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Article The Inversion Results for the Limit q-bernstein Operator(Springer Basel Ag, 2018) Ostrovska, SofiyaThe limit q-Bernstein operator B-q appears as a limit for a sequence of the q-Bernstein or for a sequence of the q-Meyer-Konig and Zeller operators in the case 0 < q < 1. Lately, various features of this operator have been investigated from several angles. It has been proved that the smoothness of f is an element of C[0, 1] affects the possibility for an analytic continuation of its image B-q f. This work aims to investigate the reciprocal: to what extent the smoothness of f can be retrieved from the analytical properties of B-q f.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: 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: 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 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 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 On a Dirichlet Problem for a Generalized Beltrami Equation(Springer Basel Ag, 2018) Gurlebeck, Klaus; Yuksel, UgurIn this article we study a Dirichlet problem for a hypercomplex Beltrami equation. We prove the existence of a unique solution of the problem and give a representation formula for the solution.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: 3Citation - Scopus: 5Necessary and Sufficient Conditions for Associated Differential Operators in Quaternionic Analysis and Applications To Initial Value Problems(Springer Basel Ag, 2013) Yuksel, UgurThis paper deals with the initial value problem of type in the space of generalized regular functions in the sense of Quaternionic Analysis satisfying the differential equation where is the time variable, x runs in a bounded and simply connected domain in is a real number, and is the Cauchy-Fueter operator. We prove necessary and sufficient conditions on the coefficients of the operator under which is associated with the operator , i.e. transforms the set of all solutions of the differential equation into solutions of the same equation for fixedly chosen t. This criterion makes it possible to construct operators for which the initial value problem is uniquely soluble for an arbitrary initial generalized regular function u (0) by the method of associated spaces constructed by W. Tutschke (Teubner Leipzig and Springer Verlag, 1989) and the solution is also generalized regular for each t.Correction Geothermal Prospectivity of the Bigadic Basin and Surrounding Area, Nw Anatolia, Turkey, by the Spectral Analysis of Magnetic Data (jun, 10.1007/S00024-021-02787-y, 2021)(Springer Basel Ag, 2021) Bilim, Funda; Aydemir, Attila; Ates, Abdullah[No Abstract Available]
