: We introduce the class of ( M, k ) -quasi- ∗ -paranormal operators on a Hilbert space H . This class extends the classes of ∗ -paranormal and k -quasi- ∗ -paranormal operators. An operator T on a complex Hilbert space is called ( M, k ) -quasi- ∗ -paranormal if there exists M > 0 such that
{"title":"Spectral and topological properties of linear operators on a Hilbert space","authors":"Salah Mecheri, Aissa Nasli Bakir","doi":"10.55730/1300-0098.3426","DOIUrl":"https://doi.org/10.55730/1300-0098.3426","url":null,"abstract":": We introduce the class of ( M, k ) -quasi- ∗ -paranormal operators on a Hilbert space H . This class extends the classes of ∗ -paranormal and k -quasi- ∗ -paranormal operators. An operator T on a complex Hilbert space is called ( M, k ) -quasi- ∗ -paranormal if there exists M > 0 such that","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":"45223259","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":"Curves and stick figures not contained in a hypersurface of a given degree","authors":"E. Ballico","doi":"10.55730/1300-0098.3384","DOIUrl":"https://doi.org/10.55730/1300-0098.3384","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":"45574496","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 consider the inverse nodal problem for a quadratic pencil of the Sturm − Liouville equations with parameter-dependent Bitsadze − Samarskii type nonlocal boundary condition and we give an algorithm for the reconstruction of the potential functions by obtaining the asymptotics of the nodal points
{"title":"Inverse nodal problem for the quadratic pencil of the Sturm$-$Liouville equations with parameter-dependent nonlocal boundary condition","authors":"Yaşar Çakmak, B. Keskin","doi":"10.55730/1300-0098.3367","DOIUrl":"https://doi.org/10.55730/1300-0098.3367","url":null,"abstract":": In this paper, we consider the inverse nodal problem for a quadratic pencil of the Sturm − Liouville equations with parameter-dependent Bitsadze − Samarskii type nonlocal boundary condition and we give an algorithm for the reconstruction of the potential functions by obtaining the asymptotics of the nodal points","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":"45656033","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}
: Inequalities are frequently used in various fields of mathematics to prove theorems. The existence of inequalities contributes significantly to the foundations of such branches. In this paper, we study the properties of order relations in the system of dual numbers, which is inspired by order relations defined on real numbers. Besides, some special inequalities that are used in various fields of mathematics, such as Cauchy-Schwarz, Minkowski, and Chebyshev are studied in this framework. An example is also provided to validate our research findings
{"title":"The inequalities on dual numbers and their topological structures","authors":"Buşra Aktaş, Olgun Durmaz, Halit Gündoğan","doi":"10.55730/1300-0098.3431","DOIUrl":"https://doi.org/10.55730/1300-0098.3431","url":null,"abstract":": Inequalities are frequently used in various fields of mathematics to prove theorems. The existence of inequalities contributes significantly to the foundations of such branches. In this paper, we study the properties of order relations in the system of dual numbers, which is inspired by order relations defined on real numbers. Besides, some special inequalities that are used in various fields of mathematics, such as Cauchy-Schwarz, Minkowski, and Chebyshev are studied in this framework. An example is also provided to validate our research findings","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":"48201538","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 weak L 1 -space meets in many areas of mathematics. For example, the conjugate functions of Lebesgue integrable functions belong to the weak L 1 -space. The difficulty of working with the weak L 1 -space is that the weak L 1 -space is not a normed space. Moreover, infinitely differentiable (even continuous) functions are not dense in this space. Due to this, the theory of approximation was not produced in this space. In the present paper, we introduced the concept of the modulus of continuity of the functions from the weak L 1 -space, studied its properties, found a criterion for convergence to zero of the modulus of continuity of the function from the weak L 1 -space, and proved in this space an analogue of the Jackson-type theorem.
{"title":"Jackson-type theorem in the weak $L_{1}$-space","authors":"R. Aliev, Eldost Ismayilov","doi":"10.55730/1300-0098.3353","DOIUrl":"https://doi.org/10.55730/1300-0098.3353","url":null,"abstract":": The weak L 1 -space meets in many areas of mathematics. For example, the conjugate functions of Lebesgue integrable functions belong to the weak L 1 -space. The difficulty of working with the weak L 1 -space is that the weak L 1 -space is not a normed space. Moreover, infinitely differentiable (even continuous) functions are not dense in this space. Due to this, the theory of approximation was not produced in this space. In the present paper, we introduced the concept of the modulus of continuity of the functions from the weak L 1 -space, studied its properties, found a criterion for convergence to zero of the modulus of continuity of the function from the weak L 1 -space, and proved in this space an analogue of the Jackson-type theorem.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41361147","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 introduce generalized Darboux frame of a spacelike curve α lying on a lightlike surface in Minkowski space E 31 . We prove that α has two such frames and obtain generalized Darboux frame’s equations. We find the relations between the curvature functions k g , k n , τ g of α with respect to its Darboux frame and the curvature functions ˜ k g , ˜ k n , ˜ τ g with respect to generalized Darboux frames. We show that such frames exist along a spacelike straight line lying on a ruled surface which is not entirely lightlike, but contains some lightlike points. We define lightlike ruled surfaces on which the tangent and the binormal indicatrix of a null Cartan curve are the principal curvature lines having ˜ τ g = 0 and give some examples.
本文引入了Minkowski空间e31中类光曲面上的类空间曲线α的广义达布坐标系。证明了α有两个这样的坐标系，得到了广义的达布坐标系方程。我们得到了α的曲率函数k g, k n， τ g与广义达布坐标系下的曲率函数~ k g， ~ k n， ~ τ g之间的关系。我们证明了这样的框架存在于位于不完全像光的直纹表面上的类空间直线上，但它包含一些像光的点。我们定义了一个零Cartan曲线的正切线和二法线指标为~ τ g = 0的主曲率线的类光直纹曲面，并给出了一些例子。
{"title":"On generalized Darboux frame of a spacelike curve lying on a lightlike surface in Minkowski space $mathbb{E}^{3}_{1}$","authors":"Jelena Djordjević, E. Nešović, U. Öztürk","doi":"10.55730/1300-0098.3399","DOIUrl":"https://doi.org/10.55730/1300-0098.3399","url":null,"abstract":": In this paper we introduce generalized Darboux frame of a spacelike curve α lying on a lightlike surface in Minkowski space E 31 . We prove that α has two such frames and obtain generalized Darboux frame’s equations. We find the relations between the curvature functions k g , k n , τ g of α with respect to its Darboux frame and the curvature functions ˜ k g , ˜ k n , ˜ τ g with respect to generalized Darboux frames. We show that such frames exist along a spacelike straight line lying on a ruled surface which is not entirely lightlike, but contains some lightlike points. We define lightlike ruled surfaces on which the tangent and the binormal indicatrix of a null Cartan curve are the principal curvature lines having ˜ τ g = 0 and give some 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":"42276723","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 prove the Kastler-Kalau-Walze type theorems for twisted Dirac operators on 5-dimensional manifolds with boundary.
本文证明了带边界的5维流形上扭曲Dirac算子的Kastler-Kalau-Wallze型定理。
{"title":"Twisted Dirac operators and the Kastler-Kalau-Walze type theorem for five dimensional manifolds with boundary","authors":"Tong Wu, Sining Wei, Yong Wang","doi":"10.55730/1300-0098.3372","DOIUrl":"https://doi.org/10.55730/1300-0098.3372","url":null,"abstract":": In this paper, we prove the Kastler-Kalau-Walze type theorems for twisted Dirac operators on 5-dimensional manifolds with boundary.","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":"49265899","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 consider a second-order nonlinear wave equation with a linear convolution term. When the convolution operator is taken as the identity operator, our equation reduces to the classical elasticity equation which can be written as a $p$-system of first-order differential equations. We first establish the local well-posedness of the Cauchy problem. We then investigate the behavior of solutions to the Cauchy problem in the limit as the kernel function of the convolution integral approaches to the Dirac delta function, that is, in the vanishing dispersion limit. We consider two different types of the vanishing dispersion limit behaviors for the convolution operator depending on the form of the kernel function. In both cases, we show that the solutions converge strongly to the corresponding solutions of the classical elasticity equation.
{"title":"Convergence of a linearly regularized nonlinear wave equation to the p-system","authors":"H. Erbay, S. Erbay, A. Erkip","doi":"10.55730/1300-0098.3407","DOIUrl":"https://doi.org/10.55730/1300-0098.3407","url":null,"abstract":"We consider a second-order nonlinear wave equation with a linear convolution term. When the convolution operator is taken as the identity operator, our equation reduces to the classical elasticity equation which can be written as a $p$-system of first-order differential equations. We first establish the local well-posedness of the Cauchy problem. We then investigate the behavior of solutions to the Cauchy problem in the limit as the kernel function of the convolution integral approaches to the Dirac delta function, that is, in the vanishing dispersion limit. We consider two different types of the vanishing dispersion limit behaviors for the convolution operator depending on the form of the kernel function. In both cases, we show that the solutions converge strongly to the corresponding solutions of the classical elasticity equation.","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":"44728769","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}
Tuangrat Chaichana, V. Laohakosol, Rattiya Meesa, Boonrod Yuttanan
: Let F q [ x ] be the ring of polynomials over a finite field F q and F q ( x ) its quotient field. Let P be the set of primes in F q [ x ] , and let I be the set of all polynomials f over F q ( x ) for which f ( P ) ⊆ F q [ x ] . The existence of a basis for I is established using the notion of characteristic ideal; this shows that I is a free F q [ x ] -module. Through localization, explicit shapes of certain bases for the localization of I are derived, and a well-known procedure is described as to how to obtain explicit forms of some bases of I .
{"title":"Polynomials taking integer values on primes in a function field","authors":"Tuangrat Chaichana, V. Laohakosol, Rattiya Meesa, Boonrod Yuttanan","doi":"10.55730/1300-0098.3413","DOIUrl":"https://doi.org/10.55730/1300-0098.3413","url":null,"abstract":": Let F q [ x ] be the ring of polynomials over a finite field F q and F q ( x ) its quotient field. Let P be the set of primes in F q [ x ] , and let I be the set of all polynomials f over F q ( x ) for which f ( P ) ⊆ F q [ x ] . The existence of a basis for I is established using the notion of characteristic ideal; this shows that I is a free F q [ x ] -module. Through localization, explicit shapes of certain bases for the localization of I are derived, and a well-known procedure is described as to how to obtain explicit forms of some bases of I .","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":"43442482","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}
: Let ( M, g ) be a compact Riemannian manifold. In this paper, we prove Struwe-type decomposition formulas for Palais-Smale sequences of functional energies corresponding to the equation:
{"title":"Struwe compactness results for a critical $p-$Laplacian equation involving critical and subcritical Hardy potential on compact Riemannian manifolds","authors":"T. Ghomari, Y. Maliki","doi":"10.55730/1300-0098.3421","DOIUrl":"https://doi.org/10.55730/1300-0098.3421","url":null,"abstract":": Let ( M, g ) be a compact Riemannian manifold. In this paper, we prove Struwe-type decomposition formulas for Palais-Smale sequences of functional energies corresponding to the equation:","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":"46780633","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}
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