This article aims to specify a new $C-$class function endows with altering distance and ultra altering distance function via generalized $Xi -$ contraction, which is called as the $mathcal{G}left( {Sigma ,vartheta ,Xi } right) - $contraction in modular $b-$metric space. Regarding these new contraction type mappings, the study includes some existence and uniqueness theorems, and to indicate the usability and productivity of these results, some applications related to integral type contractions and an application to the graph structure.
{"title":"On Some Fixed Point Theorems for G (Σ, θ , Ξ)− Contractions in Modular b−Metric Spaces","authors":"Abdurrahman Büyükkaya, M. Öztürk","doi":"10.33401/fujma.1107963","DOIUrl":"https://doi.org/10.33401/fujma.1107963","url":null,"abstract":"This article aims to specify a new $C-$class function endows with altering distance and ultra altering distance function via generalized $Xi -$ contraction, which is called as the $mathcal{G}left( {Sigma ,vartheta ,Xi } right) - $contraction in modular $b-$metric space. Regarding these new contraction type mappings, the study includes some existence and uniqueness theorems, and to indicate the usability and productivity of these results, some applications related to integral type contractions and an application to the graph structure.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124669306","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}
In this study, we consider a partitioned linear model with linear partial parameter constrains, known as a constrained partitioned linear model (CPLM), and its reduced models. A group of formulas on best linear unbiased predictors (BLUPs) and best linear unbiased estimators (BLUEs) in CPLM is derived via some quadratic matrix optimization methods, and further many basic properties of the predictors and estimators are established under some general assumptions. Our main purpose is to derive various inequalities and equalities for the comparison of covariance matrices of BLUPs and BLUEs under CPLM and its reduced models.
在本研究中,我们考虑了一个具有线性部分参数约束的分割线性模型,即约束分割线性模型(constrained partitioned linear model, CPLM)及其简化模型。利用二次矩阵优化方法导出了CPLM中最优线性无偏预测量和最优线性无偏估计量的一组公式,并在一些一般假设下建立了预测量和估计量的许多基本性质。我们的主要目的是推导出在CPLM及其简化模型下blup和BLUEs协方差矩阵比较的各种不等式和等式。
{"title":"On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models","authors":"Melek Eriş Büyükkaya, Nesrin Güler","doi":"10.33401/fujma.1134600","DOIUrl":"https://doi.org/10.33401/fujma.1134600","url":null,"abstract":"In this study, we consider a partitioned linear model with linear partial parameter constrains, known as a constrained partitioned linear model (CPLM), and its reduced models. A group of formulas on best linear unbiased predictors (BLUPs) and best linear unbiased estimators (BLUEs) in CPLM is derived via some quadratic matrix optimization methods, and further many basic properties of the predictors and estimators are established under some general assumptions. Our main purpose is to derive various inequalities and equalities for the comparison of covariance matrices of BLUPs and BLUEs under CPLM and its reduced models.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134104122","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}
In this paper, the intuitionistic fuzzy counterparts of the collineations defined in classical projective planes are defined in intuitionistic fuzzy projective planes. The properties of intuitionistic fuzzy projective plane left invariant under the intuitionistic fuzzy collineations are characterized depending on the base point, base line and the membership degrees of intuitionistic fuzzy projective plane.
{"title":"Characterization of Intuitionistic Fuzzy Collineations in Intuitionistic Fuzzy Projective Planes","authors":"E. Altıntaş, A. Bayar","doi":"10.33401/fujma.1049786","DOIUrl":"https://doi.org/10.33401/fujma.1049786","url":null,"abstract":"In this paper, the intuitionistic fuzzy counterparts of the collineations defined in classical projective planes are defined in intuitionistic fuzzy projective planes. The properties of intuitionistic fuzzy projective plane left invariant under the intuitionistic fuzzy collineations are characterized depending on the base point, base line and the membership degrees of intuitionistic fuzzy projective plane.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128442399","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}
In this paper, we give a new approach for Bertrand and Mannheim curves in 3D Lie groups with bi-invariant metric. By the this way, some conditions including the known results have been given for a curve to be Bertrand or Mannheim curve in 3D Euclidean space and in 3D Lie groups.
{"title":"Generalized Bertrand and Mannheim Curves in 3D Lie Groups","authors":"O. Okuyucu, Bahar Doğan Yazıcı","doi":"10.33401/fujma.1127839","DOIUrl":"https://doi.org/10.33401/fujma.1127839","url":null,"abstract":"In this paper, we give a new approach for Bertrand and Mannheim curves in 3D Lie groups \u0000with bi-invariant metric. By the this way, some conditions including the known results have \u0000been given for a curve to be Bertrand or Mannheim curve in 3D Euclidean space and in 3D \u0000Lie groups.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124094753","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}
Let $Wsubset mathbb{P}^5$ be a general complete intersection of a quadric hypersurface and a quartic hypersurface. In this paper we prove that $W$ contains only finitely many smooth curves $Csubset mathbb{P}^5$ such that $d:= deg ({C}) le 11$, $g:= p_a({C}) le 3$ and $h^1(mathcal{O} _C(1)) =0$.
设$W子集mathbb{P}^5$是二次超曲面与四次超曲面的一般完全交。本文证明了$W$只包含有限多条光滑曲线$C子集mathbb{P}^5$使得$d:= deg ({C}) le 11$, $g:= p_a({C}) le 3$和$h^1(mathcal{O} _C(1)) =0$。
{"title":"The finiteness of smooth curves of degree $le 11$ and genus $le 3$ on a general complete intersection of a quadric and a quartic in $mathbb{P}^5$","authors":"E. Ballico","doi":"10.33401/fujma.1069957","DOIUrl":"https://doi.org/10.33401/fujma.1069957","url":null,"abstract":"Let $Wsubset mathbb{P}^5$ be a general complete intersection of a quadric hypersurface and a quartic hypersurface. In this paper we prove that $W$ contains only finitely many smooth curves \u0000$Csubset mathbb{P}^5$ such that $d:= deg ({C}) le 11$, $g:= p_a({C}) le 3$ and $h^1(mathcal{O} _C(1)) =0$.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128616065","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}
Let $m$ be a positive integer. In this paper we consider the exponential Diophantine equation $(6m^{2}+1)^{x}+(3m^{2}-1)^{y}=(3m)^{z}$ and we show that it has only unique positive integer solution $(x,y,z)=(1,1,2)$ for all $ m>1. $ The proof depends on so called classification method and famous primitive divisor theorem.
{"title":"On the Exponential Diophantine Equation $(6m^{2}+1)^{x}+(3m^{2}-1)^{y}=(3m)^{z}$","authors":"M. Alan, Ruhsar Gizem Bi̇ratli","doi":"10.33401/fujma.1038699","DOIUrl":"https://doi.org/10.33401/fujma.1038699","url":null,"abstract":"Let $m$ be a positive integer. In this paper we consider the exponential Diophantine equation $(6m^{2}+1)^{x}+(3m^{2}-1)^{y}=(3m)^{z}$ and we show that it has only unique positive integer solution $(x,y,z)=(1,1,2)$ for all $ m>1. $ The proof depends on so called classification method and famous primitive divisor theorem.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121171337","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}
I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, in the light of recent evaluations of Neumann-Bessel series with trigonometric coefficients. A proper choice of the angle allows for an efficient choice of the trigonometric sum. Based on these series, I also obtain straightforward non-standard evaluations of new parametric sums with powers of cosine and sine functions.
{"title":"A note on trigonometric approximations of Bessel functions of the first kind, and trigonometric power sums","authors":"L. Molinari","doi":"10.33401/fujma.1166846","DOIUrl":"https://doi.org/10.33401/fujma.1166846","url":null,"abstract":"I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, in the light of recent evaluations of Neumann-Bessel series with trigonometric coefficients. A proper choice of the angle allows for \u0000an efficient choice of the trigonometric sum. Based on these series, I also obtain straightforward non-standard \u0000evaluations of new parametric sums with powers of cosine and sine functions.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114178339","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}
The surface patterns of natural and experimental deposits are important as they are a result of the internal microstructure. For this purpose, lacunarity analysis is applied to determine the heterogeneous nature of deposit surface patterns. In this study, images were digitally moved onto square mesh to determine the heterogeneous situation of manganese dendrite patterns on the natural manganese surface. The relation between the lacunarity values of the images and the box size were examined. The lacunarity values corresponding to the box size values was estimated using the gliding-box algorithm. This relation was determined numerically as a power-law function using nonlinear regression method. It has been shown that the system examined with the generated numerical model function can be defined with three specific parameters. As a result, it has been shown that it is possible to describe the relationship between numerical solution-based lacunarity-box size and also with a third-order nonlinear differential equation. With this study, the lacunarity-box size value on different system images can be determined by using the gliding box algorithm and calculating the coefficient value from the power-law relationship.
{"title":"Determination of Heterogeneity for Manganese Dendrites using Lacunarity Analysis","authors":"F. Evirgen, Mehmet Bayirli","doi":"10.33401/fujma.1037940","DOIUrl":"https://doi.org/10.33401/fujma.1037940","url":null,"abstract":"The surface patterns of natural and experimental deposits are important as they are a result of the internal microstructure. For this purpose, lacunarity analysis is applied to determine the heterogeneous nature of deposit surface patterns. In this study, images were digitally moved onto square mesh to determine the heterogeneous situation of manganese dendrite patterns on the natural manganese surface. The relation between the lacunarity values of the images and the box size were examined. The lacunarity values corresponding to the box size values was estimated using the gliding-box algorithm. This relation was determined numerically as a power-law function using nonlinear regression method. It has been shown that the system examined with the generated numerical model function can be defined with three specific parameters. As a result, it has been shown that it is possible to describe the relationship between numerical solution-based lacunarity-box size and also with a third-order nonlinear differential equation. With this study, the lacunarity-box size value on different system images can be determined by using the gliding box algorithm and calculating the coefficient value from the power-law relationship.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127663892","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}
In this paper, the bi-periodic mersenne sequence, which is a generalization of the mersenne sequence, is defined. The characteristic function, generating function and Binet's formula for this sequence are obtained. Also, using Binet's formula, some important identities and properties for this sequence are presented.
{"title":"On the Bi-Periodic Mersenne Sequence","authors":"Gül ÖZKAN KIZILIRMAK, D. Taşcı","doi":"10.33401/fujma.1078410","DOIUrl":"https://doi.org/10.33401/fujma.1078410","url":null,"abstract":"In this paper, the bi-periodic mersenne sequence, which is a generalization of the mersenne sequence, is defined. The characteristic function, generating function and Binet's formula for this sequence are obtained. Also, using Binet's formula, some important identities and properties for this sequence are presented.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125138190","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}
{"title":"Fixed Point Theorems in G - Fuzzy Convex Metric Spaces","authors":"M. Jeyaraman","doi":"10.33401/fujma.1034862","DOIUrl":"https://doi.org/10.33401/fujma.1034862","url":null,"abstract":"","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123951580","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}