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Yayın Positive solutions for a sum-type singular fractional integro-differential equation with m-point boundary conditions(Politechnica University of Bucharest, 2017) Aydoğan, Seher Melike; Nazemi, Sayyedeh Zahra; Rezapour, ShahramWe study the existence and uniqueness of positive solutions for a sum-type singular fractional integro-differential equation with m-point boundary condition. Also, we provide an example to illustrate our main result.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 Harmonic function for which the second dilatation is ?-spiral(Springer International Publishing AG, 2012) Aydoğan, Seher Melike; Duman, Emel Yavuz; Polatoğlu, Yaşar; Kahramaner, YaseminLet f = h + (g) over bar be a harmonic function in the unit disc . We will give some properties of f under the condition the second dilatation is alpha-spiral.Yayın Head-on collision of the solitary waves in fluid-filled elastic tubes(Işık University Press, 2018-04-12) Özden, Ali Erinç; Demiray, HilmiIn the present work, by employing the field equations given in [15] and the extended PLK method derived in [9], we have studied the head-on collision of solitary waves in arteries. Introducing a set of stretched coordinates which include some unknown functions characterizing the higher order dispersive effects and the trajectory functions to be determined from the removal of possible secularities that might occur in the solution. Expanding these unknown functions and the field variables into power series of the smallness parameter epsilon and introducing the resulting expansions into the field equations we obtained the sets of partial differential equations. By solving these differential equations and imposing the requirements for the removal of possible secularities we obtained the speed correction terms and the trajectory functions. The results of our calculation show that both the evolution equations and the phase shifts resulting from the head-on collision of solitary waves are quite different from those of Xue [15], who employed the incorrect formulation of Su and Mirie [4]. As opposed to the result of previous works on the same subject, in the present work the phase shifts depend on the amplitudes of both colliding waves.Yayın An approximate wave solution for perturbed KDV and dissipative NLS equations: weighted residual method(Işık University Press, 2019-06-21) Demiray, HilmiIn the present work, we modified the conventional "weighted residual method" to some nonlinear evolution equations and tried to obtain the approximate progressive wave solutions for these evolution equations. For the illustration of the method we studied the approximate progressive wave solutions for the perturbed KdV and the dissipative NLS equations. The results obtained here are in complete agreement with the solutions of inverse scattering method. The present solutions are even valid when the dissipative effects are considerably large. The results obtained are encouraging and the method can be used to study the cylindrical and spherical evolution equations.Yayın On progressive wave solution for non-planar KDV equation in a plasma with q-nonextensive electrons and two oppositely charged ions(Işık University Press, 2020) Demiray, Hilmi; El-Zahar, Essam Roshdy; Shan, Shaukat AliIn this paper, the ion-acoustic wave is investigated in a plasma with q-nonextensive electrons and two oppositely charged ions with varying masses. These parameters are found to modify the linear dispersion relation and nonlinear solitary structures. The reductive perturbation method is employed to derive modified Korteweg-de Vries (KdV) equation. To solve the obtained governing evolution equation, the exact solution in the planar geometry is obtained and used to obtain an analytical approximate progressive wave solution for the nonplanar evolution equation. The analytical approximate solution so obtained is compared with the numerical solution of the same nonplanar evolution equation and the results are presented in 2D and 3D figures. The results revealed that both solutions are in good agreement. A parametric study is carried out to investigate the effect of different physical parameters on the nonlinear evolution solution behavior. The obtained solution allows us to study the impact of various plasma parameters on the behavior of the nonplanar ion-acoustic solitons. The suitable application of the present investigations can be found in laboratory plasmas, where oppositely charged ions and nonthermal electrons dwell.Yayın Book Review: Oktay Veliyev. Multidimensional Periodic Schrödinger Operator (Perturbation Theory and Applications)(Işık University Press, 2015) Hasanoğlu, Elman[No abstract available]Yayın Dendrimers are the unique chemical trees with maximum spectral radius(Univ Kragujevac, 2012) Bıyıkoğlu, Türker; Leydold, JosefIt is shown that dendrimers have maximum spectral radius and maximum Collatz-Sinogowitz index among all chemical trees of given size. The result is also generalized for the class of chemical trees with prescribed number of pendant vertices.Yayın Some properties concerning close-to-convexity of certain analytic functions(Springer International Publishing AG, 2012) Nunokawa, Mamoru; Aydoğan, Seher Melike; Kuroki, Kazuo; Yıldız, İsmet; Owa, ShigeyoshiLet f(z) be an analytic function in the open unit disk D normalized with f(0) = 0 and f'(0) = 1. With the help of subordinations, for convex functions f(z) in D, the order of close-to-convexity for f(z) is discussed with some example.
