary row operations. For example, adding a non-zero scalar multiple of a row to another row does not change the determinant of a matrix, but this operation changes its permanent. In this article, the variation in the permanent by applying the operation, which adds a scalar multiple of a row to another row, is examined. The relationship between the permanent of the matrix to which this operation is applied and the permanent of the initial matrix is given by a theorem. Finally, the paper inquires the need for further research.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116304304","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
Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre Curves (2+s)维框架度量流形的广义叉积及其在Legendre曲线上的应用
Journal of New Theory Pub Date : 2023-03-31 DOI: 10.53570/jnt.1213002
S. Can, Ç. Camcı
{"title":"Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre Curves","authors":"S. Can, Ç. Camcı","doi":"10.53570/jnt.1213002","DOIUrl":"https://doi.org/10.53570/jnt.1213002","url":null,"abstract":"This study generalizes the cross product defined in 3-dimensional almost contact metric manifolds and describes a new generalized cross product for n=1 in (2n+s)-dimensional framed metric manifolds. Moreover, it studies some of the proposed product’s basic properties. It also performs characterizations of the curvature of a Legendre curve on an S-manifold and calculates the curvature of a Legendre curve. Furthermore, it shows that Legendre curves are also biharmonic curves. Next, this study observes that a Legendre curve of osculating order 5 on S-manifolds is imbedded in the 3-dimensional K-contact space. Lastly, the current paper discusses the need for further research.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129420234","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 Hybridization of Modified Rough Bipolar Soft Sets and TOPSIS for MCGDM MCGDM的改进粗糙双极软集与TOPSIS的杂交
Journal of New Theory Pub Date : 2023-03-31 DOI: 10.53570/jnt.1195099
Rizwana Gul, M. Shabir, Saba Ayub
{"title":"A Hybridization of Modified Rough Bipolar Soft Sets and TOPSIS for MCGDM","authors":"Rizwana Gul, M. Shabir, Saba Ayub","doi":"10.53570/jnt.1195099","DOIUrl":"https://doi.org/10.53570/jnt.1195099","url":null,"abstract":"Uncertain data is a challenge to decision-making (DM) problems. Multi-criteria group decision-making (MCGDM) problems are among these problems that have received much attention. MCGDM is difficult because the existing alternatives frequently conflict with each other. In this article, we suggest a novel hybrid model for an MCGDM approach based on modified rough bipolar soft sets (MRBSs) using a well-known method of technique for order of preference by similarity to ideal solution (TOPSIS), which combines MRBSs theory and TOPSIS for the prioritization of alternatives in an uncertain environment. In this technique, we first introduce an aggregated parameter matrix with the help of modified bipolar soft lower and upper matrices to identify the positive and negative ideal solutions. After that, we define the separation measurements of these two solutions and compute relative closeness to choose the best alternative. Next, an application of the proposed technique in the MCGDM problem is introduced. Afterward, an algorithm for this application is developed, which is illustrated by a case study. The application demonstrates the usefulness and efficiency of the proposal. Compared to some existing studies, we additionally present several merits of our proposed technique. Eventually, the paper handles whether additional studies on these topics are needed.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133410228","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 Quasi Quadratic Modules of Lie Algebras 李代数的拟二次模
Journal of New Theory Pub Date : 2022-12-31 DOI: 10.53570/jnt.1176779
Emre Özel, U. EGE ARSLAN
{"title":"On Quasi Quadratic Modules of Lie Algebras","authors":"Emre Özel, U. EGE ARSLAN","doi":"10.53570/jnt.1176779","DOIUrl":"https://doi.org/10.53570/jnt.1176779","url":null,"abstract":"This study introduces the category of quasi-quadratic modules of Lie algebras and discusses the functorial relations between quasi-quadratic modules and quadratic modules of Lie algebras.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115435073","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
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