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Article Citation - WoS: 15Citation - Scopus: 14Generalized Transportation Cost Spaces(Springer Basel Ag, 2019) Ostrovska, Sofiya; Ostrovskii, Mikhail I.The paper is devoted to the geometry of transportation cost spaces and their generalizations introduced by Melleray et al. (Fundam Math 199(2):177-194, 2008). Transportation cost spaces are also known as Arens-Eells, Lipschitz-free, or Wasserstein 1 spaces. In this work, the existence of metric spaces with the following properties is proved: (1) uniformly discrete metric spaces such that transportation cost spaces on them do not contain isometric copies of l(1), this result answers a question raised by Cuth and Johanis (Proc Am Math Soc 145(8):3409-3421, 2017); (2) locally finite metric spaces which admit isometric embeddings only into Banach spaces containing isometric copies of l(1); (3) metric spaces for which the double-point norm is not a norm. In addition, it is proved that the double-point norm spaces corresponding to trees are close to l(infinity)(d) of the corresponding dimension, and that for all finite metric spaces M, except a very special class, the infimum of all seminorms for which the embedding of M into the corresponding seminormed space is isometric, is not a seminorm.Article Citation - WoS: 5Citation - Scopus: 5Geophysical Investigation of the Geothermal Potential Under the Largest Volcanic Cover in Anatolia: Kars Plateau, Ne Turkey(Springer Basel Ag, 2020) Aydemir, Attila; Bilim, Funda; Avci, Birgul; Kosaroglu, SinanIn this study, Curie-point depth (CPD), geothermal gradient, radiogenic heat production, and heat flow maps were constructed based on different thermal conductivity coefficients using magnetic anomaly data for the Kars Plateau, which has the largest volcanic cover in Turkey. The bottom depths of the magnetic crust in the research area were revealed by the CPD map for the first time in this investigation. There are two apparent magnetic anomaly trends in the study area: the first is the Horasan-Senkaya-Sarikamis-Selim-Arpacay trend in the NE-SW direction, and the other is the Hanak-Ardahan-Arpacay trend in the NW-SE direction. Two other prominent elongations extend into the Ardahan-Gole-Senkaya and Kars-Digor axes. All these trends represent mountain chains and/or stratovolcanoes in the region, and no anomalies are observed around the non-volcanic outcrops. Curie depths are shallow, up to 14 km between Horasan and Kagizman towns, and 12 km in the northwestern part of the study area. Gradient values can reach 50 degrees C km(-1) in the northwestern sector, together with the high heat flows represented by the 150 Wm(-1) K-1 contours. The deepest CPD region lies between Gole and Susuz towns, where the geothermal gradient decreases to 27 degrees C km(-1). Heat flows decrease 60 Wm(-1) K-1 in the same area. An apparent gap around the Kars Plateau was observed in previous regional heat flow maps of Turkey by other authors (who used the bottom hole temperatures of boreholes and hot springs temperatures). This gap has been accurately filled from the results of this study, and geothermal exploration areas and the geothermal potential of the Kars Plateau have thus been determined for future exploration activity on the basis of the tectonic elements and earthquake data.Article On the Convergence of the q-bernstein Polynomials for Power Functions(Springer Basel Ag, 2021) Ostrovska, Sofiya; Ozban, Ahmet YasarThe aim of this paper is to present new results related to the convergence of the sequence of the complex q-Bernstein polynomials {B-n,B-q(f(alpha); z)}, where 0 < q not equal 1 and f(alpha) = x(alpha), alpha >= 0, is a power function on [0, 1]. This study makes it possible to describe all feasible sets of convergence K for such polynomials. Specifically, if either 0 < q < 1 or alpha is an element of N-0, then K = C, otherwise K = {0} boolean OR {q(-j)}(j=0)(infinity). In the latter case, this identifies the sequence K = {0} boolean OR {q(-j)}(j=0)(infinity) as the 'minimal' set of convergence for polynomials B-n,B-q(f; z), f is an element of C[0, 1] in the case q > 1. In addition, the asymptotic behavior of the polynomials {B-n,B-q(f(alpha); z)}, with q > 1 has been investigated and the obtained results are illustrated by numerical examples.Article Citation - WoS: 4Citation - Scopus: 3On Orlicz-Power Series Spaces(Springer Basel Ag, 2010) Karapinar, Erdal; Zakharyuta, VyacheslavIn this manuscript, we investigate the isomorphisms of Orlicz-Kothe sequence spaces and quasidiagonal isomorphisms of Cartesian products of Orlicz-power series spaces.Article Citation - WoS: 6Citation - Scopus: 5Geothermal Prospectivity of the Bigadic Basin and Surrounding Area, Nw Anatolia, Turkey, by the Spectral Analysis of Magnetic Data(Springer Basel Ag, 2021) Bilim, Funda; Aydemir, Attila; Ates, AbdullahThe Curie Point Depths (CPDs) are estimated from the spectral analysis of magnetic data in order to determine the geothermal potential of the Bigadic Basin and its surrounding region in NW Anatolia, Turkey. The estimated CPD range is from 7 to 17-18 km. The shallowest depth (7 km) lies to the north of Balikesir. The estimated geothermal gradient and heat flow values range from 33 to 80 degrees C/km, and 83 to 200 mWm(-2), respectively. All results in the study area support the previous studies from the geological or geophysical investigations for western Anatolia by other researchers. High temperatures may be resulted indirectly from the continental collision and consequent thermal relaxation and/or heating from the interiors of the Earth due to the mantle delamination or asthenospheric upwelling in response to lithospheric extension in the western Anatolia. The high heat flow and shallow CPDs can also be associated with the magmatic rocks as a consequence of the recent tectonic extension and granitoids in the studied region.Article Citation - WoS: 2Citation - Scopus: 2On the eigenfunctions of the q-Bernstein operators(Springer Basel Ag, 2023) Ostrovska, Sofiya; Turan, MehmetThe eigenvalue problems for linear operators emerge in various practical applications in physics and engineering. This paper deals with the eigenvalue problems for the q-Bernstein operators, which play an important role in the q-boson theory of modern theoretical physics. The eigenstructure of the classical Bernstein operators was investigated in detail by S. Cooper and S. Waldron back in 2000. Some of their results were extended for other Bernstein-type operators, including the q-Bernstein and the limit q-Bernstein operators. The current study is a pursuit of this research. The aim of the present work is twofold. First, to derive for the q-Bernstein polynomials analogues of the Cooper-Waldron results on zeroes of the eigenfunctions. Next, to present in detail the proof concerning the existence of non-polynomial eigenfunctions for the limit q-Bernstein operator.Article The Saturation of Convergence for the Complex q-durrmeyer Polynomials(Springer Basel Ag, 2025) Gurel, Ovgu; Ostrovska, Sofiya; Turan, MehmetThe aim of this paper is to establish a saturation result for the complex q-Durrmeyer polynomials (Dn,qf)(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(D_{n,q}f)(z)$$\end{document}, where q is an element of(0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q \in (0,1)$$\end{document}, f is an element of C[0,1].\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f \in C[0,1].$$\end{document} It is known that the sequence {(Dn,qf)(z)}n is an element of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{(D_{n,q}f)(z)\}_{n \in {\mathbb {N}}}$$\end{document} converges uniformly on any compact set in C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}$$\end{document} to the limit function (D infinity,qf)(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(D_{\infty ,q}f)(z)$$\end{document}, which, therefore, is entire. Previously, the rate of this convergence has been estimated as O(qn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(q<^>n)$$\end{document}, n ->infinity.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \rightarrow \infty . $$\end{document} In the present article, this result is refined to derive Voronovskaya-type formula and to demonstrate that this rate is o(qn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$o(q<^>n)$$\end{document}, n ->infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \rightarrow \infty $$\end{document} on a set possessing an accumulation point if and only if f takes on the same value at all qj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q<^>j$$\end{document}, j is an element of N0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$j \in {\mathbb {N}}_{0}$$\end{document}.Article Citation - WoS: 1Citation - Scopus: 1On a Quadratic Eigenvalue Problem and Its Applications(Springer Basel Ag, 2013) Atalan, Ferihe; Guseinov, Gusein ShWe investigate the eigenvalues and eigenvectors of a special quadratic matrix polynomial and use the results obtained to solve the initial value problem for the corresponding linear system of differential equations.Article Citation - WoS: 1Citation - Scopus: 1Prescribed Asymptotic Behavior of Nonlinear Dynamic Equations Under Impulsive Perturbations(Springer Basel Ag, 2024) Zafer, Agacik; Dogru Akgol, SibelThe asymptotic integration problem has a rich historical background and has been extensively studied in the context of ordinary differential equations, delay differential equations, dynamic equations, and impulsive differential equations. However, the problem has not been explored for impulsive dynamic equations due to the lack of essential tools such as principal and nonprincipal solutions, as well as certain compactness results. In this work, by making use of the principal and nonprincipal solutions of the associated linear dynamic equation, recently obtained in [Acta Appl. Math. 188, 2 (2023)], we investigate the asymptotic integration problem for a specific class of nonlinear impulsive dynamic equations. Under certain conditions, we prove that the given impulsive dynamic equation possesses solutions with a prescribed asymptotic behavior at infinity. These solutions can be expressed in terms of principal and nonprincipal solutions as in differential equations. In addition, the necessary compactness results are also established. Our findings are particularly valuable for better understanding the long-time behavior of solutions, modeling real-world problems, and analyzing the solutions of boundary value problems on semi-infinite intervals.Article 3-D Gravity Modeling of the Kars Basin as a Hidden Extension of the Caspian Petroleum System, Ne-Anatolia, Turkey(Springer Basel Ag, 2024) Aydemir, Attila; Bilim, FundaThe Kars Basin in northeastern Turkey is closely related to the Caspian Petroleum System but it is hidden by a great extent of volcanic rocks. The Oligo-Miocene Komurlu Formation within the basin is the Turkish equivalent of the Maikopian Formation which is the main source rock in the Caspian region. Although the Kars Basin has considerable hydrocarbon potential it is one of the least explored basins in Turkey and there is only a limited literature on the region. This study is the first comprehensive investigation to determine the basement geometry, depth, internal structure and basin boundaries. Gravity data and power spectrum analysis were used in this study. The gravity anomalies were low-pass filtered and the average depth of the basin is found to be approximately 5 km. Boundaries of the basin are entirely confined within the Turkish territorial borders. The basin geometry is remarkably consistent with the crustal thickness geometry across the region and the maximum crustal thickness is 42 km, indicating that the basin was formed on the thickest part of the crust in the region. A 3-D model of the Kars Plateau indicates that the Kars Basin is made up of four different deep (> 6 km) depressions forming a channel-like trend from southwest to northeast from the Horasan area to the Arpacay area. There are four less deep sections (< 6 km) to the north of this trend. The depressions in the north are separated by the Allahuekber Mountains that are marked by a distinctive magnetic anomaly, from the deep SW-NE trend. High-standing regions between the depressions could be prospective areas for the oil accumulation.
