Browsing by Author "Celebi, A. O."

Now showing 1 - 8 of 8

Citation - WoS: 5
Citation - Scopus: 8
Dirichlet Problem for a Generalized Inhomogeneous Polyharmonic Equation in an Annular Domain
(Taylor & Francis Ltd, 2012) Aksoy, U.; Celebi, A. O.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In 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.
Citation - WoS: 12
Dirichlet Problems for the Generalized n-poisson Equation
(Birkhauser verlag Ag, 2010) Aksoy, U.; Celebi, A. O.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Polyharmonic hybrid Green functions, obtained by convoluting polyharmonic Green and Almansi Green functions, are taken as kernels to define a hierarchy of integral operators. They are used to investigate the solvability of some types of Dirichlet problems for linear complex partial differential equations with leading term as the polyharmonic operator.
Citation - WoS: 8
Citation - Scopus: 15
Identification of Linear Handling Models for Road Vehicles
(Taylor & Francis Ltd, 2008) Arikan, K. B.; Unlusoy, Y. S.; Korkmaz, I.; Celebi, A. O.; Department of Mechatronics Engineering; 01. Atılım University
This 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.
Citation - WoS: 14
Citation - Scopus: 19
Neumann problem for generalized n-Poisson equation
(Academic Press inc Elsevier Science, 2009) Aksoy, Ue.; Celebi, A. O.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Using 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.
Citation - WoS: 7
Citation - Scopus: 9
Norm Estimates of a Class of Calderon-Zygmund Type Strongly Singular Integral Operators
(Taylor & Francis Ltd, 2007) Aksoy, Ue; Celebi, A. O.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In 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.
Citation - WoS: 3
Citation - Scopus: 5
Polyharmonic Robin Problem for Complex Linear Partial Differential Equations
(Taylor & Francis Ltd, 2014) Aksoy, U.; Celebi, A. O.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In 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.
Citation - WoS: 2
Citation - Scopus: 5
Schwarz problem for higher order linear equations in a polydisc
(Taylor & Francis Ltd, 2017) Aksoy, U.; Celebi, A. O.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In 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.
Citation - WoS: 13
Citation - Scopus: 15
Schwarz problem for higher-order complex elliptic partial differential equations
(Taylor & Francis Ltd, 2008) Aksoy, U.; Celebi, A. O.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In 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.