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Turkish Journal of Mathematics and Computer Science最新文献

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On the Convergence of Stochastic Aggregated Gradient Method 关于随机聚集梯度法的收敛性
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-06-30 DOI: 10.47000/tjmcs.1037384
Figen OZTOPRAK TOPKAYA
{"title":"On the Convergence of Stochastic Aggregated Gradient Method","authors":"Figen OZTOPRAK TOPKAYA","doi":"10.47000/tjmcs.1037384","DOIUrl":"https://doi.org/10.47000/tjmcs.1037384","url":null,"abstract":"The minimization problem of the sum of a large set of convex functions arises in various applications. Methods such as incremental gradient, stochastic gradient, and aggregated gradient are popular choices for solving those problems as they do not require a full gradient evaluation at every iteration. In this paper, we analyze a generalization of the stochastic aggregated gradient method via an alternative technique based on the convergence of iterative linear systems. The technique provides a short proof for the $O(kappa^{-1})$ linear convergence rate in the quadratic case. We observe that the technique is rather restrictive for the general case, and can provide weaker results.","PeriodicalId":177259,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122444778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On $(k,mu )$-Paracontact Manifold Satisfying Some Curvature Conditions $(k，mu)$-副接触流形满足某些曲率条件
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-06-30 DOI: 10.47000/tjmcs.1153650
Pakize Uygun, M. Atc̣eken
{"title":"On $(k,mu )$-Paracontact Manifold Satisfying Some Curvature Conditions","authors":"Pakize Uygun, M. Atc̣eken","doi":"10.47000/tjmcs.1153650","DOIUrl":"https://doi.org/10.47000/tjmcs.1153650","url":null,"abstract":"In this work, we studied the curvature tensors of (k,$mu$) satisfying the conditions $widetilde{Z}(xi ,alpha _{3})cdot P=0$, $widetilde{Z}(xi ,alpha _{3})cdot S=0$, $R(xi ,alpha _{3})cdot P=0$, $R(xi ,alpha _{3})cdot S=0$ and $Pcdot C=0$. Besides this, we classify $(k,mu)$-paracontact manifolds. Also we researched conformally flat and $phi $-conformally flat a $(k,mu )-$paracontact metric manifolds.","PeriodicalId":177259,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"16 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122446342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hyper-Fibonacci and Hyper-Lucas Polynomials 超斐波那契和超卢卡斯多项式
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-06-30 DOI: 10.47000/tjmcs.1123369
Efruz Özlem Mersin
{"title":"Hyper-Fibonacci and Hyper-Lucas Polynomials","authors":"Efruz Özlem Mersin","doi":"10.47000/tjmcs.1123369","DOIUrl":"https://doi.org/10.47000/tjmcs.1123369","url":null,"abstract":"In this paper, hyper-Fibonacci and hyper-Lucas polynomials are defined and some of their algebraic and combinatorial properties such as the recurrence relations, summation formulas, and generating functions are presented. In addition, some relationships between the hyper-Fibonacci and hyper-Lucas polynomials are given.","PeriodicalId":177259,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132420831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Some New Improvements of Huygen's Inequality 惠更不等式的几个新改进
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-06-30 DOI: 10.47000/tjmcs.1167007
Seyran İbrahi̇mov, Ahmad Issa
{"title":"Some New Improvements of Huygen's Inequality","authors":"Seyran İbrahi̇mov, Ahmad Issa","doi":"10.47000/tjmcs.1167007","DOIUrl":"https://doi.org/10.47000/tjmcs.1167007","url":null,"abstract":"First, some improvements of Young’s inequality are given in this article. Then, using these improve- \u0000ments, stronger results were obtained from the Huygens inequality.","PeriodicalId":177259,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122801642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New Fractional Operators Including Wright Function in Their Kernels 核中包含Wright函数的新分数算子
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-06-30 DOI: 10.47000/tjmcs.999775
E. Ata, İ. O. Kıymaz
{"title":"New Fractional Operators Including Wright Function in Their Kernels","authors":"E. Ata, İ. O. Kıymaz","doi":"10.47000/tjmcs.999775","DOIUrl":"https://doi.org/10.47000/tjmcs.999775","url":null,"abstract":"In this paper, we defined new two-fractional derivative operators with a Wright function in their kernels. We also gave their Laplace and inverse Laplace transforms. Then, we presented some connections between the new fractional operators. Furthermore, as examples, we obtained solutions of differential equations involving new fractional operators. Finally, we examined the relations of the new fractional operators with the fractional operators, which can be found in the literature.","PeriodicalId":177259,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121141612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Padovan, Perrin and Pell-Padovan Dual Quaternions Padovan, Perrin和Pell-Padovan对偶四元数
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-06-30 DOI: 10.47000/tjmcs.999069
Zehra İşbilir, N. Gürses
{"title":"Padovan, Perrin and Pell-Padovan Dual Quaternions","authors":"Zehra İşbilir, N. Gürses","doi":"10.47000/tjmcs.999069","DOIUrl":"https://doi.org/10.47000/tjmcs.999069","url":null,"abstract":"In this present study, we intend to determine the Padovan, Perrin and Pell-Padovan dual quaternions with nonnegative and negative subscripts. In line with this purpose, we construct some new properties such as; special determinant equalities, new recurrence relations, matrix formulas, Binet-like formulas, generating functions, exponential generating functions, summation formulas, and binomial properties for these special dual quaternions.","PeriodicalId":177259,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"410 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115231780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A Note on Invariant Submanifolds of Metallic Riemannian Manifolds 关于金属黎曼流形的不变子流形的一个注记
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-06-30 DOI: 10.47000/tjmcs.1110240
Mustafa Gök
{"title":"A Note on Invariant Submanifolds of Metallic Riemannian Manifolds","authors":"Mustafa Gök","doi":"10.47000/tjmcs.1110240","DOIUrl":"https://doi.org/10.47000/tjmcs.1110240","url":null,"abstract":"The goal of this paper is to examine invariant submanifolds in metallic Riemannian manifolds with the help of induced structures on them by the metallic Riemannian structure of the ambient manifold. We obtain a useful characterization of invariant submanifolds. Wealso discuss some necessary conditions for invariant submanifolds to be totally geodesic. Finally, we provide an example of an invariant submanifold.","PeriodicalId":177259,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114804051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Quaternions with Gaussian Oresme Coefficients 关于高斯奥勒姆系数的四元数
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-06-30 DOI: 10.47000/tjmcs.1133973
Fatih Yılmaz, Aybüke Ertaş
{"title":"On Quaternions with Gaussian Oresme Coefficients","authors":"Fatih Yılmaz, Aybüke Ertaş","doi":"10.47000/tjmcs.1133973","DOIUrl":"https://doi.org/10.47000/tjmcs.1133973","url":null,"abstract":"At this paper, we describe Gaussian Oresme numbers taking into account the Oresme numbers. Furthermore, we investigate their some basic characteristic properties such as Binet formula and Cassini identity, etc. Moreover, we define quaternions with Gaussian Oresme coefficients and obtain their some spectacular properties.","PeriodicalId":177259,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115868304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Catalan Numbers in Terms of $(alpha, k)-$Gamma Function and $(alpha, k)-$Beta Function 用$(alpha, k)-$Gamma函数和$(alpha, k)-$Beta函数表示的加泰罗尼亚数字
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-06-30 DOI: 10.47000/tjmcs.1182387
A. Akkurt, H. Yildirim
{"title":"Catalan Numbers in Terms of $(alpha, k)-$Gamma Function and $(alpha, k)-$Beta Function","authors":"A. Akkurt, H. Yildirim","doi":"10.47000/tjmcs.1182387","DOIUrl":"https://doi.org/10.47000/tjmcs.1182387","url":null,"abstract":"In the paper, the authors discuss some extended results involving the Catalan numbers and establish an integral representation of the Catalan numbers in terms of the $(alpha,k)$-gamma and $(alpha,k)$-beta function. We refer to the results available in the literature by giving special values to the parameters in the obtained theorems.","PeriodicalId":177259,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127447682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximately Gamma-Near Rings 近似伽马近环
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-03-07 DOI: 10.47000/tjmcs.938957
M. Uçkun, Mehmet Gürbüzcan
{"title":"Approximately Gamma-Near Rings","authors":"M. Uçkun, Mehmet Gürbüzcan","doi":"10.47000/tjmcs.938957","DOIUrl":"https://doi.org/10.47000/tjmcs.938957","url":null,"abstract":"The focus of this work is to introduce approximately gamma-near ring, approximately gamma-ideal and approximately \u0000gamma-near ring of all descriptive approximately cosets. Also, some properties of approximately gamma-near ring and \u0000approximately gamma-ideal were given.","PeriodicalId":177259,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114234270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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