Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 9Citation - Scopus: 8Scattering and Spectral Problems of the Direct Sum Sturm-Liouville Operators(Ministry Communications & High Technologies Republic Azerbaijan, 2017) Allahverdiev, Bilender P.; Uğurlu, Ekin; Ugurlu, Ekin; MatematikIn this paper a space of boundary values is constructed for direct sum minimal symmetric Sturm-Liouville operators and description of all maximal dissipative, maximal accumulative, selfadjoint and other extensions of such a symmetric operator is given in terms of boundary conditions. We construct a selfadjoint dilation of dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and define its characteristic function. We prove a theorem on completeness of the system of eigenfunctions and associated functions of the dissipative operators.Article Citation - WoS: 2Citation - Scopus: 2Experimental Design and Optimization for the Spectral Analysis of Two-Component Mixture(Chiminform Data S A, 2007) Dinc, Erdal; Baleanu, Dumitru; Arslan, Fahrettin; Baleanu, Dumitru; MatematikA chemometric experimental design was applied to obtain the optimal settings for spectrophotomeric quantitative resolution of two-component mixture containing benazepril hydrochloride (BE) and hydrochlorothiazide (HCT) in tablets. As it is known, the digital parameters for instance divisor concentration and All-interval are very important concepts for the application of the ratio spectra derivative spectrophotometry to the resolution of binary mixture systems. In this manuscript, a three-level full factor design was used to optimize the effects of the divisor concentration and Delta lambda-interval on the quantitative analysis of the above mentioned drugs in samples. Desirable results were obtained: firstly, with the divisor concentrations and Delta lambda-interval, 21.20 mu g/mL and Delta lambda=27.50 nm for BE in the ratio spectra first derivative spectrophotometry, secondly 27.20 mu g/mL and Delta = 5.4 for HCT in the ratio spectra second derivative method Under the above mentioned conditions, both first and second derivative approaches showed good precision, accuracy and linearity in the quantitative analysis of BE and HCT in two different pharmaceutical tablet products.Article Citation - WoS: 1Citation - Scopus: 1Fractional Differential Equation With a Complex Potential(Univ Nis, Fac Sci Math, 2020) Ugurlu, Ekin; Tas, Kenan; Baleanu, DumitruIn this manuscript, we discuss the square-integrable property of a fractional differential equation having a complex-valued potential function and we show that at least one of the linearly independent solutions of the fractional differential equation must be squarely integrable with respect to some function containing the imaginary parts of the spectral parameter and the potential function.Article The Characteristic Matrix Function of a Dissipative Hamiltonian Operator(Wiley, 2021) Ugurlu, EkinIn this paper, we consider a singular dissipative even-order Hamiltonian operator with a finite number of transmission conditions. Using coordinate-free approach, we construct the characteristic matrix-function of the Cayley transform of the dissipative operator. Using the equivalence of completeness property of root functions of Cayley transform and dissipative operator, we prove some completeness theorems. Moreover, we construct an explicit form of the resolvent operator of dissipative operator.Article Citation - WoS: 1Citation - Scopus: 1Direct Approach for the Characteristic Function of a Dissipative Operator With Distributional Potentials(Springer Basel Ag, 2020) Ugurlu, EkinThe main aim of this paper is to investigate the spectral properties of a singular dissipative differential operator with the help of its Cayley transform. It is shown that the Cayley transform of the dissipative differential operator is a completely non-unitary contraction with finite defect indices belonging to the class C-0. Using its characteristic function and the spectral properties of the resolvent operator, the complete spectral analysis of the dissipative differential operator is obtained. Embedding the Cayley transform to its natural unitary colligation, a Caratheodory function is obtained. Moreover, the truncated CMV matrix is established which is unitary equivalent to the Cayley transform of the dissipative differential operator. Furthermore, it is proved that the imaginary part of the inverse operator of the dissipative differential operator is a rank-one operator and the model operator of the associated dissipative integral operator is constructed as a semi-infinite triangular matrix. Using the characteristic function of the dissipative integral operator with rank-one imaginary component, associated Weyl functions are established.Article Citation - WoS: 2Citation - Scopus: 2Singular Dissipative Third-Order Operator and Its Characteristic Function(Springer Basel Ag, 2020) Ugurlu, EkinIn this work, we describe well-defined dissipative boundary conditions related with a singular third-order differential equation in lim-3 case at singular point. Using the characteristic function of the corresponding dissipative operator we introduce a completeness theorem.Article Citation - WoS: 9Citation - Scopus: 10Extensions of a Minimal Third-Order Formally Symmetric Operator(Malaysian Mathematical Sciences Soc, 2020) Ugurlu, EkinIn this paper, we consider some regular boundary value problems generated by a third-order differential equation and some boundary conditions. In particular, we construct maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal operator. Further using Lax-Phillips scattering theory and Sz.-Nagy-Foias characteristic function theory we prove a completeness theorem.Article Citation - WoS: 12Citation - Scopus: 15A Novel Method To Detect Almost Cyclostationary Structure(Elsevier, 2020) Baleanu, Dumitru; Bui Anh Tuan; Kim-Hung Pho; Mahmoudi, Mohammad Reza; Pho, Kim-hung; Tuan, Bui Anh; Anh Tuan, BuiThis paper is devoted to establish a computational approach to investigate that a discrete-time almost cyclostationary model is a suitable choice to fit on an observed dataset. The main idea is estimating the support of spectra and applying multiple testing. The simulated and real datasets are applied to study the performance of the introduced approach. The results confirm that the presented method acts efficiently in view of power study. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).Article Citation - WoS: 2Citation - Scopus: 3Investigation of the Eigenvalues and Root Functions of the Boundary Value Problem Together With a Transmission Matrix(Taylor & Francis Ltd, 2020) Ugurlu, EkinIn this paper, we consider a singular even-order Hamiltonian system on the union of two intervals together with appropriate boundary and transmission conditions. For investigating the spectral properties of the problem we pass to the inverse operator with an explicit form and we prove some completeness theorems.Article Citation - WoS: 1Citation - Scopus: 1Coordinate-Free Approach for the Characteristic Function of a Fourth-Order Dissipative Operator(Taylor & Francis inc, 2019) Ugurlu, EkinIn this article, we investigate some spectral properties of a singular dissipative fourth-order dissipative operator in case at the singular point. For this purpose we construct the characteristic function of both maximal simple dissipative operator and completely non-unitary contraction which is the Cayley transform of the dissipative operator. Using the properties of the characteristic operator-function we obtain the related results of the boundary value problem. Moreover we obtain the selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing eigenfunctions by using coordinate-free approach.