Pub Date : 2023-03-30DOI: 10.31801/cfsuasmas.1107024
V. Gürdal, M. Huban
We consider operator $V$ on the reproducing kernel Hilbert space $mathcal{H}=mathcal{H}(Omega)$ over some set $Omega$ with the reproducing kernel $K_{mathcal{H},lambda}(z)=K(z,lambda)$ and define A-Davis-Wielandt-Berezin radius $eta_{A}(V)$ by the formula $eta_{A}(V):=sup{sqrt{| langle Vk_{mathcal{H},lambda},k_{mathcal{H},lambda} rangle_{A}|^{2}+|Vk_{mathcal{H},lambda}|_{A}^{4}}:lambda in Omega}$ and $tilde{V}$ is the Berezin symbol of $V$ where any positive operator $A$-induces a semi-inner product on $mathcal{H}$ is defined by $langle x,y rangle_{A}=langle Ax,y rangle$ for $x,y in mathcal{H}.$ We study equality of the lower bounds for A-Davis-Wielandt-Berezin radius mentioned above. We establish some lower and upper bounds for the A-Davis-Wielandt-Berezin radius of reproducing kernel Hilbert space operators. In addition, we get an upper bound for the A-Davis-Wielandt-Berezin radius of sum of two bounded linear operators.
{"title":"A-Davis-Wielandt-Berezin radius inequalities","authors":"V. Gürdal, M. Huban","doi":"10.31801/cfsuasmas.1107024","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1107024","url":null,"abstract":"We consider operator $V$ on the reproducing kernel Hilbert space $mathcal{H}=mathcal{H}(Omega)$ over some set $Omega$ with the reproducing kernel \u0000$K_{mathcal{H},lambda}(z)=K(z,lambda)$ and define A-Davis-Wielandt-Berezin radius $eta_{A}(V)$ by the formula \u0000$eta_{A}(V):=sup{sqrt{| langle Vk_{mathcal{H},lambda},k_{mathcal{H},lambda} rangle_{A}|^{2}+|Vk_{mathcal{H},lambda}|_{A}^{4}}:lambda in Omega}$\u0000and $tilde{V}$ is the Berezin symbol of $V$ where any positive operator $A$-induces a semi-inner product on $mathcal{H}$ is defined by $langle x,y rangle_{A}=langle Ax,y rangle$ for $x,y in mathcal{H}.$ We study equality of the lower bounds for A-Davis-Wielandt-Berezin radius mentioned above. We establish some lower and upper bounds for the A-Davis-Wielandt-Berezin radius of reproducing kernel Hilbert space operators. In addition, we get an upper bound for the A-Davis-Wielandt-Berezin radius of sum of two bounded linear operators.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43165464","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1089508
Esra KIR ARPAT, Turhan Köprübaşi
In the present work, the inverse problem of the scattering theory for Klein-Gordon s-wave equation with a spectral parameter in the boundary condition is investigated. We define the scattering data set, and obtain the main equation of operator. Furthermore, the uniqueness of the solution of the inverse problem is proved.
{"title":"Uniqueness of the solution to the inverse problem of scattering theory for spectral parameter dependent Klein-Gordon s-wave equation","authors":"Esra KIR ARPAT, Turhan Köprübaşi","doi":"10.31801/cfsuasmas.1089508","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1089508","url":null,"abstract":"In the present work, the inverse problem of the scattering theory for Klein-Gordon s-wave equation with a spectral parameter in the boundary condition is investigated. We define the scattering data set, and obtain the main equation of operator. Furthermore, the uniqueness of the solution of the inverse problem is proved.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49143797","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1089790
S. Saltan, Nazlı Baskan
The Berezin transform $widetilde{A}$ and the Berezin number of an operator $A$ on the reproducing kernel Hilbert space over some set $Omega$ with normalized reproducing kernel $widehat{k}_{lambda}$ are defined, respectively, by $widetilde{A}(lambda)=leftlangle {A}widehat{k}_{lambda },widehat{k}_{lambda}rightrangle , lambdainOmega$ and $mathrm{ber}% (A):=sup_{lambdainOmega}leftvert widetilde{A}{(lambda)}rightvert .$ A straightforward comparison between these characteristics yields the inequalities $mathrm{ber}left( Aright) leqfrac{1}{2}left( leftVert ArightVert _{mathrm{ber}}+leftVert A^{2}rightVert _{mathrm{ber}}% ^{1/2}right) $. In this paper, we study further inequalities relating them. Namely, we obtained some refinement of Berezin number inequalities involving convex functions. In particular, for $Ainmathcal{B}left( mathcal{H}% right) $ and $rgeq1$ we show that [ mathrm{ber}^{2r}left( Aright) leqfrac{1}{4}left( leftVert A^{ast }A+AA^{ast}rightVert _{mathrm{ber}}^{r}+leftVert A^{ast}A-AA^{ast }rightVert _{mathrm{ber}}^{r}right) +frac{1}{2}mathrm{ber}^{r}left( A^{2}right) . ]
{"title":"Some refinements of Berezin number inequalities via convex functions","authors":"S. Saltan, Nazlı Baskan","doi":"10.31801/cfsuasmas.1089790","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1089790","url":null,"abstract":"The Berezin transform $widetilde{A}$ and the Berezin number of an operator\u0000$A$ on the reproducing kernel Hilbert space over some set $Omega$ with\u0000normalized reproducing kernel $widehat{k}_{lambda}$ are defined,\u0000respectively, by $widetilde{A}(lambda)=leftlangle {A}widehat{k}_{lambda\u0000},widehat{k}_{lambda}rightrangle , lambdainOmega$ and $mathrm{ber}%\u0000(A):=sup_{lambdainOmega}leftvert widetilde{A}{(lambda)}rightvert .$\u0000A straightforward comparison between these characteristics yields the\u0000inequalities $mathrm{ber}left( Aright) leqfrac{1}{2}left( leftVert\u0000ArightVert _{mathrm{ber}}+leftVert A^{2}rightVert _{mathrm{ber}}%\u0000^{1/2}right) $. In this paper, we study further inequalities relating them.\u0000Namely, we obtained some refinement of Berezin number inequalities involving\u0000convex functions. In particular, for $Ainmathcal{B}left( mathcal{H}%\u0000right) $ and $rgeq1$ we show that\u0000[\u0000mathrm{ber}^{2r}left( Aright) leqfrac{1}{4}left( leftVert A^{ast\u0000}A+AA^{ast}rightVert _{mathrm{ber}}^{r}+leftVert A^{ast}A-AA^{ast\u0000}rightVert _{mathrm{ber}}^{r}right) +frac{1}{2}mathrm{ber}^{r}left(\u0000A^{2}right) .\u0000]","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44917761","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1094170
Zehra İşbilir, Kahraman Esen Özen, M. Tosun
The concept of a pair of curves, called as Bertrand partner curves, was introduced by Bertrand in 1850. Bertrand partner curves have been studied widely in the literature from past to present. In this study, we take into account of the concept of Bertrand partner trajectories according to Positional Adapted Frame (PAF) for the particles moving in 3-dimensional Euclidean space. Some characterizations are given for these trajectories with the aid of the PAF elements. Then, we obtain some special cases of these trajectories. Moreover, we provide a numerical example.
{"title":"Bertrand partner P-trajectories in the Euclidean 3-space $E^3$","authors":"Zehra İşbilir, Kahraman Esen Özen, M. Tosun","doi":"10.31801/cfsuasmas.1094170","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1094170","url":null,"abstract":"The concept of a pair of curves, called as Bertrand partner curves, was introduced by Bertrand in 1850. Bertrand partner curves have been studied widely in the literature from past to present. In this study, we take into account of the concept of Bertrand partner trajectories according to Positional Adapted Frame (PAF) for the particles moving in 3-dimensional Euclidean space. Some characterizations are given for these trajectories with the aid of the PAF elements. Then, we obtain some special cases of these trajectories. Moreover, we provide a numerical example.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42666685","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1086966
Cansu Ergenç, B. Şenoğlu
In this study, the performances of the different parameter estimation methods are compared for the Kumaraswamy Weibull distribution via Monte Carlo simulation study. Maximum Likelihood (ML), Least Squares (LS), Weighted Least Squares (WLS), Cramer-von Mises (CM) and Anderson Darling (AD) methods are used in the comparisons. The results of the Monte Carlo simulation study demonstrate that ML estimators for the parameters of the Kumaraswamy Weibull distribution are more efficient than the other estimators. It is followed by AD estimator. At the end of the study, a real data set taken from the literature is used to illustrate the applicability of the Kumaraswamy Weibull distribution.
{"title":"Comparison of estimation methods for the Kumaraswamy Weibull distribution","authors":"Cansu Ergenç, B. Şenoğlu","doi":"10.31801/cfsuasmas.1086966","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1086966","url":null,"abstract":"In this study, the performances of the different parameter estimation methods are compared for the Kumaraswamy Weibull distribution via Monte Carlo simulation study. Maximum Likelihood (ML), Least Squares (LS), Weighted Least Squares (WLS), Cramer-von Mises (CM) and Anderson Darling (AD) methods are used in the comparisons. The results of the Monte Carlo simulation study demonstrate that ML estimators for the parameters of the Kumaraswamy Weibull distribution are more efficient than the other estimators. It is followed by AD estimator. At the end of the study, a real data set taken from the literature is used to illustrate the applicability of the Kumaraswamy Weibull distribution.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47184326","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1142926
Efruz Özlem Mersin, M. Bahşı
In this paper, we define hybrinomials related to hyper-Leonardo numbers. We study some of their properties such as the recurrence relation and summation formulas. In addition, we introduce hybrid hyper Leonardo numbers.
{"title":"Hybrinomials related to hyper-Leonardo numbers","authors":"Efruz Özlem Mersin, M. Bahşı","doi":"10.31801/cfsuasmas.1142926","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1142926","url":null,"abstract":"In this paper, we define hybrinomials related to hyper-Leonardo numbers. We study some of their properties such as the recurrence relation and summation formulas. In addition, we introduce hybrid hyper Leonardo numbers.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47284778","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1074557
Gülsüm Yeliz ŞENTÜRK, Nurten GÜRSES, Salim YÜCE
This paper aims to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced. An alternative approach for a generalized quaternion matrix with elliptic number entries has been developed as a crucial part.
{"title":"New insight into quaternions and their matrices","authors":"Gülsüm Yeliz ŞENTÜRK, Nurten GÜRSES, Salim YÜCE","doi":"10.31801/cfsuasmas.1074557","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1074557","url":null,"abstract":"This paper aims to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced. An alternative approach for a generalized quaternion matrix with elliptic number entries has been developed as a crucial part.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136002451","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1061950
Syed Zakar HUSSAİN BUKHARİ, A. Shahzad
We define certain subclasses $delta-mathcal{UM}(ell,eta_{1},eta_{2})$ and $delta-mathcal{UM}_{Im}(ell,eta_{1},eta_{2})$ of holomorphic mappings involving some differential inequalities. These functions are actually generalizations of some basic families of starlike and convex mappings. We study sufficient conditions for $fin delta-mathcal{UM}(ell,eta_{1}% ,eta_{2}).$ We also discuss the characterization for $fin delta -mathcal{UM}_{Im}(ell,eta_{1},eta_{2})$ along with the coefficient bounds and other problems. Using certain conditions for functions in the class $delta-mathcal{UM}(ell,eta_{1},eta_{2}),$ we also define another class $delta-mathcal{UM}^{ast}(ell,eta_{1},eta_{2})$ and study some subordination related result.
{"title":"Hadamard product of holomorphic mappings associated with the conic shaped domain","authors":"Syed Zakar HUSSAİN BUKHARİ, A. Shahzad","doi":"10.31801/cfsuasmas.1061950","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1061950","url":null,"abstract":"We define certain subclasses $delta-mathcal{UM}(ell,eta_{1},eta_{2})$ and\u0000$delta-mathcal{UM}_{Im}(ell,eta_{1},eta_{2})$ of holomorphic mappings\u0000involving some differential inequalities. These functions are actually\u0000generalizations of some basic families of starlike and convex mappings. We\u0000study sufficient conditions for $fin delta-mathcal{UM}(ell,eta_{1}%\u0000,eta_{2}).$ We also discuss the characterization for $fin delta\u0000-mathcal{UM}_{Im}(ell,eta_{1},eta_{2})$ along with the coefficient bounds\u0000and other problems. Using certain conditions for functions in the class\u0000$delta-mathcal{UM}(ell,eta_{1},eta_{2}),$ we also define another class\u0000$delta-mathcal{UM}^{ast}(ell,eta_{1},eta_{2})$ and study some\u0000subordination related result.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42356629","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1126635
N. Aslan, M. Saltan, B. Demir
In this paper, it is aimed to construct two different dynamical systems on the Sierpinski tetrahedron. To this end, we consider the dynamical systems on a quotient space of ${ 0,1,2,3 }^{mathbb{N}}$ by using the code representations of the points on the Sierpinski tetrahedron. Finally, we compare the periodic points to investigate topological conjugacy of these dynamical systems and we conclude that they are not topologically equivalent.
{"title":"Comparison of some dynamical systems on the quotient space of the Sierpinski tetrahedron","authors":"N. Aslan, M. Saltan, B. Demir","doi":"10.31801/cfsuasmas.1126635","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1126635","url":null,"abstract":"In this paper, it is aimed to construct two different dynamical systems on the Sierpinski tetrahedron. To this end, we consider the dynamical systems on a quotient space of ${ 0,1,2,3 }^{mathbb{N}}$ by using the code representations of the points on the Sierpinski tetrahedron. Finally, we compare the periodic points to investigate topological conjugacy of these dynamical systems and we conclude that they are not topologically equivalent.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43222744","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1117855
Nil Sahin
In this article, we study minimal graded free resolutions of Cohen-Macaulay tangent cones of some monomial curves associated to 4-generated pseudo symmetric numerical semigroups. We explicitly give the matrices in these minimal free resolutions.
{"title":"Free resolutions for the tangent cones of some homogeneous pseudo symmetric monomial curves","authors":"Nil Sahin","doi":"10.31801/cfsuasmas.1117855","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1117855","url":null,"abstract":"In this article, we study minimal graded free resolutions of Cohen-Macaulay tangent cones of some monomial curves associated to 4-generated pseudo symmetric numerical semigroups. We explicitly give the matrices in these minimal free resolutions.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46676066","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：