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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 Citation - WoS: 13Citation - Scopus: 14Coincidence Point Theorems on Quasi-Metric Spaces Via Simulation Functions and Applications To g-metric Spaces(Springer Basel Ag, 2018) Lopez de Hierro, A. F. Roldan; Karapinar, E.; O'Regan, D.In this paper, we present some coincidence point results in the framework of quasi-metric spaces using contractive conditions involving simulation functions. As consequences, we are able to particularize these results to a variety of situations including G-metric spaces. The results presented in this paper generalize and extend several comparable results in the existing literature. In addition, some examples are given.Article Citation - WoS: 69Citation - Scopus: 71An Approach To Best Proximity Points Results Via Simulation Functions(Springer Basel Ag, 2017) Karapinar, Erdal; Khojasteh, FarshidIn this paper, we investigate of the existence of the best proximity points of certain mapping defined via simulation functions in the frame of complete metric spaces. We consider the uniqueness criteria for such mappings. The obtained results unify a number of the existing results on the topic in the literature.Article Citation - WoS: 17Citation - Scopus: 16The Approximation by q-bernstein Polynomials in the Case q ↓ 1(Springer Basel Ag, 2006) Ostrovska, SLet B-n (f, q; x), n = 1, 2, ... , 0 < q < infinity, be the q-Bernstein polynomials of a function f, B-n (f, 1; x) being the classical Bernstein polynomials. It is proved that, in general, {B-n (f, q(n); x)} with q(n) down arrow 1 is not an approximating sequence for f is an element of C[0, 1], in contrast to the standard case q(n) up arrow 1. At the same time, there exists a sequence 0 < delta(n) down arrow 0 such that the condition 1 <= q(n) <= delta(n) implies the approximation of f by {B-n(f, qn; x)} for all f is an element of C[0, 1].Article Citation - WoS: 11Citation - Scopus: 15The q-versions of the Bernstein Operator: From Mere Analogies To Further Developments(Springer Basel Ag, 2016) Ostrovska, SofiyaThe article exhibits a review of results on two popular q-versions of the Bernstein polynomials, namely, the LupaAY q-analogue and the q-Bernstein polynomials. Their similarities and distinctions are discussed.Article Citation - WoS: 4Citation - Scopus: 7Necessary and Sufficient Conditions for First Order Differential Operators To Be Associated With a Disturbed Dirac Operator in Quaternionic Analysis(Springer Basel Ag, 2015) Abbas, Usman Yakubu; Yuksel, UgurRecently the initial value problem partial derivative(t)u = Lu :- Sigma(3)(i=1) A((i)) (t, x)partial derivative(xi) u + B(t, x)u + C(t, x) u(0, x) = u(0)(x) has been solved uniquely by N. Q. Hung (Adv. appl. Clifford alg., Vol. 22, Issue 4 (2012), pp. 1061-1068) using the method of associated spaces constructed by W. Tutschke (Teubner Leipzig and Springer Verlag, 1989) in the space of generalized regular functions in the sense of quaternionic analysis satisfying the equation D(alpha)u = 0, where D(alpha)u := Du + alpha u, alpha is an element of R, and D = Sigma(3)(j=1) e(j)partial derivative(xj) is the Dirac operator, x = (x(1), x(2), x(3)) is the space like variable running in a bounded domain in R-3 , and t is the time. The author has proven only sufficient conditions on the coefficients of the operator L under which L is associated with the operator D-alpha, i.e. L transforms the set of all solutions of the differential equation D(alpha)u = 0 into solutions of the same equation for fixedly chosen t. In the present paper we prove necessary and sufficient conditions for the underlined operators to be associated. This criterion makes it possible to construct all linear operators L for which the initial value problem with an arbitrary initial generalized regular function is always solvable.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.Article Citation - WoS: 1Automatic Boundedness of Adjointable Operators on Barreled Vh-Spaces(Springer Basel Ag, 2022) Ay, SerdarWe consider the space of adjointable operators on barreled VH (Vector Hilbert) spaces and show that such operators are automatically bounded. This generalizes the well known corresponding result for locally Hilbert C*-modules. We pick a consequence of this result in the dilation theory of VH-spaces and show that, when barreled VH-spaces are considered, a certain boundedness condition for the existence of VH-space linearisations, equivalently, of reproducing kernel VH-spaces, is automatically satisfied.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.
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