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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 A new method for the source localization in sectionally homogeneous bounded domains involving finitely many inner interfaces of arbitrary shapes(Pergamon-Elsevier Science, 2001-05) İdemen, Mehmet Mithat; Alkumru, AliA new method to localize a static point source buried in a nonhomogeneous bounded domain composed of finitely many homogeneous parts separated by interfaces of arbitrary shapes was established. The source can be a simple point charge or current or a dipole of them. The method requires only the knowledge of the potential function Phi (x, y, z) at five or six points on the outermost interface depending on whether the source is simple or dipole. The new and basic feature of the method consists of determining the potential function Phi (0)(x, y, z) which would be observed if the whole space was filled with a homogeneous material. Then, in the case of a simple source, the position P-0 as well as the strengths can be determined, in general, by solving a system of three linear algebraic equations. When the source consists of a dipole, its position P-0 and moment (p) over right arrow can be found by solving a system of six nonlinear algebraic equations. The determination of Phi (0) P-0 and s (or (p) over right arrow) is achieved iteratively by solving the above-mentioned algebraic equations along with a singular integral equation satisfied by Phi (0) Some illustrative examples show the applicability and accuracy of the method. The method can have effective applications in heat conduction, matter diffusion, electrostatics, steady-state current flow, electroencephalography, electrocardiography, etc.Yayın Image recovery of inaccessible rough surfaces profiles having impedance boundary condition(IEEE, 2022) Sefer, Ahmet; Yapar, AliThis letter addresses a reconstruction algorithm of locally rough inaccessible surface profiles via the knowledge of the scattered field data under the consideration of the impedance boundary condition (IBC). To this aim, first, the synthetic scattered field data are obtained through the solution of the conventional surface integral equation (SIE) written on the rough surface. Then, the same SIE together with the data equation is solved iteratively via Newton's method to obtain the image of the rough surface profile. In the numerical implementation, the nonlinear ill-posed inverse problem is linearized in an iterative fashion via the Newton method and regularized by Tikhonov in the least-squares sense. The feasibility of the algorithm is provided via numerical examples, which shows that the method is effective and promising.Yayın Achieving the capacity region boundary of fading CDMA channels via generalized iterative waterfilling(IEEE, 2006-11) Kaya, Onur; Ulukuş, ŞennurWe characterize the optimum power control policies that achieve arbitrary rate tuples on the boundary of the, capacity region of a power controlled, code division multiple access (CDMA) system in a fading channel with perfect channel state information (CSI). We propose a "generalized" waterfilling approach, and provide an iterative algorithm that solves for the optimum power allocation policy, for A given arbitrary rate tuple on the boundary of the capacity region. We then investigate the effects of limited feedback on the capacity region, and demonstrate that a good power control policy may require only a very low rate feedback.Yayın A parametric approach to construct two-variable positive real impedance functions for the real frequency design of mixed lumped-distributed matching networks(IEEE, 2004) Aksen, Ahmet; Pınarbaşı, Hacı; Yarman, Bekir Sıddık BinboğaIn this paper, a parametric approach to construct two-variable positive real driving point impedance functions characterizing lossless ladder networks with mixed lumped and distributed elements is presented. The proposed approach is based on the generation of two-variable positive real impedance functions from the single variable boundary conditions. Utilizing the proposed parametric construction algorithm, real frequency matching technique is extended to the design of matching networks with mixed lumped and distributed elements. The application of the approach is illustrated by a broadband microwave amplifier design incorporating mixed lumped and distributed type matching networks. The resultant design has been compared with the AWR Microwave Office software simulation.Yayın Confluent tip singularity of the electromagnetic field at the apex of a material cone(Elsevier Science, 2003-09) İdemen, Mehmet MithatThe tip singularity of the electromagnetic field at the apex of a cone (conical sheet) is investigated in its most general framework. To this end one considers, without loss of generality, a circularly symmetric cone which separates two simple media having different constitutive parameters, and tries to reveal the asymptotic behaviour of the electromagnetic field created near the apex of the cone by any rotationally symmetric source distribution. To cover various boundary conditions which are extensively used in actual investigations, the cone is supposed to be formed by an infinitely thin material sheet having its own constitutive parameters. The results show that the type and order of the singularity depend, in general, on various parameters such as (i) the apex angle of the cone, (ii) the constitutive parameters of the mediums separated by the cone, (iii) the constitutive parameters of the material cone itself and (iv) the topology of the conical surface. The problem of determining the order in question gives rise to a transcendental algebraic equation involving the Legendre functions of the first kind with complex orders. If the order is a simple root of this equation, then the singularity is always of the algebraic typed whereas a multiple root gives rise also to logarithmic singularities. A numerical method suitable to find a good approximate solution to this equation is also established. Since the general expressions of the boundary conditions on the material cone, which, are compatible with both the Maxwell equations and the topology of the cone, are not known, an attempt has also been made to derive these expressions. Some examples concerning the boundary conditions which are extensively considered in actual investigations are given.Yayın Reconstruction algorithm for impenetrable rough surface profile under Neumann boundary condition(Taylor and Francis Ltd., 2022-05-24) Sefer, Ahmet; Yapar, AliIn this paper, an algorithm to reconstruct one-dimensional impenetrable rough surface from the knowledge of scattering field is presented. The rough surface is considered as locally perturbed and the scattering field data are collected above the roughness in a simple non-magnetic medium considering Neumann boundary condition. First, the surface integral equation constituted via the Neumann boundary condition is solved and scattering field data are observed synthetically. Then, the same surface integral equation together with the data equation are solved in an iterative fashion to reconstruct the surface variation. In the numerical implementation, the so-called ill-posed inverse problem is regularized with Tikhonov method and a least-squares solution is obtained by using Gaussian-type basis function. Finally, numerical examples are carried out to illustrate effectiveness of the method.Yayın The concept of confluence and the edge conditions for a wedge bounded by material sheets(IEEE, 2000) İdemen, Mehmet MithatThe edge conditions which dictate the asymptotic behaviour of the electromagnetic field near the edges play a crucial role in solving boundary-value problems involving boundaries having edges, in analytical studies they permit one to determine some unknown functions while in numerical investigations they enable one to improve the convergence of some processes by introducing beforehand the edge singularities into the field functions. This work is devoted to the analysis of wedge configurations bounded by material sheets having different constitutive parameters. From mathematical point of view, the problem can be reduced to 9 canonical types. These canonical types are investigated in full detail by introducing the confluence concept which permits one to reveal also the logarithmic singularities, if any.
