Pub Date : 2023-06-23DOI: 10.31801/cfsuasmas.1114983
R. Savaş
In 1971, the definition of Orlicz $widetilde{phi}$ functions was introduced by Lindenstrauss and Tzafriri and moreover in 2006, the notion of double lacunary sequences was presented by Savaş and Patterson. The primary focus of this article is to introduce the double statistically $widetilde{phi }$-convergence and double lacunary statistically $widetilde{phi }$-convergence which are generalizations of the double statistically convergence [19] and double lacunary statistically convergence [24]. Additionally, some essential inclusion theorems are examined.
{"title":"New summability methods via $widetilde{phi}$ functions","authors":"R. Savaş","doi":"10.31801/cfsuasmas.1114983","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1114983","url":null,"abstract":"In 1971, the definition of Orlicz $widetilde{phi}$ functions was introduced by Lindenstrauss and Tzafriri and moreover in 2006, the notion of double lacunary sequences was presented by Savaş and Patterson. The primary focus of this article is to introduce the double statistically $widetilde{phi }$-convergence and double lacunary statistically $widetilde{phi }$-convergence which are generalizations of the double statistically convergence [19] and double lacunary statistically convergence [24]. Additionally, some essential inclusion theorems are examined.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44654381","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}
Pub Date : 2023-06-23DOI: 10.31801/cfsuasmas.1124351
Canan Sümbül, Cemal Belen, M. Yıldırım
In this study, we define a new type of statistical limit point using the notions of statistical convergence with respect to the $J_p$ power series method and then we present some examples to show the relations between these points and ordinary limit points. After that we also study statistical limit points of a sequence with the help of a modulus function in the sense of the $J_p$ power series method. Namely, we define $f-J_p$-statistical limit and cluster points of the real sequences and compare the set of these limit points with the set of ordinary points.
{"title":"On statistical limit points with respect to power series methods and modulus functions","authors":"Canan Sümbül, Cemal Belen, M. Yıldırım","doi":"10.31801/cfsuasmas.1124351","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1124351","url":null,"abstract":"In this study, we define a new type of statistical limit point using the notions of statistical convergence with respect to the $J_p$ power series method and then we present some examples to show the relations between these points and ordinary limit points. After that we also study statistical limit points of a sequence with the help of a modulus function in the sense of the $J_p$ power series method. Namely, we define $f-J_p$-statistical limit and cluster points of the real sequences and compare the set of these limit points with the set of ordinary points.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47333476","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}
Pub Date : 2023-06-23DOI: 10.31801/cfsuasmas.1067247
F. Ocak
Let $(M,nabla)$ be an $n$-dimensional differentiable manifold with a torsion-free linear connection and $T^{*}M$ its cotangent bundle. In this context we study some properties of the natural Riemann extension (M. Sekizawa (1987), O. Kowalski and M. Sekizawa (2011)) on the cotangent bundle $T^{*}M$. First, we give an alternative definition of the natural Riemann extension with respect to horizontal and vertical lifts. Secondly, we investigate metric connection for the natural Riemann extension. Finally, we present geodesics on the cotangent bundle $T^{*}M$ endowed with the natural Riemann extension.
设$(M，nabla)$是一个具有无扭线性连接的n维可微流形，且$T^{*}M$是它的余切束。在这种情况下，我们研究了余切束$T^{*}M$上的自然黎曼扩展(M. Sekizawa (1987)， O. Kowalski和M. Sekizawa(2011))的一些性质。首先，我们给出了关于水平和垂直提升的自然黎曼扩展的另一种定义。其次，我们研究了自然黎曼扩展的度量联系。最后，给出了具有自然黎曼扩展的余切束$T^{*}M$上的测地线。
{"title":"Notes on some properties of the natural Riemann extension","authors":"F. Ocak","doi":"10.31801/cfsuasmas.1067247","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1067247","url":null,"abstract":"Let $(M,nabla)$ be an $n$-dimensional differentiable manifold with a torsion-free linear connection and $T^{*}M$ its cotangent bundle. In this context we study some properties of the natural Riemann extension (M. Sekizawa (1987), O. Kowalski and M. Sekizawa (2011)) on the cotangent bundle $T^{*}M$. First, we give an alternative definition of the natural Riemann extension with respect to horizontal and vertical lifts. Secondly, we investigate metric connection for the natural Riemann extension. Finally, we present geodesics on the cotangent bundle $T^{*}M$ endowed with the natural Riemann extension.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48862624","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}
Pub Date : 2023-06-23DOI: 10.31801/cfsuasmas.1127250
İbrahim Teki̇n
In this article, identification of the time-dependent lowest term in a fourth order in time partial differential equation (PDE) from knowledge of a boundary measurement is studied by means of contraction mapping.
{"title":"Identification of the time-dependent lowest term in a fourth order in time partial differential equation","authors":"İbrahim Teki̇n","doi":"10.31801/cfsuasmas.1127250","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1127250","url":null,"abstract":"In this article, identification of the time-dependent lowest term in a fourth order in time partial differential equation (PDE) from knowledge of a boundary measurement is studied by means of contraction mapping.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42249286","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}
Pub Date : 2023-06-23DOI: 10.31801/cfsuasmas.1187009
Serdar Cihat Gören, O. Arslan
This article aims to determine the features affecting the price of a product with the hedonic regression model and to estimate the contribution of each feature to the price by using robust regression estimation methods. For the analysis, the price and feature information of the laptop product group were obtained from the big data source by using the web scraping method. Four alternatives of the hedonic regression model are used to determine the features affecting the price of the laptops. The contribution of each feature to the laptop price is estimated by using the robust (Huber M-estimator) estimation method and the Ordinary Least Squares (OLS) estimation method, and the resulting estimates are compared for both methods. In the framework of the data set used in the study, it is observed that the effective model is the Logarithmic Robust Hedonic Regression Model.
{"title":"A study on using robust hedonic regression implementation","authors":"Serdar Cihat Gören, O. Arslan","doi":"10.31801/cfsuasmas.1187009","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1187009","url":null,"abstract":"This article aims to determine the features affecting the price of a product with the hedonic regression model and to estimate the contribution of each feature to the price by using robust regression estimation methods. For the analysis, the price and feature information of the laptop product group were obtained from the big data source by using the web scraping method. Four alternatives of the hedonic regression model are used to determine the features affecting the price of the laptops. The contribution of each feature to the laptop price is estimated by using the robust (Huber M-estimator) estimation method and the Ordinary Least Squares (OLS) estimation method, and the resulting estimates are compared for both methods. In the framework of the data set used in the study, it is observed that the effective model is the Logarithmic Robust Hedonic Regression Model.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47240737","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}
Pub Date : 2023-06-23DOI: 10.31801/cfsuasmas.1087827
P. Senel
In this paper FHD flow in a rectangular pipe constricted by two analogous semi-cylinders attached to the left and the bottom walls is investigated. The laminar, axial flow is produced by a constant pressure gradient, and the flow is affected by a spatially varying non-uniform magnetic field caused by two electric wires. The current-carrying wires are placed along the axes of the semi-cylinders. The fully developed flow is studied on the 2D cross-section of the pipe, a cavity, where the wires act as point magnetic sources. The pressure equation is added to the mathematical model, and the velocity-pressure form governing equations are numerically solved by the dual reciprocity boundary element method (DRBEM). The Dirichlet type pressure boundary conditions are approximated through a process using the radial basis functions and a finite difference. The flow, velocity, and pressure variations are investigated for different magnetic field strengths and current ratios. The grid independence study is also carried out. The proposed iterative scheme is capable of generating numerical results by performing a non-uniform discretization for the boundary. Dense discretizations are applied at the places where the flow shows a sudden fluctuation. It is shown by the numerical results that the flow and the pressure variations are dominated by the strong magnetic source. With an increment in the magnetic number, the planar flow is accelerated, the axial flow is decelerated, and the pressure increases, especially around the strong point magnetic source.
{"title":"FHD flow in an irregular cavity subjected to a non-uniform magnetic field","authors":"P. Senel","doi":"10.31801/cfsuasmas.1087827","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1087827","url":null,"abstract":"In this paper FHD flow in a rectangular pipe constricted by two analogous semi-cylinders attached to the left and the bottom walls is investigated. The laminar, axial flow is produced by a constant pressure gradient, and the flow is affected by a spatially varying non-uniform magnetic field caused by two electric wires. The current-carrying wires are placed along the axes of the semi-cylinders. The fully developed flow is studied on the 2D cross-section of the pipe, a cavity, where the wires act as point magnetic sources. The pressure equation is added to the mathematical model, and the velocity-pressure form governing equations are numerically solved by the dual reciprocity boundary element method (DRBEM). The Dirichlet type pressure boundary conditions are approximated through a process using the radial basis functions and a finite difference. The flow, velocity, and pressure variations are investigated for different magnetic field strengths and current ratios. The grid independence study is also carried out. The proposed iterative scheme is capable of generating numerical results by performing a non-uniform discretization for the boundary. Dense discretizations are applied at the places where the flow shows a sudden fluctuation. It is shown by the numerical results that the flow and the pressure variations are dominated by the strong magnetic source. With an increment in the magnetic number, the planar flow is accelerated, the axial flow is decelerated, and the pressure increases, especially around the strong point magnetic source.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48874176","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}
Pub Date : 2023-06-23DOI: 10.31801/cfsuasmas.1163955
Merve Kara, Ömer Aktaş
In this study, we show that the system of difference equations begin{align} x_{n}=frac{x_{n-2}y_{n-3}}{y_{n-1}left(a+bx_{n-2}y_{n-3} right) }, nonumber y_{n}=frac{y_{n-2}z_{n-3}}{z_{n-1}left(c+dy_{n-2}z_{n-3} right) },~ninmathbb{N}_{0}, ~ nonumber z_{n}=frac{z_{n-2}x_{n-3}}{x_{n-1}left(e+fz_{n-2}x_{n-3} right) }, nonumber end{align} where the initial values $x_{-i}, y_{-i}, z_{-i}$, $i=overline{1,3}$ and the parameters $a$, $b$, $c$, $d$, $e$, $f$ are non-zero real numbers, can be solved in closed form. Moreover, we obtain the solutions of above system in explicit form according to the parameters $a$, $c$ and $e$ are equal $1$ or not equal $1$. In addition, we get periodic solutions of aforementioned system. Finally, we define the forbidden set of the initial conditions by using the acquired formulas.
{"title":"On solutions of three-dimensional system of difference equations with constant coefficients","authors":"Merve Kara, Ömer Aktaş","doi":"10.31801/cfsuasmas.1163955","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1163955","url":null,"abstract":"In this study, we show that the system of difference equations \u0000begin{align}\u0000x_{n}=frac{x_{n-2}y_{n-3}}{y_{n-1}left(a+bx_{n-2}y_{n-3} right) }, nonumber \u0000y_{n}=frac{y_{n-2}z_{n-3}}{z_{n-1}left(c+dy_{n-2}z_{n-3} right) },~ninmathbb{N}_{0}, ~ nonumber \u0000z_{n}=frac{z_{n-2}x_{n-3}}{x_{n-1}left(e+fz_{n-2}x_{n-3} right) }, nonumber \u0000end{align}\u0000where the initial values $x_{-i}, y_{-i}, z_{-i}$, $i=overline{1,3}$ and the parameters $a$, $b$, $c$, $d$, $e$, $f$ are non-zero real numbers, can be solved in closed form. Moreover, we obtain the solutions of above system in explicit form according to the parameters $a$, $c$ and $e$ are equal $1$ or not equal $1$. In addition, we get periodic solutions of aforementioned system. Finally, we define the forbidden set of the initial conditions by using the acquired formulas.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44217659","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}
Pub Date : 2023-06-23DOI: 10.31801/cfsuasmas.1202806
Öznur Özaltin, Özgür Yeni̇ay
Monkeypox has recently become an endemic disease that threatens the whole world. The most distinctive feature of this disease is occurring skin lesions. However, in other types of diseases such as chickenpox, measles, and smallpox skin lesions can also be seen. The main aim of this study was to quickly detect monkeypox disease from others through deep learning approaches based on skin images. In this study, MobileNetv2 was used to determine in images whether it was monkeypox or non-monkeypox. To find splitting methods and optimization methods, a comprehensive analysis was performed. The splitting methods included training and testing (70:30 and 80:20) and 10 fold cross validation. The optimization methods as adaptive moment estimation (adam), root mean square propagation (rmsprop), and stochastic gradient descent momentum (sgdm) were used. Then, MobileNetv2 was tasked as a deep feature extractor and features were obtained from the global pooling layer. The Chi-Square feature selection method was used to reduce feature dimensions. Finally, selected features were classified using the Support Vector Machine (SVM) with different kernel functions. In this study, 10 fold cross validation and adam were seen as the best splitting and optimization methods, respectively, with an accuracy of 98.59%. Then, significant features were selected via the Chi-Square method and while classifying 500 features with SVM, an accuracy of 99.69% was observed.
{"title":"Detection of monkeypox disease from skin lesion images using Mobilenetv2 architecture","authors":"Öznur Özaltin, Özgür Yeni̇ay","doi":"10.31801/cfsuasmas.1202806","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1202806","url":null,"abstract":"Monkeypox has recently become an endemic disease that threatens the whole world. The most distinctive feature of this disease is occurring skin lesions. However, in other types of diseases such as chickenpox, measles, and smallpox skin lesions can also be seen. The main aim of this study was to quickly detect monkeypox disease from others through deep learning approaches based on skin images. In this study, MobileNetv2 was used to determine in images whether it was monkeypox or non-monkeypox. To find splitting methods and optimization methods, a comprehensive analysis was performed. The splitting methods included training and testing (70:30 and 80:20) and 10 fold cross validation. The optimization methods as adaptive moment estimation (adam), root mean square propagation (rmsprop), and stochastic gradient descent momentum (sgdm) were used. Then, MobileNetv2 was tasked as a deep feature extractor and features were obtained from the global pooling layer. The Chi-Square feature selection method was used to reduce feature dimensions. Finally, selected features were classified using the Support Vector Machine (SVM) with different kernel functions. In this study, 10 fold cross validation and adam were seen as the best splitting and optimization methods, respectively, with an accuracy of 98.59%. Then, significant features were selected via the Chi-Square method and while classifying 500\u0000features with SVM, an accuracy of 99.69% was observed.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41961566","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}
Pub Date : 2023-06-23DOI: 10.31801/cfsuasmas.1146782
Yavuz Di̇nç, E. Pişkin, Prof.dr.cemil Tunc
In this research, we take into account the Kirchhoff type equation with variable exponent. The Kirchhoff type equation is known as a kind of evolution equations,namely, PDEs, where t is an independent variable. This type problem can be extensively used in many mathematical models of various applied sciences such as flows of electrorheological fluids, thin liquid films, and so on. This research, we investigate the upper bound for blow up time under suitable conditions.
{"title":"Upper bounds for the blow up time for the Kirchhoff- type equation","authors":"Yavuz Di̇nç, E. Pişkin, Prof.dr.cemil Tunc","doi":"10.31801/cfsuasmas.1146782","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1146782","url":null,"abstract":"In this research, we take into account the Kirchhoff type equation with variable exponent. The Kirchhoff type equation is known as a kind of evolution equations,namely, PDEs, where t is an independent variable. This type problem can be extensively used in many mathematical models of various applied sciences such as flows of electrorheological fluids, thin liquid films, and so on. This research, we investigate the upper bound for blow up time under suitable conditions.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45140857","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}
Pub Date : 2023-06-23DOI: 10.31801/cfsuasmas.1144644
E. Ata
In this paper, using the modified beta function involving the generalized M-series in its kernel, we described new extensions for the Lauricella hypergeometric functions $F_{A}^{(r)}$, $F_{B}^{(r)}$, $F_{C}^{(r)}$ and $F_{D}^{(r)}$. Furthermore, we obtained various integral representations for the newly defined extended Lauricella hypergeometric functions. Then, we obtained solution of fractional differential equations involving new extensions of Lauricella hypergeometric functions, as examples.
{"title":"M-Lauricella hypergeometric functions: integral representations and solutions of fractional differential equations","authors":"E. Ata","doi":"10.31801/cfsuasmas.1144644","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1144644","url":null,"abstract":"In this paper, using the modified beta function involving the generalized M-series in its kernel, we described new extensions for the Lauricella hypergeometric functions $F_{A}^{(r)}$, $F_{B}^{(r)}$, $F_{C}^{(r)}$ and $F_{D}^{(r)}$. Furthermore, we obtained various integral representations for the newly defined extended Lauricella hypergeometric functions. Then, we obtained solution of fractional differential equations involving new extensions of Lauricella hypergeometric functions, as examples.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47545772","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}
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