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Generalized elliptical quaternions with some applications 广义椭圆四元数及其一些应用
IF 1 4区 数学
Turkish Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.55730/1300-0098.3364
H. B. Çolakoğlu, M. Özdemir
{"title":"Generalized elliptical quaternions with some applications","authors":"H. B. Çolakoğlu, M. Özdemir","doi":"10.55730/1300-0098.3364","DOIUrl":"https://doi.org/10.55730/1300-0098.3364","url":null,"abstract":": In this article, quaternions, which is a preferred and elegant method for expressing spherical rotations, are generalized with the help of generalized scalar product spaces, and elliptical rotations on any given ellipsoid are examined by them. To this end, firstly, we define the generalized elliptical scalar product space which accepts the given ellipsoid as a sphere and determines skew symmetric matrices, and the generalized vector product related to this scalar product space. Then we define the generalized elliptical quaternions by using these notions. Finally, elliptical rotations on any ellipsoid in the space are examined by using the unit generalized elliptical quaternions. The formulas and results obtained are supported with numerical examples.","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":"41731256","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}
引用次数: 1
An invariant of regular isotopy for disoriented links 定向链路的正则同构不变量
IF 1 4区 数学
Turkish Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.55730/1300-0098.3345
Ismet Altintas, H. Parlatıcı
{"title":"An invariant of regular isotopy for disoriented links","authors":"Ismet Altintas, H. Parlatıcı","doi":"10.55730/1300-0098.3345","DOIUrl":"https://doi.org/10.55730/1300-0098.3345","url":null,"abstract":": In this paper, we define a two-variable p olynomial i nvariant o f r egular i sotopy, M K f or a d isoriented link diagram K . By normalizing the polynomial M K using complete writhe, we obtain a polynomial invariant of ambient isotopy, N K , for a disoriented link diagram K . The polynomial N K is a generalization of the expanded Jones polynomial for disoriented links and is an expansion of the Kauffman polynomial F to the disoriented l inks. Moreover, the polynomial M K is an expansion of the Kauffman p olynomial L to the disoriented links.","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":"46737543","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}
引用次数: 0
The class of demi KB-operators on Banach lattices Banach格上的半kb算子类
IF 1 4区 数学
Turkish Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.55730/1300-0098.3366
Hedi Benkhaled, A. Jeribi
{"title":"The class of demi KB-operators on Banach lattices","authors":"Hedi Benkhaled, A. Jeribi","doi":"10.55730/1300-0098.3366","DOIUrl":"https://doi.org/10.55730/1300-0098.3366","url":null,"abstract":": In this paper, we introduce and study the new concept of demi KB-operators. Let E be a Banach lattice. An operator T : E −→ E is said to be a demi KB-operator if, for every positive increasing sequence { x n } in the closed unit ball B E of E such that { x n − Tx n } is norm convergent to x ∈ E , there is a norm convergent subsequence of { x n } . If the latter sequence has a weakly convergent subsequence then T is called a weak demi KB-operator. We also investigate the relationship of these classes of operators with classical notions of operators, such as b-weakly demicompact operators and demi Dunford-Pettis operators.","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":"49215909","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}
引用次数: 1
Separation, connectedness, and disconnectedness 分离、连通和断开
IF 1 4区 数学
Turkish Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.55730/1300-0098.3360
M. Baran
{"title":"Separation, connectedness, and disconnectedness","authors":"M. Baran","doi":"10.55730/1300-0098.3360","DOIUrl":"https://doi.org/10.55730/1300-0098.3360","url":null,"abstract":": The aim of this paper is to introduce the notions of hereditarily disconnected and totally disconnected objects in a topological category and examine the relationship as well as interrelationships between them. Moreover, we characterize each of T 2 , connected, hereditarily disconnected, and totally disconnected objects in some topological categories and compare our results with the ones in the category of topological spaces","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":"49594432","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}
引用次数: 3
On solvability of homogeneous Riemann boundary value problems in Hardy-Orlicz classes Hardy-Orlicz类齐次Riemann边值问题的可解性
IF 1 4区 数学
Turkish Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.55730/1300-0098.3379
Y. Zeren, Fi̇dan A. Ali̇zadeh, Feyza Eli̇f Dal
{"title":"On solvability of homogeneous Riemann boundary value problems in Hardy-Orlicz classes","authors":"Y. Zeren, Fi̇dan A. Ali̇zadeh, Feyza Eli̇f Dal","doi":"10.55730/1300-0098.3379","DOIUrl":"https://doi.org/10.55730/1300-0098.3379","url":null,"abstract":": This work deals with the Orlicz space and the Hardy-Orlicz classes generated by this space, which consist of analytic functions inside and outside the unit disk. The homogeneous Riemann boundary value problems with piecewise continuous coefficients are considered in these classes. New characteristic of Orlicz space is defined which depends on whether the power function belongs to this space or not. Relationship between this characteristic and Boyd indices of Orlicz space is established. The concept of canonical solution of homogeneous problem is defined, which depends on the argument of the coefficient. In terms of the above characteristic, a condition on the jumps of the argument is found which is sufficient for solvability of these problems, and, in case of solvability, a general solution is constructed. It is established the basicity of the parts of exponential system in Hardy-Orlicz classes.","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":"46628035","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}
引用次数: 0
Pell-Lucas collocation method for solving a class of second order nonlinear differential equations with variable delays 一类二阶变时滞非线性微分方程的Pell-Lucas配点法
IF 1 4区 数学
Turkish Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.55730/1300-0098.3344
Ş. Yüzbaşı, Gamze Yıldırım
{"title":"Pell-Lucas collocation method for solving a class of second order nonlinear differential equations with variable delays","authors":"Ş. Yüzbaşı, Gamze Yıldırım","doi":"10.55730/1300-0098.3344","DOIUrl":"https://doi.org/10.55730/1300-0098.3344","url":null,"abstract":": In this study, the approximate solution of the nonlinear differential equation with variable delays is investigated by means of a collocation method based on the truncated Pell-Lucas series. In the first stage of the method, the assumed solution form (the truncated Pell-Lucas polynomial solution) is expressed in the matrix form of the standard bases. Next, the matrix forms of the necessary derivatives, the nonlinear terms, and the initial conditions are written. Then, with the help of the equally spaced collocation points and these matrix relations, the problem is reduced to a system of nonlinear algebraic equations. Finally, the obtained system is solved by using MATLAB. The solution of this system gives the coefficient matrix in the assumed solution form. Moreover, the error analysis is performed. Accordingly, two theorems about the upper limit of the errors and the error estimation are given and these theorems are proven. In addition, the residual improvement technique is presented. The presented methods are applied to three examples. The obtained results are displayed in tables and graphs. Also, the obtained results are compared with the results of other methods in the literature. All results in this study have been calculated by using MATLAB.","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":"41818012","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}
引用次数: 2
On conditions of regular solvability for two classes of third-order operator-differential equations in a fourth-order Sobolev-type space 四阶sobolev型空间中两类三阶算子微分方程正则可解的条件
IF 1 4区 数学
Turkish Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.55730/1300-0098.3382
A. R. Aliev, N. L. Muradova
{"title":"On conditions of regular solvability for two classes of third-order operator-differential equations in a fourth-order Sobolev-type space","authors":"A. R. Aliev, N. L. Muradova","doi":"10.55730/1300-0098.3382","DOIUrl":"https://doi.org/10.55730/1300-0098.3382","url":null,"abstract":": In this paper, we study two classes of operator-differential equations of the third order with a multiple characteristic, considered on the whole axis. We introduce the concept of a smooth regular solution of order 1 and obtain sufficient conditions for the ”smoothly” regular solvability of these equations","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":"41388777","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}
引用次数: 0
Atomic systems in Krein spaces 克莱恩空间中的原子系统
IF 1 4区 数学
Turkish Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.55730/1300-0098.3432
Osmin Ferrer Villar, Edilberto Arroyo Ortiz, José Naranjo Martínez
{"title":"Atomic systems in Krein spaces","authors":"Osmin Ferrer Villar, Edilberto Arroyo Ortiz, José Naranjo Martínez","doi":"10.55730/1300-0098.3432","DOIUrl":"https://doi.org/10.55730/1300-0098.3432","url":null,"abstract":": In the present article, we establish a definition of atomic systems in the Krein spaces, specifically, we establish the fundamental tools of the theory of atomic systems in the formalism of the Krein spaces and give a complete characterization of them. We also show that the atomic systems do not depend on the decomposition of the Krein space","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":"41421119","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}
引用次数: 0
On the geometry of nearly trans-Sasakian manifolds 关于近跨sasakian流形的几何
IF 1 4区 数学
Turkish Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.55730/1300-0098.3417
A. Rustanov, T. L. Melekhina, S. Kharitonova
{"title":"On the geometry of nearly trans-Sasakian manifolds","authors":"A. Rustanov, T. L. Melekhina, S. Kharitonova","doi":"10.55730/1300-0098.3417","DOIUrl":"https://doi.org/10.55730/1300-0098.3417","url":null,"abstract":"The geometry of nearly trans-Sasakian manifolds is researched in this paper. The complete group of structural equations and the components of the Lee vector on the space of the associated G -structure are obtained for such manifolds. Conditions are found under which a nearly trans-Sasakian structure is a trans-Sasakian, a cosymplectic, a closely cosymplectic, a Sasakian structure or a Kenmotsu structure. The conditions are obtained when the nearly transSasakian structure is a special generalized Kenmotsu structure of the second kind. A complete classification of nearly trans-Sasakian manifolds is obtained, i.e. it is proved that a nearly trans-Sasakian manifold is either a trans-Sasakian manifold or has a closed contact form. It is proved that the nearly trans-Sasakian structure with a nonclosed contact form is homothetic to the Sasakian structure. The criterion of ownership of a nearly trans-Sasakian structure is obtained. It is proved that the class of nearly trans-Sasakian manifolds with a closed contact form and a closed Lee form coincides with the class of almost contact metric manifolds with a closed contact form, which are locally conformal to the closely cosymplectic manifolds. Examples of such manifolds are given. The necessary and sufficient conditions for the complete integrability of the first fundamental distribution of a nearly trans-Sasakian manifold are obtained. It is proved that a nearly Kähler structure on the leaves of the first fundamental distribution of a nearly trans-Sasakian manifold is induced.","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":"47975824","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}
引用次数: 2
Global regularity for the 3D axisymmetric incompressible Hall-MHD system with partial dissipation and diffusion 具有部分耗散和扩散的三维轴对称不可压缩Hall-MHD系统的全局正则性
IF 1 4区 数学
Turkish Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.55730/1300-0098.3403
Meilin Jin, Q. Jiu, Huan Yu
{"title":"Global regularity for the 3D axisymmetric incompressible Hall-MHD system with partial dissipation and diffusion","authors":"Meilin Jin, Q. Jiu, Huan Yu","doi":"10.55730/1300-0098.3403","DOIUrl":"https://doi.org/10.55730/1300-0098.3403","url":null,"abstract":": In this paper, we study the Cauchy problem for the 3D incompressible axisymmetric Hall-MHD system with horizontal velocity dissipation and vertical magnetic diffusion. We obtain a unique global smooth solution of which in the cylindrical coordinate system the swirl velocity fields, the radial and the vertical components of the magnetic fields are trivial. This type of solution has been studied for the MHD system in [17], [16] and [15] and for the Hall-MHD system with total dissipation and diffusion in [11]. Some new and fine estimates are obtained in this paper to overcome the difficulties raised from the Hall term and the loss of vertical velocity dissipation and horizontal magnetic diffusion. Finally we can show that the estimates ∫ T 0 ∥∇ u ( t ) ∥ L ∞ dt and ∫ T 0 ∥∇ b ( t ) ∥ L ∞ dt are finite in a priori way and hence obtain the global well-posedness to the system under considered.","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":"47008895","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}
引用次数: 0
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