: This is from Birkhoff, the “father of lattice theory” in Trends in Lattice Theory. Van Nostrand 1970: “Lattices can do things for you, no matter what kind of mathematician you are!”. The aim of this paper is to show that the le -semigroups (lattice ordered semigroups possessing a greatest element) play the main role in studying the ordered hypersemigroups. From many results on lattice ordered semigroups corresponding results on ordered semigroups can be obtained. The converse is also possible but the beauty and simplicity of “order” makes it easier to investigate the lattice ordered semigroup at first. After getting the results on ordered semigroups, by an easy modification corresponding results on ordered hypersemigroups can be obtained.
{"title":"What can lattices do for hypersemigroups?","authors":"N. Kehayopulu","doi":"10.55730/1300-0098.3448","DOIUrl":"https://doi.org/10.55730/1300-0098.3448","url":null,"abstract":": This is from Birkhoff, the “father of lattice theory” in Trends in Lattice Theory. Van Nostrand 1970: “Lattices can do things for you, no matter what kind of mathematician you are!”. The aim of this paper is to show that the le -semigroups (lattice ordered semigroups possessing a greatest element) play the main role in studying the ordered hypersemigroups. From many results on lattice ordered semigroups corresponding results on ordered semigroups can be obtained. The converse is also possible but the beauty and simplicity of “order” makes it easier to investigate the lattice ordered semigroup at first. After getting the results on ordered semigroups, by an easy modification corresponding results on ordered hypersemigroups can be obtained.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42301824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: In this article we define a new form of unipotence in groups of finite Morley rank which extends Burdges unipotence to any characteristic. In particular, we show that every connected solvable group of finite Morley rank G has a definable connected subgroup H whose derived subgroup H ′ is a good unipotent subgroup of finite Morley rank
{"title":"Unipotence in positive characteristic for groups of finite Morley rank","authors":"Jules Tindzogho Ntsiri","doi":"10.55730/1300-0098.3435","DOIUrl":"https://doi.org/10.55730/1300-0098.3435","url":null,"abstract":": In this article we define a new form of unipotence in groups of finite Morley rank which extends Burdges unipotence to any characteristic. In particular, we show that every connected solvable group of finite Morley rank G has a definable connected subgroup H whose derived subgroup H ′ is a good unipotent subgroup of finite Morley rank","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46550579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: The metallic-like ( a, b ) -manifold is a manifold endowed with a polynomial structure of second degree which unifies the almost product, complex structures and includes metallic structures. We introduce the metallic-like maps between metallic-like ( a, b ) -manifolds and we give a criterion for the nonconstancy of these maps. We prove that an almost contact structure on a Riemannian manifold induces a metallic-like ( a, b ) -structure and we give an example of a nonconstant metallic-like endomorphism of a particular almost contact manifold
{"title":"Metallic-like structures and metallic-like maps","authors":"Adelina Manea","doi":"10.55730/1300-0098.3446","DOIUrl":"https://doi.org/10.55730/1300-0098.3446","url":null,"abstract":": The metallic-like ( a, b ) -manifold is a manifold endowed with a polynomial structure of second degree which unifies the almost product, complex structures and includes metallic structures. We introduce the metallic-like maps between metallic-like ( a, b ) -manifolds and we give a criterion for the nonconstancy of these maps. We prove that an almost contact structure on a Riemannian manifold induces a metallic-like ( a, b ) -structure and we give an example of a nonconstant metallic-like endomorphism of a particular almost contact manifold","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41756718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: In this article, we study 3-dimensional biconservative and biharmonic submanifolds of E 5 with parallel normalized mean curvature vector (PNMCV). First, we prove that the principal curvartures and principal directions of biconservative PNMCV isometric immersions into E 5 can be determined intrinsically. Then, we complete the proof of Chen’s biharmonic conjecture for PNMCV submanifolds of E 5 .
{"title":"Biharmonic PNMCV submanifolds in Euclidean 5-space","authors":"R. Şen, N. Turgay","doi":"10.55730/1300-0098.3361","DOIUrl":"https://doi.org/10.55730/1300-0098.3361","url":null,"abstract":": In this article, we study 3-dimensional biconservative and biharmonic submanifolds of E 5 with parallel normalized mean curvature vector (PNMCV). First, we prove that the principal curvartures and principal directions of biconservative PNMCV isometric immersions into E 5 can be determined intrinsically. Then, we complete the proof of Chen’s biharmonic conjecture for PNMCV submanifolds of E 5 .","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44833047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: Matrix commutator and anticommutator play an important role in mathematics, mathematical physic, and quantum physic. The commutator and anticommutator of two n × n complex matrices A and B are defined by [ A, B ] = AB − BA and ( A, B ) = AB + BA , respectively. Cauchy-Toeplitz matrix and exchange matrix are two of the special matrices and they have excellent properties. In this study, we mainly focus on Frobenius norm of the commutator of Cauchy-Toeplitz matrix and exchange matrix. Moreover, we give upper and lower bounds for the Frobenius norm of the commutator of Cauchy-Toeplitz matrix and exchange matrix.
矩阵换向子和反换向子在数学、数学物理和量子物理中起着重要的作用。两个n × n复矩阵A和B的对易子和反对易子分别定义为[A, B] = AB−BA和(A, B) = AB + BA。Cauchy-Toeplitz矩阵和交换矩阵是两种特殊的矩阵，它们具有优异的性质。本文主要研究Cauchy-Toeplitz矩阵和交换矩阵的交换子的Frobenius范数。并给出了Cauchy-Toeplitz矩阵和交换矩阵对易子的Frobenius范数的上界和下界。
{"title":"On the Frobenius norm of commutator of Cauchy-Toeplitz matrix and exchange matrix","authors":"Süleyman Solak, M. Bahşı","doi":"10.55730/1300-0098.3447","DOIUrl":"https://doi.org/10.55730/1300-0098.3447","url":null,"abstract":": Matrix commutator and anticommutator play an important role in mathematics, mathematical physic, and quantum physic. The commutator and anticommutator of two n × n complex matrices A and B are defined by [ A, B ] = AB − BA and ( A, B ) = AB + BA , respectively. Cauchy-Toeplitz matrix and exchange matrix are two of the special matrices and they have excellent properties. In this study, we mainly focus on Frobenius norm of the commutator of Cauchy-Toeplitz matrix and exchange matrix. Moreover, we give upper and lower bounds for the Frobenius norm of the commutator of Cauchy-Toeplitz matrix and exchange matrix.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44160165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: We give a new way to obtain the standard isomorphisms of complex Clifford algebras, known as the tensor product of Pauli matrices, by representing the complex Clifford algebras on the space of complex valued functions defined over a finite subset of the Cantor set
{"title":"A new approach to matrix isomorphisms of complex Clifford algebras via Cantor set","authors":"D. Çelik","doi":"10.55730/1300-0098.3346","DOIUrl":"https://doi.org/10.55730/1300-0098.3346","url":null,"abstract":": We give a new way to obtain the standard isomorphisms of complex Clifford algebras, known as the tensor product of Pauli matrices, by representing the complex Clifford algebras on the space of complex valued functions defined over a finite subset of the Cantor set","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44215578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Approximation results for the moments of random walk with normally distributed interference of chance","authors":"Zulfiye Hanalioglu, Aynura Poladova, T. Khaniyev","doi":"10.55730/1300-0098.3363","DOIUrl":"https://doi.org/10.55730/1300-0098.3363","url":null,"abstract":"","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47352681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: We are concerned with the first-order differential system of the form
：我们关注的是形式为
{"title":"Global bifurcation of positive solutions for a class of superlinear first-order differential systems","authors":"Lijuan Yang, Ruyun Ma","doi":"10.55730/1300-0098.3350","DOIUrl":"https://doi.org/10.55730/1300-0098.3350","url":null,"abstract":": We are concerned with the first-order differential system of the form","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42353327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: In this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator [ E 1 , E 2 ] = E 1 E 2 − E 2 E 1 involving idempotents E 1 , E 2 in certain subrings of M 2 ( Z )
{"title":"Characterizations of the commutators involving idempotents in certain subrings of $M_{2}(mathbb{Z})$","authors":"Tufan Özdi̇n, Günseli Gümüşel","doi":"10.55730/1300-0098.3443","DOIUrl":"https://doi.org/10.55730/1300-0098.3443","url":null,"abstract":": In this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator [ E 1 , E 2 ] = E 1 E 2 − E 2 E 1 involving idempotents E 1 , E 2 in certain subrings of M 2 ( Z )","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43225828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: A combination of interval-valued Fermatean fuzzy sets with Fermatean hesitant fuzzy elements in the form of interval values is known as an interval-valued Fermatean hesitant fuzzy set. Since Fermatean hesitant fuzzy sets are effective instruments for representing more complex, ambiguous, and hazy information, interval-valued Fermatean hesitant fuzzy sets are expansions of these sets. This investigation will concentrate on four different types of correlation coefficients for Fermatean hesitant fuzzy sets and expand them to include correlation coefficients and weighted correlation coefficients for interval-valued Fermatean hesitant fuzzy sets. Finally, the numerical examples demonstrate the viability and usefulness of the suggested methodologies in decision-making under many criteria.
{"title":"Novel correlation coefficients for interval-valued Fermatean hesitant fuzzy sets with pattern recognition application","authors":"I. Demir","doi":"10.55730/1300-0098.3355","DOIUrl":"https://doi.org/10.55730/1300-0098.3355","url":null,"abstract":": A combination of interval-valued Fermatean fuzzy sets with Fermatean hesitant fuzzy elements in the form of interval values is known as an interval-valued Fermatean hesitant fuzzy set. Since Fermatean hesitant fuzzy sets are effective instruments for representing more complex, ambiguous, and hazy information, interval-valued Fermatean hesitant fuzzy sets are expansions of these sets. This investigation will concentrate on four different types of correlation coefficients for Fermatean hesitant fuzzy sets and expand them to include correlation coefficients and weighted correlation coefficients for interval-valued Fermatean hesitant fuzzy sets. Finally, the numerical examples demonstrate the viability and usefulness of the suggested methodologies in decision-making under many criteria.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43323988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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：