3 sonuçlar
Arama Sonuçları
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Yayın A new theory of complex rays(Oxford Univ Press, 2004-12) Hasanoğlu, ElmanA new approach to the theory of complex rays is presented. It is shown that the three-dimensional Minkowski space, the variant of the well known four-dimensional space-time Minkowski space of the special theory of relativity, is more appropriate for describing both real and complex rays than the usual Euclidean space. It turns out that in this space complex rays, as real ones, may have quite definite directions and magnitudes. This allows us to understand the geometrical meaning of the complex magnitudes such as complex distances and complex angles, intensively discussed over the last several decades. From this point of view a new interpretation of the Gaussian beams and reflection laws is presented.Yayın On the realization of optical mappings and transformation of amplitudes by means of an aspherical "thick" lens(Gustav Fischer Verlag, 2000) Hasanoğlu, Elman; Polat, Burak DenizThe constraints for the realization of a given optical mapping by means of an aspherical ''thick" lens are investigated by using the laws of geometrical optics. The analysis yields us a partial differential equation which the optical mapping functions must satisfy as a necessary and sufficient condition. It is shown that thick lenses, which convert plane waves to plane waves, can be considered as a pure amplitude element, An interesting feature of this equation is that it does not involve the lens profiles. The problem of realization is later discussed for some special mappings and graphical illustrations of the aspherical lens profiles for a linear mapping are presented.Yayın A new form of Kakutani fixed point theorem and intersection theorem with applications(Ministry Communications & High Technologies, 2021) Farajzadeh, Ali P.; Zanganehmehr, Parastoo; Hasanoğlu, ElmanThe first aim of this paper is to extend the Kakutani's fixed point theorem from locally convex topological vector spaces to linear topological spaces. The second goal is to present sufficient conditions under which the intersection of a family of sets is nonempty. The third step is to provide an existence theorem for a set valued mapping. Finally, as an application, an existence result of a solution for quasi-equilibrium problem is given.
