Browsing by Author "Celebi, A. O."
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Article Citation Count: 3Dirichlet problem for a generalized inhomogeneous polyharmonic equation in an annular domain(Taylor & Francis Ltd, 2012) Aksoy, Ümit; Celebi, A. O.; MathematicsIn this article, we investigate the solvability of the Dirichlet problems in ring domains for elliptic linear complex partial differential equations having polyharmonic operators as main parts. First, we give higher order Green functions as fundamental solutions of the homogeneous problems using the iteration of harmonic Green functions for ring domains. Second, we introduce some classes of operators related to Dirichlet problems together with their basic properties. Next, we transform the original problems into equivalent singular integral equations. Finally, solvability of the problems is discussed by defining the adjoint problems and using Fredholm alternative.Article Citation Count: 9Identification of linear handling models for road vehicles(Taylor & Francis Ltd, 2008) Arıkan, Kutluk Bilge; Unlusoy, Y. S.; Korkmaz, I.; Celebi, A. O.; Department of Mechatronics EngineeringThis study reports the identification of linear handling models for road vehicles starting from structural identifiability analysis, continuing with the experiments to acquire data on a vehicle equipped with a sensor set and data acquisition system, and ending with the estimation of parameters using the collected data. The model structure originates from the well-known linear bicycle model that is frequently used in handling analysis of road vehicles. Physical parameters of the bicycle model structure are selected as the unknown parameter set that is to be identified. Global identifiability of the model structure is analysed, in detail, and concluded according to various available sensor sets. Physical parameters of the bicycle model structure are estimated using prediction error estimation method. Genetic algorithms are used in the optimisation phase of the identification algorithm to overcome the difficulty in the selection of initial values for parameter estimates. Validation analysis of the identified model is also presented. The identified model is shown to track the system response successfully.Article Citation Count: 14Neumann problem for generalized n-Poisson equation(Academic Press inc Elsevier Science, 2009) Aksoy, Ümit; Celebi, A. O.; MathematicsUsing a hierarchy of integral operators having higher-order Neumann functions and their derivatives as kernels, the Neumann problem for a 2nth order linear partial complex differential equation is discussed. The solvability of the problem is obtained. (C) 2009 Elsevier Inc. All rights reserved.Article Citation Count: 7Norm estimates of a class of Calderon-Zygmund type strongly singular integral operators(Taylor & Francis Ltd, 2007) Aksoy, Ümit; Celebi, A. O.; MathematicsIn this article, we prove the L-p boundedness of a class of Calderon - Zygmund type strongly singular operators. In particular, we give an estimate for the L-2 norm of these operators in the unit disc of the complex plane.Article Citation Count: 3Polyharmonic Robin problem for complex linear partial differential equations(Taylor & Francis Ltd, 2014) Aksoy, Ümit; Celebi, A. O.; MathematicsIn this article, generalized polyharmonic Robin functions are introduced together with some of their properties. A hierarchy of integral operators with relevant kernel functions are investigated. These operators are used to transform the Robin problem for a 2nth order linear partial complex differential equation with polyharmonic leading term (generalized n-Poisson equation) into a singular integral equation having Fredholm property.Article Citation Count: 2Schwarz problem for higher order linear equations in a polydisc(Taylor & Francis Ltd, 2017) Aksoy, Ümit; Celebi, A. O.; MathematicsIn this paper, we discuss the Schwarz boundary value problem for higher order linear complex differential equations in the unit polydisc of C-2. After the relevant preparations, we give the solution for a model equation with homogeneous boundary conditions. Then we obtain the solutions of a linear equation involving Schwarz boundary conditions on the unit polydisc.Article Citation Count: 12Schwarz problem for higher-order complex elliptic partial differential equations(Taylor & Francis Ltd, 2008) Aksoy, Ümit; Celebi, A. O.; MathematicsIn this paper, we investigate the solvability of a higher order elliptic differential equation with the Schwarz conditions on the unit disc of the complex plane.