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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 Hopf-cyclic cohomology of quantum enveloping algebras(European Mathematical Society Publishing House, 2016) Kaygun, Atabey; Sütlü, Serkan SelçukIn this paperwe calculate both the periodic and non-periodic Hopf-cyclic cohomology of Drinfeld-Jimbo quantum enveloping algebra Uq.g/ for an arbitrary semi-simple Lie algebra g with coefficients in a modular pair in involution. We obtain this result by showing that the coalgebra Hochschild cohomology of these Hopf algebras are concentrated in a single degree determined by the rank of the Lie algebra g.Yayın Hom-Lie-Hopf algebras(Academic Press Inc., 2020-07-01) Halıcı, Serpil; Karataş, Adnan; Sütlü, Serkan SelçukWe studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general (α,β)-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of (α,Id)-type. We show that the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras form a matched pair of Hom-Hopf algebras. We observe also that, the semi-dualization of a double cross product Hom-Hopf algebra is a bicrossproduct Hom-Hopf algebra. In particular, we apply this result to the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras to obtain Hom-Lie-Hopf algebras.Yayın Complex travelling wave solutions to the KdV and Burgers equations(Elsevier Science Inc, 2005-03) Demiray, HilmiIn the present work, making use of the hyperbolic tangent method, some complex travelling wave solutions to the Korteweg-deVries and Burgers equations are obtained. It is observed that the real part of the Solution for the Burgers equation is of shock type whereas the imaginary part is the localized travelling wave. However, for the solution of the Korteweg-deVries equation the real part is a solitary wave while the imaginary part is the product of a solitary wave with a shock.Yayın The modified reductive perturbation method as applied to Boussinesq equation: strongly dispersive case(Elsevier Science Inc, 2005-05-05) Demiray, HilmiIn this work, we extended the application of "the modified reductive perturbation method" to Boussinesq equation for strongly dispersive case and tried to obtain the contribution of higher order terms in the perturbation expansion. It is shown that the first order term in the perturbation expansion is governed by the non-linear Schrodinger equation and the second order term is governed by the linearized Schrodinger equation with a non-homogeneous term. In the long-wave limit, a travelling wave type of solution to these equations is also given.Yayın Graphs of given order and size and minimum algebraic connectivity(Elsevier Science Inc, 2012-04-01) Bıyıkoğlu, Türker; Leydold, JosefThe structure of connected graphs of given size and order that have minimal algebraic connectivity is investigated. It is shown that they must consist of a chain of cliques. Moreover, an upper bound for the number of maximal cliques of size 2 or larger is derived.Yayın Higher analogues of discrete topological complexity(Springer-Verlag Italia S.R.L., 2024-06-13) Alabay, Hilal; Borat, Ayşe; Cihangirli, Esra; Erdal, Esma DiricanIn this paper, we introduce the nth discrete topological complexity and study its properties such as its relation with simplicial Lusternik–Schnirelmann category and how the higher dimensions of discrete topological complexity relate with each other. Moreover, we find a lower bound of n-th discrete topological complexity which is given by the nth usual topological complexity of the geometric realisation of that complex. Furthermore, we give an example for the strict case of that lower bound.
