: We introduce and study a deformation of the geodesic curvature for a given spherical curve γ . Also, we define a new type of evolute and two Fermi-Walker type derivatives for γ . Some concrete examples are detailed with a special attention towards space curves with a constant torsion
{"title":"The flow-geodesic curvature and the flow-evolute of spherical curves","authors":"M. Crășmăreanu","doi":"10.55730/1300-0098.3538","DOIUrl":"https://doi.org/10.55730/1300-0098.3538","url":null,"abstract":": We introduce and study a deformation of the geodesic curvature for a given spherical curve γ . Also, we define a new type of evolute and two Fermi-Walker type derivatives for γ . Some concrete examples are detailed with a special attention towards space curves with a constant torsion","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141682333","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 group Γ is said to be CCII if the quotient Γ /Z (Γ) is 2 -Engel or, equivalently, commutator-inversion invariant, where Z (Γ) is the center of Γ . In this article, we prove algebraic and topological properties of gyrogroups that are induced by CCII groups. Then, using a classification of non-abelian groups of order n with n < 32 , we determine all finite CCII groups of order less than 32 .
{"title":"Properties of gyrogroups induced by groups whose central quotients being 2-Engel","authors":"Jaturon Wattanapan, T. Suksumran","doi":"10.55730/1300-0098.3531","DOIUrl":"https://doi.org/10.55730/1300-0098.3531","url":null,"abstract":": A group Γ is said to be CCII if the quotient Γ /Z (Γ) is 2 -Engel or, equivalently, commutator-inversion invariant, where Z (Γ) is the center of Γ . In this article, we prove algebraic and topological properties of gyrogroups that are induced by CCII groups. Then, using a classification of non-abelian groups of order n with n < 32 , we determine all finite CCII groups of order less than 32 .","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141682124","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, Caputo boundary value problems of order 3 < ζ ≤ 4 are investigated on the interval [0 , 1] . By Guo-Krasnoselskii fixed point theorem, some criteria of existence and multiplicity of positive and decreasing solutions are established. The main novelty of the paper lies in its capability to achieve positive solutions while the corresponding Green’s function changes sign. Finally, two examples are provided to illustrate the application of these results.
{"title":"Positive and decreasing solutions for higher order Caputo boundary valueproblems with sign-changing Green’s function","authors":"Rian Yan, Yige Zhao, Xuan Leng, Yabing Li","doi":"10.55730/1300-0098.3532","DOIUrl":"https://doi.org/10.55730/1300-0098.3532","url":null,"abstract":": In this paper, Caputo boundary value problems of order 3 < ζ ≤ 4 are investigated on the interval [0 , 1] . By Guo-Krasnoselskii fixed point theorem, some criteria of existence and multiplicity of positive and decreasing solutions are established. The main novelty of the paper lies in its capability to achieve positive solutions while the corresponding Green’s function changes sign. Finally, two examples are provided to illustrate the application of these results.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141681106","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 study Bernstein-Nikol’skii-Markov type inequalities for arbitrary algebraic polynomials with respect to a weighted Lebesgue space, where the weight functions have some singularities on a given contour. We consider curves which can contain a finite number of exterior and interior corners with power law tangency of the boundary arcs at those points where the weight functions have both zeros and poles of finite order. The estimates are given for the growth of the module of derivatives for algebraic polynomials on the closure of a region bounded by a given curve, depending on the behavior of weight functions, on the property of curve, and on the degree of contact of the boundary arcs, which form zero angles on the boundary.
{"title":"Bernstein-Nikol’skii-Markov-type inequalities for algebraic polynomials in aweighted Lebesgue space in regions with cusps","authors":"U. Değer, Fahreddi̇n Abdullayev","doi":"10.55730/1300-0098.3536","DOIUrl":"https://doi.org/10.55730/1300-0098.3536","url":null,"abstract":": In this paper, we study Bernstein-Nikol’skii-Markov type inequalities for arbitrary algebraic polynomials with respect to a weighted Lebesgue space, where the weight functions have some singularities on a given contour. We consider curves which can contain a finite number of exterior and interior corners with power law tangency of the boundary arcs at those points where the weight functions have both zeros and poles of finite order. The estimates are given for the growth of the module of derivatives for algebraic polynomials on the closure of a region bounded by a given curve, depending on the behavior of weight functions, on the property of curve, and on the degree of contact of the boundary arcs, which form zero angles on the boundary.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141681534","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 study, we investigate the m -th order elliptic operators on n -dimensional bounded domain Ω ⊂ R n with discontinuous coefficients in the rearrangement-invariant Sobolev space W mX (Ω) . In general, the considered rearrangement-invariant spaces are not separable, so the use of classical methods in these spaces requires substantial modification of classical methods and a lot of preparation, concerning correctness of substitution operator, problems related to the extension operator in such spaces, etc. For this purpose, the corresponding separable subspaces of these spaces, in which the set of compact supported infinitely differentiable functions is dense, are introduced based on the shift operator. We establish interior Schauder-type estimates in the above subspaces. Note that Lebesgue spaces L p (Ω) , grand-Lebesgue spaces, Marcinkiewicz spaces, weak-type L wp spaces, etc. are also covered by such spaces.
:在本研究中，我们研究了 n 维有界域 Ω ⊂ R n 上的 m 阶椭圆算子，这些算子在重排不变 Sobolev 空间 W mX (Ω) 中具有不连续系数。一般来说，所考虑的重排不变空间是不可分离的，因此在这些空间中使用经典方法需要对经典方法进行大量修改，并进行大量准备工作，涉及置换算子的正确性、与此类空间中扩展算子有关的问题等。为此，我们根据移位算子引入了这些空间的相应可分离子空间，其中紧凑支持的无穷微分函数集是密集的。我们在上述子空间中建立了内部肖德型估计。需要注意的是，Lebesgue 空间 L p (Ω) 、grand-Lebesgue 空间、Marcinkiewicz 空间、弱型 L wp 空间等也属于此类空间的范畴。
{"title":"Interior Schauder-type estimates for m − th order elliptic operators inrearrangement-invariant Sobolev spaces","authors":"Emi̇nağa M. Mamedov, S. Cetin","doi":"10.55730/1300-0098.3541","DOIUrl":"https://doi.org/10.55730/1300-0098.3541","url":null,"abstract":": In this study, we investigate the m -th order elliptic operators on n -dimensional bounded domain Ω ⊂ R n with discontinuous coefficients in the rearrangement-invariant Sobolev space W mX (Ω) . In general, the considered rearrangement-invariant spaces are not separable, so the use of classical methods in these spaces requires substantial modification of classical methods and a lot of preparation, concerning correctness of substitution operator, problems related to the extension operator in such spaces, etc. For this purpose, the corresponding separable subspaces of these spaces, in which the set of compact supported infinitely differentiable functions is dense, are introduced based on the shift operator. We establish interior Schauder-type estimates in the above subspaces. Note that Lebesgue spaces L p (Ω) , grand-Lebesgue spaces, Marcinkiewicz spaces, weak-type L wp spaces, etc. are also covered by such spaces.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141682688","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}
: This paper addresses the second-order nonlocal dynamic thermistor problem with two-point boundary conditions on time scales. Utilizing the fixed point theorems by Schaefer and Rus, we establish some sufficient conditions for the existence and uniqueness of solutions. Furthermore, we discuss the continuous dependence of solutions and four types of Ulam stability. We provide examples to support the applicability of our results
:本文探讨了时间尺度上具有两点边界条件的二阶非局部动态热敏电阻问题。利用 Schaefer 和 Rus 的定点定理，我们建立了一些解的存在性和唯一性的充分条件。此外，我们还讨论了解的连续依赖性和四种乌兰稳定性。我们举例说明了我们结果的适用性
{"title":"Some Qualitative Results for Nonlocal Dynamic Boundary Value Problem of Thermistor Type","authors":"S. Georgiev, Mahammad Khuddush, Sanket Tikare","doi":"10.55730/1300-0098.3539","DOIUrl":"https://doi.org/10.55730/1300-0098.3539","url":null,"abstract":": This paper addresses the second-order nonlocal dynamic thermistor problem with two-point boundary conditions on time scales. Utilizing the fixed point theorems by Schaefer and Rus, we establish some sufficient conditions for the existence and uniqueness of solutions. Furthermore, we discuss the continuous dependence of solutions and four types of Ulam stability. We provide examples to support the applicability of our results","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141683088","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":"Stacks in Einstein gravity","authors":"Kadri .Ilker Berktav","doi":"10.55730/1300-0098.3534","DOIUrl":"https://doi.org/10.55730/1300-0098.3534","url":null,"abstract":"","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141683452","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":"On a class of permutation trinomials over finite fields","authors":"Burcu GÜLMEZ TEMÜR, Buket Özkaya","doi":"10.55730/1300-0098.3540","DOIUrl":"https://doi.org/10.55730/1300-0098.3540","url":null,"abstract":"","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141681523","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":"New oscillation criteria for first-order differential equations with general delayargument","authors":"E. R. Attia, Irena Jadlovská","doi":"10.55730/1300-0098.3537","DOIUrl":"https://doi.org/10.55730/1300-0098.3537","url":null,"abstract":"","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141681414","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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