M. B. D. Ngaha, Salomon Joseph Mbatakou, Romain Nimpa Pefoukeu
: In this paper, Szabó’s algorithm is used as the main tool to find locally symmetric left invariant Riemannian metrics on some 4 -dimensional Lie groups. Locally symmetric left invariant Riemannian Lie groups constitute an important subclass of Riemannian Lie groups with zero-divergence Weyl-tensor the so-called C-manifolds. Some properties of the curvature operator of these 4-dimensional C-manifolds are studied.
{"title":"Szabos algorithm and applications","authors":"M. B. D. Ngaha, Salomon Joseph Mbatakou, Romain Nimpa Pefoukeu","doi":"10.55730/1300-0098.3419","DOIUrl":"https://doi.org/10.55730/1300-0098.3419","url":null,"abstract":": In this paper, Szabó’s algorithm is used as the main tool to find locally symmetric left invariant Riemannian metrics on some 4 -dimensional Lie groups. Locally symmetric left invariant Riemannian Lie groups constitute an important subclass of Riemannian Lie groups with zero-divergence Weyl-tensor the so-called C-manifolds. Some properties of the curvature operator of these 4-dimensional C-manifolds are studied.","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":"45571953","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 results on Γ -hypersemigroups are obtained either as corollaries of corresponding results on ∨ e or poe - semigroups or on the line of the corresponding results on le -semigroups. It has come to our attention that Theorem 3.22 in [4] cannot be obtained as corollary to Theorem 2.2 of the same paper as for a Γ -hypersemigroup, ( P ∗ ( M ) , Γ , ⊆ ) is a ∨ e -semigroup and not an le -semigroup. Also on p. 1850, l. 12 in [4], the “ le -semigroup” should be changed to “ ∨ e -semigroup”. In the present paper we prove Theorems 3.26 and 3.28 stated without proof in [4]. On this occasion, some further results are given to emphasize what we say. The results on Γ -hypersemigroups are obtained from the more abstract structure of the poe -semigroups. Further investigation on poe -semigroups and le -semigroups is interesting.
{"title":"On $Gamma$-hypersemigroups","authors":"N. Kehayopulu","doi":"10.55730/1300-0098.3414","DOIUrl":"https://doi.org/10.55730/1300-0098.3414","url":null,"abstract":": The results on Γ -hypersemigroups are obtained either as corollaries of corresponding results on ∨ e or poe - semigroups or on the line of the corresponding results on le -semigroups. It has come to our attention that Theorem 3.22 in [4] cannot be obtained as corollary to Theorem 2.2 of the same paper as for a Γ -hypersemigroup, ( P ∗ ( M ) , Γ , ⊆ ) is a ∨ e -semigroup and not an le -semigroup. Also on p. 1850, l. 12 in [4], the “ le -semigroup” should be changed to “ ∨ e -semigroup”. In the present paper we prove Theorems 3.26 and 3.28 stated without proof in [4]. On this occasion, some further results are given to emphasize what we say. The results on Γ -hypersemigroups are obtained from the more abstract structure of the poe -semigroups. Further investigation on poe -semigroups and le -semigroups is interesting.","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":"46205260","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 develop and study an explicit time-space discrete discontinuous Galerkin finite element method to approximate the solution of one-dimensional nonlinear wave equations. We show that the numerical scheme is stable if a nonuniform time mesh is considered. We also investigate the blow-up phenomena and we prove that under weak convergence assumptions, the numerical blow-up time tends toward the theoretical one. The validity of our results is confirmed throughout several examples and benchmarks
{"title":"Discontinuous Galerkin method for blow-up solutions of nonlinear wave equations","authors":"Asma Azaiez, M. Benjemaa, Aida Jrajria, H. Zaag","doi":"10.55730/1300-0098.3408","DOIUrl":"https://doi.org/10.55730/1300-0098.3408","url":null,"abstract":": We develop and study an explicit time-space discrete discontinuous Galerkin finite element method to approximate the solution of one-dimensional nonlinear wave equations. We show that the numerical scheme is stable if a nonuniform time mesh is considered. We also investigate the blow-up phenomena and we prove that under weak convergence assumptions, the numerical blow-up time tends toward the theoretical one. The validity of our results is confirmed throughout several examples and benchmarks","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":"43484263","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 article is inspired by the reciprocal Catalan sums associated with problem 11765, proposed by David Beckwith and Sag Harbor. For this reason, partial derivative equations, the first-order linear differentiation equation and integral representations for series and generating functions for reciprocal Catalan-type sums containing the Catalan-type numbers are constructed. Some special values of these series and generating functions, which are given solutions of problem 11765, are found. Partial derivative equations of the generating function for the Catalan-type numbers are given. By using these equations, recurrence relations and derivative formulas involving these numbers are found. Finally, applying the p -adic Volkenborn integral to the Catalan-type polynomials, some combinatorial sums and identities involving the Bernoulli numbers, the Stirling numbers and the Catalan-type numbers are derived.
{"title":"Generating functions for reciprocal Catalan-type sums: approach to linear differentiation equation and ($p$-adic) integral equations","authors":"Damla Gün, Yilmaz Simsek","doi":"10.55730/1300-0098.3396","DOIUrl":"https://doi.org/10.55730/1300-0098.3396","url":null,"abstract":": This article is inspired by the reciprocal Catalan sums associated with problem 11765, proposed by David Beckwith and Sag Harbor. For this reason, partial derivative equations, the first-order linear differentiation equation and integral representations for series and generating functions for reciprocal Catalan-type sums containing the Catalan-type numbers are constructed. Some special values of these series and generating functions, which are given solutions of problem 11765, are found. Partial derivative equations of the generating function for the Catalan-type numbers are given. By using these equations, recurrence relations and derivative formulas involving these numbers are found. Finally, applying the p -adic Volkenborn integral to the Catalan-type polynomials, some combinatorial sums and identities involving the Bernoulli numbers, the Stirling numbers and the Catalan-type numbers are derived.","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":"43893427","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 prove that Bergman projections on weighted mixed norm spaces on smoothly bounded domains in R n are bounded for a certain range of parameters of such spaces and assuming certain conditions on weights. The proof relies on estimates of integral means of M p ( P γ f, r ) in terms of integral means of f . This result complements earlier result on boundedness of P γ on a closely related space L p,qα (Ω)
{"title":"Boundedness of Bergman projections acting on weighted mixed norm spaces","authors":"Ivana Savković","doi":"10.55730/1300-0098.3387","DOIUrl":"https://doi.org/10.55730/1300-0098.3387","url":null,"abstract":": We prove that Bergman projections on weighted mixed norm spaces on smoothly bounded domains in R n are bounded for a certain range of parameters of such spaces and assuming certain conditions on weights. The proof relies on estimates of integral means of M p ( P γ f, r ) in terms of integral means of f . This result complements earlier result on boundedness of P γ on a closely related space L p,qα (Ω)","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":"42093079","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 work, we investigate generalized coupled nonlinear Klein-Gordon equations with nonlinear damping and source terms and initial-boundary value conditions, in a bounded domain. We obtain decay of solutions by use of Nakao inequality. The blow up of solutions with negative initial energy is also established
{"title":"Energy decay and blow-up of solutions for a class of system of generalized nonlinear Klein-Gordon equations with source and damping terms","authors":"Z. S. Çelik, S. Gür, E. Pişkin","doi":"10.55730/1300-0098.3428","DOIUrl":"https://doi.org/10.55730/1300-0098.3428","url":null,"abstract":": In this work, we investigate generalized coupled nonlinear Klein-Gordon equations with nonlinear damping and source terms and initial-boundary value conditions, in a bounded domain. We obtain decay of solutions by use of Nakao inequality. The blow up of solutions with negative initial energy is also established","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":"46409680","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, the main identities on locally product-like statistical submersions are obtained with the aid of statistical structures and their Riemannian curvature tensors. Some examples of locally product-like statistical submersions are presented. Some results on F -invariant, F ∗ -invariant and antiinvariant locally product-like statistical submersions are given
{"title":"Locally product-like statistical submersions","authors":"K. Takano, Esra Erkan, M. Gülbahar","doi":"10.55730/1300-0098.3397","DOIUrl":"https://doi.org/10.55730/1300-0098.3397","url":null,"abstract":": In this paper, the main identities on locally product-like statistical submersions are obtained with the aid of statistical structures and their Riemannian curvature tensors. Some examples of locally product-like statistical submersions are presented. Some results on F -invariant, F ∗ -invariant and antiinvariant locally product-like statistical submersions are given","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":"44946746","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 ring R is called semiclean if every element of R can be expressed as sum of a periodic element and a unit. In this paper, we introduce a new class of ring, which is the ∗ -version of the semiclean ring, i.e. the ∗ -semiclean ring. A ∗ -ring is ∗ -semiclean if each element is a sum of a ∗ -periodic element and a unit. The term ∗ -semiclean is a stronger notion than semiclean. In this paper, many properties of ∗ -semiclean rings are discussed. It is proved that if p ∈ P ( R ) such that pRp and (1 − p ) R (1 − p ) are ∗ -semiclean rings, then R is also a ∗ -semiclean ring. As a result, the matrix ring M n ( R ) over a ∗ -semiclean ring is ∗ -semiclean. A characterization that when the group rings RC r and RG are ∗ -semiclean is done, where R is a finite commutative local ring, C r is a cyclic group of order r , and G is a locally finite abelian group. We have also found sufficient conditions when the group rings RC 3 , RC 4 , RQ 8 , and RQ 2 n are ∗ -semiclean, where R is a commutative local ring. We have also demonstrated that the group ring Z 2 D 6 is a ∗ -semiclean ring (which is not a ∗ -clean ring).
{"title":"$ast$-Semiclean rings","authors":"Shefali Gupta, Dinesh Udar","doi":"10.55730/1300-0098.3437","DOIUrl":"https://doi.org/10.55730/1300-0098.3437","url":null,"abstract":": A ring R is called semiclean if every element of R can be expressed as sum of a periodic element and a unit. In this paper, we introduce a new class of ring, which is the ∗ -version of the semiclean ring, i.e. the ∗ -semiclean ring. A ∗ -ring is ∗ -semiclean if each element is a sum of a ∗ -periodic element and a unit. The term ∗ -semiclean is a stronger notion than semiclean. In this paper, many properties of ∗ -semiclean rings are discussed. It is proved that if p ∈ P ( R ) such that pRp and (1 − p ) R (1 − p ) are ∗ -semiclean rings, then R is also a ∗ -semiclean ring. As a result, the matrix ring M n ( R ) over a ∗ -semiclean ring is ∗ -semiclean. A characterization that when the group rings RC r and RG are ∗ -semiclean is done, where R is a finite commutative local ring, C r is a cyclic group of order r , and G is a locally finite abelian group. We have also found sufficient conditions when the group rings RC 3 , RC 4 , RQ 8 , and RQ 2 n are ∗ -semiclean, where R is a commutative local ring. We have also demonstrated that the group ring Z 2 D 6 is a ∗ -semiclean ring (which is not a ∗ -clean ring).","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":"43048230","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 the present manuscript, the Benjamin-Bona-Mahony-Burgers (BBMB) equation will be handled numerically by Strang time-splitting technique. While applying this technique, collocation method based on quintic B-spline basis functions is applied. In line with our purpose, after splitting the BBM-Burgers equation given with appropriate initial boundary conditions into two subequations containing the derivative in terms of time, the quintic B-spline based collocation finite element method (FEM) for spatial discretization and the suitable finite difference approaches for time discretization is applied to each subequation and hereby two different systems of algebraic equations are obtained. Four test problems are utilized to test the efficiency and reliability of the presented method. The error norms L 2 and L ∞ with mass, energy, and momentum conservation constants I 1 , I 2 and I 3 , respectively, are computed. To do a comparison with the other studies in the literature, the newly found approximate solutions are exhibited in both tabular and graphical formats. Also, stability analysis of numerical approach by the von Neumann method is researched.
：在本手稿中，Benjamin Bona Mahony Burgers（BBMB）方程将通过Strang时间分裂技术进行数值处理。在应用该技术的同时，采用了基于五次B样条基函数的配置方法。根据我们的目的，在将具有适当初始边界条件的BBM-Burgers方程分解为包含时间导数的两个子方程后，将基于五次B样条的配置有限元方法（FEM）用于空间离散化，并将合适的有限差分方法用于时间离散化，从而获得两个不同的代数方程组。利用四个测试问题来测试所提出方法的有效性和可靠性。计算了质量、能量和动量守恒常数分别为I1、I2和I3的误差范数L2和L∞。为了与文献中的其他研究进行比较，新发现的近似解以表格和图形形式显示。此外，还研究了冯-诺依曼方法数值逼近的稳定性分析。
{"title":"Numerical solution for Benjamin-Bona-Mahony-Burgers equation with Strang time-splitting technique","authors":"Melike Karta","doi":"10.55730/1300-0098.3377","DOIUrl":"https://doi.org/10.55730/1300-0098.3377","url":null,"abstract":": In the present manuscript, the Benjamin-Bona-Mahony-Burgers (BBMB) equation will be handled numerically by Strang time-splitting technique. While applying this technique, collocation method based on quintic B-spline basis functions is applied. In line with our purpose, after splitting the BBM-Burgers equation given with appropriate initial boundary conditions into two subequations containing the derivative in terms of time, the quintic B-spline based collocation finite element method (FEM) for spatial discretization and the suitable finite difference approaches for time discretization is applied to each subequation and hereby two different systems of algebraic equations are obtained. Four test problems are utilized to test the efficiency and reliability of the presented method. The error norms L 2 and L ∞ with mass, energy, and momentum conservation constants I 1 , I 2 and I 3 , respectively, are computed. To do a comparison with the other studies in the literature, the newly found approximate solutions are exhibited in both tabular and graphical formats. Also, stability analysis of numerical approach by the von Neumann method is researched.","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":"42273138","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 an initial value problem related to the equation
我们考虑一个与方程有关的初值问题
{"title":"Blow-up of solutions for wave equation with multiple ?(x)-Laplacian and variable exponent nonlinearities","authors":"A. Khaldi, Amar Ouaoua, M. Maouni","doi":"10.55730/1300-0098.3409","DOIUrl":"https://doi.org/10.55730/1300-0098.3409","url":null,"abstract":": We consider an initial value problem related 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":"43943490","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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