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Article Citation - WoS: 1Citation - Scopus: 1ON THE DERIVATION OF EXPLICIT FORMULAE FOR SOLUTIONS OF THE WAVE EQUATION IN HYPERBOLIC SPACE(Hacettepe Univ, Fac Sci, 2013) Guseinov, Gusein Sh.We offer a new approach to solving the initial value problem for the wave equation in hyperbolic space in arbitrary dimensions. Our approach is based on the spectral analysis of the Laplace-Beltrami operator in hyperbolic space and some structural formulae for rapidly decreasing functions of this operator.Article Citation - WoS: 1Citation - Scopus: 1A Short Note on Some Arithmetical Properties of the Integer Part of Ap(Tubitak Scientific & Technological Research Council Turkey, 2019) Akbal, YıldırımLet $a>0$ be an irrational number. We study some of the arithmetical properties of ${\\{\\lfloor ap\\rfloor\\}}_{p=2}^\\infty$ where pdenotes a prime number and $\\lfloor x\\rfloor$ denotes the largest integer not exceeding x.Article Citation - WoS: 16Citation - Scopus: 20Common Fixed Point Theorems in Cone Banach Spaces(Hacettepe Univ, Fac Sci, 2011) Abdeljawad, Thabet; Karapinar, Erdal; Tas, Kenan; MathematicsRecently, E. Karapinar (Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Applications, Article ID 609281, 9 pages, 2009) presented some fixed point theorems for self-mappings satisfying certain contraction principles on a cone Banach space. Here we will give some generalizations of this theorem.Article Citation - Scopus: 69An integrated intuitionistic fuzzy multi criteria decision making method for facility location selection(Association for Scientific Research, 2011) Boran,F.E.The facility location selection, which is one of the important activities in strategic planning for a wide range of private and public companies, is a multi-criteria decision making problem including both quantitative and qualitative criteria. Traditional methods for facility location selection can not be effectively handled because information can not be represented by precise information under many conditions. This paper proposes the integration of intuitionistic fuzzy preference relation aiming to obtain weights of criteria and intuitionistic fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method aiming to rank alternatives for dealing with imprecise information on selecting the most desirable facility location. To illustrate the application of the proposed method, a practical application is given. Copyright © Association for Scientific Research.Article Citation - WoS: 1Citation - Scopus: 1Construction of a Complex Jacobi Matrix From Two-Spectra(Hacettepe Univ, Fac Sci, 2011) Guseinov, Gusein Sh; MathematicsIn this paper we study the inverse spectral problem for two-spectra of finite order complex Jacobi matrices (tri-diagonal matrices). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by deleting the first column and the first row of the Jacobi matrix. An explicit procedure of reconstruction of the matrix from the two-spectra is given.Article Citation - WoS: 1An exhaustive computer search for finding new curves with many points among fibre products of two Kummer covers over F5 and F7(Tubitak Scientific & Technological Research Council Turkey, 2013) Ozbudak, Ferruh; Temur, Burcu Gulmez; Yayla, Oguz; Gülmez Temür, BurcuIn this paper we make an exhaustive computer search for finding new curves with many points among fibre products of 2 Kummer covers of the projective line over F-5 and F-7. At the end of the search, we have 12 records and 6 new entries for the current Table of Curves with Many Points. In particular, we observe that the fibre product y(1)(3)= 5(x + 2)(x + 5)/x, y(2)(3)= 3x(2()x + 5)/x + 3 over F-7 has genus 7 with 36 rational points. As this coincides with the Ihara bound, we conclude that the maximum number N-7(7) of F-7-rational points among all curves of genus 7 is 36. Our exhaustive search has been possible because of the methods given in the recent work by Ozbudak and Temur (2012) for determining the number of rational points of such curves.Article Characterizations of the Commutators Involving Idempotents in Certain Subrings of $m_{2}(\\mathbb{z})$(2023) Gümüşel, Günseli; Özdın, TufanIn this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator $[E_1, E_2]$ = $E_1E_2 − E_2E_1$ involving idempotents $E_1, E_2$ in certain subrings of $M_2(Z)$.Article Citation - WoS: 6Citation - Scopus: 6Dynamic Reliability and Performance Evaluation of Multi-State Systems With Two Components(Hacettepe Univ, Fac Sci, 2011) Eryilmaz, Serkan; Industrial EngineeringIn this paper we study multi-state systems consisting of two components when the number of system states and the number of states of each component are the same, i.e. the systems under consideration are homogeneous multi-state systems. In particular we evaluate multi-state series and cold standby systems assuming that the degradation in their components follow a Markov process. The behaviour of systems with respect to degradation rates is also investigated in terms of stochastic ordering.Article Citation - Scopus: 1On the Derivation of Explicit Formulae for Solutions of the Wave Equation in Hyperbolic Space(Hacettepe University, 2013) Guseinov,G.S.We offer a new approach to solving the initial value problem for the wave equation in hyperbolic space in arbitrary dimensions. Our approach is based on the spectral analysis of the Laplace-Beltrami operator in hyperbolic space and some structural formulae for rapidly decreasing functions of this operator. © 2013, Hacettepe University. All rights reserved.Article Characterizations of the Commutators Involving Idempotents in Certain Subrings of $m_{2}(\mathbb{z})$(Tubitak Scientific & Technological Research Council Turkey, 2023) Ozdin, Tufan; Gumusel, GunseliIn this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator [E1, E2] = E1E2 - E2E1 involving idempotents E1, E2 in certain subrings of M2(Z).
