Pub Date : 2023-08-21DOI: 10.31801/cfsuasmas.1328691
Babar SULTAN, Mehvish SULTAN, Ferit GÜRBÜZ
Let $mathbb{S}^{n-1}$ denote the unit sphere in $mathbb{R}^n$ with the normalized Lebesgue measure. Let $Phiin L^{r}(mathbb{S}^{n-1})$ is a homogeneous function of degree zero and $b$ is a locally integrable function on $mathbb{R}^n$. In this paper we define the higher order commutators of Marcinkiewicz integral $[b,mu_{Phi}]^m$ and prove the boundedness of $[b,mu_{Phi}]^m$ under some proper assumptions on grand variable Herz-Morrey spaces $Mdot{K}^{alpha(.),beta}_{u,v(.)}(mathbb{R}^n)$.
{"title":"BMO estimate for the higher order commutators of Marcinkiewicz integral operator on grand Herz-Morrey spaces","authors":"Babar SULTAN, Mehvish SULTAN, Ferit GÜRBÜZ","doi":"10.31801/cfsuasmas.1328691","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1328691","url":null,"abstract":"Let $mathbb{S}^{n-1}$ denote the unit sphere in $mathbb{R}^n$ with the normalized Lebesgue measure. Let $Phiin L^{r}(mathbb{S}^{n-1})$ is a homogeneous function of degree zero and $b$ is a locally integrable function on $mathbb{R}^n$. In this paper we define the higher order commutators of Marcinkiewicz integral $[b,mu_{Phi}]^m$ and prove the boundedness of $[b,mu_{Phi}]^m$ under some proper assumptions on grand variable Herz-Morrey spaces $Mdot{K}^{alpha(.),beta}_{u,v(.)}(mathbb{R}^n)$.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135875940","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 : 2023-08-07DOI: 10.31801/cfsuasmas.1195058
Thatayaone MOAKOFİ, Broderick OLUYEDE
In this study, we propose a new heavy-tailed distribution, namely, the type I heavy-tailed odd power generalized Weibull-G family of distributions. Several statistical properties including hazard rate function, quantile function, moments, distribution of the order statistics and Renyi entropy are presented. Actuarial measures such as value at risk, tail value at risk, tail variance and tail variance premium are also derived. To obtain the estimates of the parameters of the new family of distributions, we adopt the maximum likelihood estimation method and assess the consistency property via a Monte Carlo simulation. Finally, we illustrate the usefulness of the new family of distributions by analyzing four real life data sets from different fields such as insurance, engineering, bio-medical and environmental sciences.
{"title":"The type I heavy-tailed odd power generalized Weibull-G family of distributions with applications","authors":"Thatayaone MOAKOFİ, Broderick OLUYEDE","doi":"10.31801/cfsuasmas.1195058","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1195058","url":null,"abstract":"In this study, we propose a new heavy-tailed distribution, namely, the type I heavy-tailed odd power generalized Weibull-G family of distributions. Several statistical properties including hazard rate function, quantile function, moments, distribution of the order statistics and Renyi entropy are presented. Actuarial measures such as value at risk, tail value at risk, tail variance and tail variance premium are also derived. To obtain the estimates of the parameters of the new family of distributions, we adopt the maximum likelihood estimation method and assess the consistency property via a Monte Carlo simulation. Finally, we illustrate the usefulness of the new family of distributions by analyzing four real life data sets from different fields such as insurance, engineering, bio-medical and environmental sciences.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135999970","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 : 2023-08-01DOI: 10.31801/cfsuasmas.1247415
Nurettin IRMAK
In this paper, we solve the equation begin{equation*} sum_{k=0}^{m} {{2m+1}brack{k}}_{F}pm F_{t}=F_{n}, end{equation*}% under weak assumptions. Here, $F_n$ is $n^{th}$ Fibonacci number and ${{.}brack {.}}_{F}$ denotes Fibonomial coefficient.
本文对该方程进行了求解 begin{equation*} sum_{k=0}^{m} {{2m+1}brack{k}}_{F}pm F_{t}=F_{n}, end{equation*}% under weak assumptions. Here, $F_n$ is $n^{th}$ Fibonacci number and ${{.}brack {.}}_{F}$ denotes Fibonomial coefficient.
{"title":"A Diophantine equation including Fibonacci and Fibonomial coefficients","authors":"Nurettin IRMAK","doi":"10.31801/cfsuasmas.1247415","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1247415","url":null,"abstract":"In this paper, we solve the equation begin{equation*} sum_{k=0}^{m} {{2m+1}brack{k}}_{F}pm F_{t}=F_{n}, end{equation*}% under weak assumptions. Here, $F_n$ is $n^{th}$ Fibonacci number and ${{.}brack {.}}_{F}$ denotes Fibonomial coefficient.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135056064","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 : 2023-07-30DOI: 10.31801/cfsuasmas.1089389
Esra BAŞARIR NOYAN, Yılmaz GÜNDÜZALP
We introduce a new class of pseudo-Riemannian submersions which are called quasi hemi-slant pseudo-Riemannian submersions from para-Kaehler manifolds to pseudo-Riemannian manifolds as a natural generalization of slant submersions, semi-invariant submersions, semi-slant submersions and hemislant Riemannian submersions in our study. Also, we give non-trivial examples of such submersions. Further, some geometric properties with two types of quasi hemi-slant pseudo-Riemannian submersions are investigated
{"title":"Quasi hemi-slant pseudo-Riemannian submersions in para-complex geometry","authors":"Esra BAŞARIR NOYAN, Yılmaz GÜNDÜZALP","doi":"10.31801/cfsuasmas.1089389","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1089389","url":null,"abstract":"We introduce a new class of pseudo-Riemannian submersions which are called quasi hemi-slant pseudo-Riemannian submersions from para-Kaehler manifolds to pseudo-Riemannian manifolds as a natural generalization of slant submersions, semi-invariant submersions, semi-slant submersions and hemislant Riemannian submersions in our study. Also, we give non-trivial examples of such submersions. Further, some geometric properties with two types of quasi hemi-slant pseudo-Riemannian submersions are investigated","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135398849","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 : 2023-07-02DOI: 10.31801/cfsuasmas.1187854
Semra YURTTANÇIKMAZ
In this paper, it has been researched curves lying on parallel-like surfaces $M^{f}$ of the ruled surface $M$ in $E^{3}$. Using the definition of parallel-like surfaces it has been found parametric expressions of parallel-like surface of the ruled surface and image curve of the directrix curve of the base surface. Moreover, obtaining Darboux frames of curves lying on surfaces $M$ and $M^{f}$, it has been compared the geodesic curvatures, the normal curvatures and the geodesic torsions of these curves.
{"title":"On the curves lying on parallel-like surfaces of the ruled surface in $E^{3}$","authors":"Semra YURTTANÇIKMAZ","doi":"10.31801/cfsuasmas.1187854","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1187854","url":null,"abstract":"In this paper, it has been researched curves lying on parallel-like surfaces $M^{f}$ of the ruled surface $M$ in $E^{3}$. Using the definition of parallel-like surfaces it has been found parametric expressions of parallel-like surface of the ruled surface and image curve of the directrix curve of the base surface. Moreover, obtaining Darboux frames of curves lying on surfaces $M$ and $M^{f}$, it has been compared the geodesic curvatures, the normal curvatures and the geodesic torsions of these curves.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135803061","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.1138441
Hayrullah Özimamoğlu, Ahmet Kaya
In this paper, we generalize the known Gaussian Pell-Lucas numbers, and call such numbers as the generalized Gaussian k-Pell-Lucas numbers. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas numbers and the known Gaussian Pell-Lucas numbers. We generalize the known Gaussian Pell-Lucas polynomials, and call such polynomials as the generalized Gaussian k-Pell-Lucas polynomials. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas polynomials and the known Gaussian Pell-Lucas polynomials. In addition, we present the new generalizations of these numbers and polynomials in matrix form. Then, we get Cassini’s identities for these numbers and polynomials.
{"title":"On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials","authors":"Hayrullah Özimamoğlu, Ahmet Kaya","doi":"10.31801/cfsuasmas.1138441","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1138441","url":null,"abstract":"In this paper, we generalize the known Gaussian Pell-Lucas numbers, and call such numbers as the generalized Gaussian k-Pell-Lucas numbers. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas numbers and the known Gaussian Pell-Lucas numbers. We generalize the known Gaussian Pell-Lucas polynomials, and call such polynomials as the generalized Gaussian k-Pell-Lucas polynomials. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas polynomials and the known Gaussian Pell-Lucas polynomials. In addition, we present the new generalizations of these numbers and polynomials in matrix form. Then, we get Cassini’s identities for these numbers and polynomials.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45135107","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.1083750
E. Öztürk
In this paper, we define a nonlinear transformation between space curves which preserves the ratio of $tau/kappa$ of the given curve in 3−dimensional Euclidean space $E^3$. We investigate invariant and associated curves of this transformation by the help of curvature and torsion functions of the base curve. Moreover, we define a new curve (family) so-called quasi-slant helix, and we obtain some characterizations in terms of the curvatures of this curve. Finally, we examine some curves in the kinematics, and give the pictures of some special curves and their images with respect to the transformation.
{"title":"A nonlinear transformation between space curves defined by curvature-torsion relations in 3-dimensional Euclidean space","authors":"E. Öztürk","doi":"10.31801/cfsuasmas.1083750","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1083750","url":null,"abstract":"In this paper, we define a nonlinear transformation between space curves which preserves the ratio of $tau/kappa$ of the given curve in 3−dimensional Euclidean space $E^3$. We investigate invariant and associated curves of this transformation by the help of curvature and torsion functions of the base curve. Moreover, we define a new curve (family) so-called quasi-slant helix, and we obtain some characterizations in terms of the curvatures of this curve. Finally, we examine some curves in the kinematics, and give the pictures of some special curves and their images with respect to the transformation.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48586849","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.1179189
H. Ünözkan, M. Yilmaz
In these days, many different techniques are implemented for generating distributions. The core aim in generating distribution, is better modeling capability. With generating new distribution more reliable and appropriate models are available for data sets. In this paper, a new distribution is gained by evaluating the conditional diagonal section of the bivariate Farlie-Gumbel-Morgenstern distribution with exponential marginals. Specifications and characteristics of this new distribution are studied. The statistical assessment and some reliability analyzes are carried out. The success of the new distribution on statistical modeling is detected by using data sets in literature. It is concluded that this new distribution suggests a model that can be used effectively in many different lifetime data sets.
{"title":"A new transmutation: conditional copula with exponential distribution","authors":"H. Ünözkan, M. Yilmaz","doi":"10.31801/cfsuasmas.1179189","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1179189","url":null,"abstract":"In these days, many different techniques are implemented for generating distributions. The core aim in generating distribution, is better modeling capability. With generating new distribution more reliable and appropriate models are available for data sets. In this paper, a new distribution is gained by evaluating the conditional diagonal section of the bivariate Farlie-Gumbel-Morgenstern distribution with exponential marginals. Specifications and characteristics of this new distribution are studied. The statistical assessment and some reliability analyzes are carried out. The success of the new distribution on statistical modeling is detected by using data sets in literature. It is concluded that this new distribution suggests a model that can be used effectively in many different lifetime data sets.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47585056","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.1062426
Erhan Güler
We introduce the timelike rotational hypersurfaces $textbf{x}$ with timelike axis in Minkowski 4-space $mathbb{E}_1^{4}$. We obtain the equations for the curvatures of the hypersurface. Moreover, we present a theorem for the rotational hypersurfaces with timelike axis supplying $Deltatextbf{x}=mathcal{T}textbf{x}$, where $mathcal{T}$ is a 4x4 real matrix.
{"title":"Timelike rotational hypersurfaces with timelike axis in Minkowski four-space","authors":"Erhan Güler","doi":"10.31801/cfsuasmas.1062426","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1062426","url":null,"abstract":"We introduce the timelike rotational hypersurfaces $textbf{x}$ with timelike axis in Minkowski 4-space $mathbb{E}_1^{4}$. We obtain the equations for the curvatures of the hypersurface. Moreover, we present a theorem for the rotational hypersurfaces with timelike axis supplying $Deltatextbf{x}=mathcal{T}textbf{x}$, where $mathcal{T}$ is a 4x4 real matrix.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46301263","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.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":null,"pages":null},"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}
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