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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

On Principles Of B-smooth Discontinuous Flows

Akalin, Ebru Cigdem 01 November 2004 (has links) (PDF)
Discontinuous dynamical system defined by impulsive autonomous differential equation is a field that has actually been considered rarely. Also, the properties of such systems have not been discussed thoroughly in the course of mathematical researches so far. This thesis comprises two parts, elaborated with a number of examples. In the first part, some results of the previous studies on the classical dynamical system are exposed. In the second part, the definition of discontinuous dynamical system defined by impulsive autonomous differential equation is formulated, and its properties are investigated, in the view of the known results of the studies on the classical dynamical system and impulsive differential equations.
2

Schwarz Problem For Complex Partial Differential Equations

Aksoy, Umit 01 December 2006 (has links) (PDF)
This study consists of four chapters. In the first chapter we give some historical background of the problem, basic definitions and properties. Basic integral operators of complex analysis and and Schwarz problem for model equations are presented in Chapter 2. Chapter 3 is devoted to the investigation of the properties of a class of strongly singular integral operators. In the last chapter we consider the Schwarz boundary value problem for the general partial complex differential equations of higher order.
3

New Classes Of Differential Equations And Bifurcation Of Discontinuous Cycles

Turan, Mehmet 01 July 2009 (has links) (PDF)
In this thesis, we introduce two new classes of differential equations, which essentially extend, in several directions, impulsive differential equations and equations on time scales. Basics of the theory for quasilinear systems are discussed, and particular results are obtained so that further investigations of the theory are guaranteed. Applications of the newly-introduced systems are shown through a center manifold theorem, and further, Hopf bifurcation Theorem is proved for a three-dimensional discontinuous dynamical system.
4

Neural Networks With Piecewise Constant Argument And Impact Activation

Yilmaz, Enes 01 June 2011 (has links) (PDF)
This dissertation addresses the new models in mathematical neuroscience: artificial neural networks, which have many similarities with the structure of human brain and the functions of cells by electronic circuits. The networks have been investigated due to their extensive applications in classification of patterns, associative memories, image processing, artificial intelligence, signal processing and optimization problems. These applications depend crucially on the dynamical behaviors of the networks. In this thesis the dynamics are presented by differential equations with discontinuities: differential equations with piecewise constant argument of generalized type, and both impulses at fixed moments and piecewise constant argument. A discussion of the models, which are appropriate for the proposed applications, are also provided. Qualitative analysis of existence and uniqueness of solutions, global asymptotic stability, uniform asymptotic stability and global exponential stability of equilibria, existence of periodic solutions and their global asymptotic stability for these networks are obtained. Examples with numerical simulations are given to validate the theoretical results. All the properties are rigorously approved by using methods for differential equations with discontinuities: existence and uniqueness theorems / stability analysis through the Second Lyapunov method and linearization. It is the first time that the problem of stability with the method of Lyapunov functions for differential equations with piecewise constant argument of generalized type is investigated. Despite the fact that these equations are with deviating argument, stability criteria are merely found in terms of Lyapunov functions.
5

Two Studies On Backward Stochastic Differential Equations

Tunc, Vildan 01 July 2012 (has links) (PDF)
Backward stochastic differential equations appear in many areas of research including mathematical finance, nonlinear partial differential equations, financial economics and stochastic control. The first existence and uniqueness result for nonlinear backward stochastic differential equations was given by Pardoux and Peng (Adapted solution of a backward stochastic differential equation. System and Control Letters, 1990). They looked for an adapted pair of processes {x(t) / y(t)} / t is in [0 / 1]} with values in Rd and Rd&times / k respectively, which solves an equation of the form: x(t) + int_t^1 f(s,x(s),y(s))ds + int_t^1 [g(s,x(s)) + y(s)]dWs = X. This dissertation studies this paper in detail and provides all the steps of the proofs that appear in this seminal paper. In addition, we review (Cvitanic and Karatzas, Hedging contingent claims with constrained portfolios. The annals of applied probability, 1993). In this paper, Cvitanic and Karatzas studied the following problem: the hedging of contingent claims with portfolios constrained to take values in a given closed, convex set K. Processes intimately linked to BSDEs naturally appear in the formulation of the constrained hedging problem. The analysis of Cvitanic and Karatzas is based on a dual control problem. One of the contributions of this thesis is an algorithm that numerically solves this control problem in the case of constant volatility. The algorithm is based on discretization of time. The convergence proof is also provided.
6

On The Wkb Asymptotic Solutionsof Differential Equations Of The Hypergeometric Type

Aksoy, Betul 01 December 2004 (has links) (PDF)
WKB procedure is used in the study of asymptotic solutions of differential equations of the hypergeometric type. Hence asymptotic forms of classical orthogonal polynomials associated with the names Jacobi, Laguerre and Hermite have been derived. In particular, the asymptotic expansion of the Jacobi polynomials $P^{(alpha, beta)}_n(x)$ as $n$ tends to infinity is emphasized.
7

Oscillation Of Second Order Matrix Equations On Time Scales

Selcuk, Aysun 01 November 2004 (has links) (PDF)
The theory of time scales is introduced by Stefan Hilger in his PhD thesis in 1998 in order to unify continuous and discrete analysis. In our thesis, by making use of the time scale calculus we study the oscillation of nonlinear matrix differential equations of second order. the first chapter is introductory in nature and contains some basic definitions and tools of the time scales calculus, while certain well-known results have been presented with regard to oscillation of the solutions of second order matrix equations and some new oscillation criteria for the same type equations have been established in the second chapter.
8

Inverse Problems For Parabolic Equations

Baysal, Arzu 01 November 2004 (has links) (PDF)
In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Problem III and IV) or on a time interval (in Problem I and II). If solution of inverse problem exists, then the temperature can be defined everywhere on the domain at all instants. The thesis consists of six chapters. In the first chapter, there is the introduction where the definition and applications of inverse problems are given and definition of the four inverse problems, that we will analyze in this thesis, are stated. In the second chapter, some definitions and theorems which we will use to obtain some conclusions about the corresponding direct problem of our four inverse problems are stated, and the conclusions about direct problem are obtained. In the third, fourth, fifth and sixth chapters we have the analysis of inverse problems I, II, III and IV, respectively.
9

Energy Bounds For Some Nonstandard Problems In Partial Differential Equations

Ozer, Ozge 01 September 2005 (has links) (PDF)
This thesis is a survey of the studies of Ames,Payne and Schaefer about the partial differential equations with nonstandard auxiliary conditions / this is where the values of the solution are prescribed as a combination of initial time t=0 and at a later time t=T. The first chaper is introductory and contains some historical background of the problem,basic definitions and theorems.In Chapter 2 energy bounds and pointwise bounds for the solutions of the nonstandard hyperbolic problems have been investigated and by means of energy bound the uniqueness of solutions is examined. Similar discussions for the nonstandard parabolic problems have been presented in Chapter 3. Lastly in Chapter 4 a new continuous dependence result has been derived for the nonstandard problem.
10

Sturm Comparison Theory For Impulsive Differential Equations

Ozbekler, Abdullah - 01 December 2005 (has links) (PDF)
In this thesis, we investigate Sturmian comparison theory and oscillation for second order impulsive differential equations with fixed moments of impulse actions. It is shown that impulse actions may greatly alter the oscillation behavior of solutions. In chapter two, besides Sturmian type comparison results, we give Leightonian type comparison theorems and obtain Wirtinger type inequalities for linear, half-linear and non-selfadjoint equations. We present analogous results for forced super linear and super half-linear equations with damping. In chapter three, we derive sufficient conditions for oscillation of nonlinear equations. Integral averaging, function averaging techniques as well as interval criteria for oscillation are discussed. Oscillation criteria for solutions of impulsive Hill&amp / #8217 / s equation with damping and forced linear equations with damping are established.

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