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Yayın Asymptotic solutions of love wave propagation in a covered half-space with inhomogeneous initial stresses G(3)(1)(Işık University Press, 2015) Hasanoğlu, Elman; Negin, MasoudThe dispersive behavior of Love waves in an elastic half-space substrate covered by an elastic layer under the effect of inhomogeneous initial stresses has been investigated. Classical linearized theory of elastic waves in initially stressed bodies for small deformations is used and the well-known WKB high-frequency asymptotic technique is applied for the theoretical derivations. Numerical results on the action of the influence of the initial stresses on the wave propagation velocity for a geophysical example are presented and discussed.Yayın Book Review: Oktay Veliyev. Multidimensional Periodic Schrödinger Operator (Perturbation Theory and Applications)(Işık University Press, 2015) Hasanoğlu, Elman[No abstract available]Yayın 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 complex solutions of the eikonal equation(IEEE, 2007) Hasanoğlu, ElmanIn this paper a new approach of complex rays in an inhomogeneous medium is presented. Complex rays are complex solutions of the eikonal equation, the main equation of the geometical optics. It is shown that solving the eikonal equation by using the characteristic method naturally leads to the pseudoriemann and Minkowski geometries. In framework of these geometries complex rays , like the real ones, can be drawn in real space and they may have caustics, and caustics also can be drawn in real space.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 Two reflector non symmetric shaped antenna systems(IEEE, 2000) Hasanoğlu, ElmanTwo reflector antenna systems with non symmetric reflecting surfaces under GO approximation are investigated. It is shown, that the problem of forming desired far field pattern leades to solving the system of partial differential equations with respect to mapping functions between wave fronts. One of these equations is non linear and expresses energy conversation law. It is shown that this equation can be solved separetly in the class of non smooth functions which has a discontinuty of first kind along a given curve.Yayın A method for calculating profiles of a dielectric thick lenses(IEEE, 2001) Hasanoğlu, ElmanHasanov and Polat (see International Journal of Electronics and Communications (AEO), vol.54, no.2, p.109-113, 2000) investigated the transformation of a plane wavefront to another plane wavefront after passing through a thick lens and described the class of optical mappings realizable by means of such lenses. However, it is desirable to describe the class of optical mappings and calculate the lens profiles for a more general case when incoming and outgoing wavefronts have arbitrary shapes. For two reflecting surfaces a similar problem has been solved by Gasanov (1991). The aim of this paper is to provide a method for calculating the profiles of symmetric thick lenses which realize an a priori given optical mapping between spherical and plane wavefronts. It is shown that this mapping may be chosen freely and be used for various purposes such as satisfying Abbe's sine law or Herscel's condition exactly. We have shown, that calculating the profiles of lenses can be reduced to solving two first-order differential equations which can be solved separately. It is also shown that the geometry of the problem provides a natural condition to control the accuracy for the numerical solution of the obtained differential equationsYayın Complex and real rays in three dimensional Minkowski space(IEEE, 2002) Hasanoğlu, ElmanA new approach to the theory of complex rays is proposed. It is shown that the Minkowski space is more appropriate for describing these rays than the usual, Euclidian spaces. Some illustrative examples are represented.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.
