 Abstract— Customers can easily change their GSM operator after accepting the legal regulation on moving the number to the new operator in Turkey. In this study, fuzzy analytic network process (FANP) is used to rank for three Global Systems for Mobile Communications (GSM) operators. Five main criteria are described and also sub-criteria are determined. Because of the pairwise comparisons is li...

Photoacoustic imaging is a non-ionizing imaging modality that provides contrast consistent with optical imaging techniques while the resolution and penetration depth is similar to ultrasound techniques. In a previous publication [Opt. Express 18, 11406 (2010)], a technique was introduced to experimentally acquire the imaging operator for a photoacoustic imaging system. While this was an importa...

For a positive integer k, the rank-k numerical range Λk(A) of an operator A acting on a Hilbert space H of dimension at least k is the set of scalars λ such that PAP = λP for some rank k orthogonal projection P . In this paper, a close connection between low rank perturbation of an operator A and Λk(A) is established. In particular, for 1 ≤ r < k it is shown that Λk(A) ⊆ Λk−r(A + F ) for any op...