Browsing Dept. of Mathematics  Master's degree by Issue Date
Now showing items 120 of 129

Unified approach to transformations of Painleve equations
(Bilkent University, 1993)In this thesis, we iind the explicit form of some transformations associated with the second, third, fourth and fifth Painleve equations. These transformations are obtained by using the Schlesinger transformations associated ... 
Homogeneous, anisotropic solutions of topologically massive gravity including a cosmological constant
(Bilkent University, 1993)I'lxact solutions l.o tin' (ic'ld (Miial.ioiis o( 'Го)о1о;г;1са,11у ma.ssiv(i gravity wit h a cosmological coiisl.anl. ai<' pix'scntisl. Tlics(' ai<‘ lK)mog<m<'o\is,a,iiisotro)ic Bianchi J ’ypc VIII and l'yx' IX ... 
An integrable family of MongeAmpere equations and their multiHamiltonian structure
(Bilkent University, 1993)We have identified a completely integrable family of MongeAmpère equations through an examination of their Hamiltonian structure. Starting with a variational formulation of the MongeAmpère equations we have constructed the ... 
On Arf rings
(Bilkent University, 1994)In this thesis, we worked with curves which have cusp type singularities. We described the Arf theory, which solves the problem of understanding and finding the multiplicity sequence of a curve branch algebraically. We ... 
Regular basis and functor Ext
(Bilkent University, 1994)This work is a study of the relation between the vanishing of Ext functor and the existence of regular bases in the cartesian product and tensor product of some special Kothe spaces. We give some new results concerning ... 
Review of an approach to obstruction theory
(Bilkent University, 1994)In this work, we summarized an approach to obstruction tlieory developed by E. Thomas. We gave some illustrative examples to demonstrate the method. These are : 2plane fields on manifolds revi(iwing works of Thotnas, 3 ... 
Aspects of Fibonacci numbers
(Bilkent University, 1994)This thesis consists of two parts. The first part, which is Chapter 2, is a survey on some aspects of Fibonacci numbers. In this part, we tried to gather some interesting properties of these numbers and some topics related ... 
Higher dimensional spherically symmetric gravitational theories
(Bilkent University, 1994)We consider all possible theories in spherically symmetric Riemannian geometry in Ddimensions. We find solutions to such theories, in particular black hole solutions of the low energy limit of the string theory in Ddimensions. 
Isomorphic classification problem and linear topological invariants
(Bilkent University, 1995)We consider all possible isomorphisms of cartesian products of Dragilev spaces, and thanks to relations between the Dragilev functions of each factor try to show that if there exists such an isomorphism, then any factor ... 
Boundary conditions compatible with the generalized symmetries
(Bilkent University, 1995)In this work evolution type integrable equations and systems are considered. An efficient method is given to construct their boundary conditions and hence boundary value problems which are compatible with the ... 
Transformation properties of Painleve VI equation
(Bilkent University, 1995)In this thesis, we studied the Schlesinger transformations of Painleve VI equation. We showed that Painleve VI equation admits Schlesinger transformations which relate a given solution of Paileve VI to solution of Painleve ... 
Analytic and asymptotic properties of nonsymmetric Linnik's probability densities
(Bilkent University, 1995)We prove that the function 1 , a 6 (0 ,2 ), ^ e R, 1 + is a characteristic function of a probability distribution if and only if ( a , 0 e P D = {{a,e) : a € (0,2), \d\ < m in (f^ , x  ^ ) (mod 27t)}. This distribution ... 
On lower bounds of character sums
(Bilkent University, 1995)111 ilii.s work wo oxlomlod llio ic.sult.s of S.A. Slc)aiiov [3], [i] about lower bouiid.s for incomplete clia.ra.cter .suiiks over a prime finite Held to the ea..se of arbitrar}^ linite field Moreover we atso a.pplied ... 
Asymptotic theory of characters of the symmetric groups
(Bilkent University, 1996)In this work, we studied the connection between ramified coverings of Riemann surfaces tt : X V oi degree n and characters of symmetric group Sn We considered asymptotics of characters of as n —> oo and normalized characters ... 
On possible deterioration of smoothness under the operation of convolution
(Bilkent University, 1996)We show that the convolution of two probability densities which are restrictions to R of entire functions can possess infinite essential supremuin on each interval. We also present several sufficient conditions of ... 
The linear mean value of the remainder term in the problem of asymptotic behaviour of eigenfunctions of the automorphic Laplacian
(Bilkent University, 1996)The purpose of this thesis is to obtain the estimate for the average mean value of the remainder term of the asymptotic formula for the quadratic mean value of the Fourier coefficients of the eigenfunctions over the ... 
Nonstationary Markov chains
(Bilkent University, 1996)In thi.s work, we studierl the Ergodicilv of NonStationary .Markov chains. We gave several e.xainples with different cases. We proved that given a sec[uence of Markov chains such that the limit of this secuence is an ... 
Partial differential equations possessing the Painleve property
(Bilkent University, 1996)111 this tli(\sis, a))lying llie l^viiilovc tost (l(ivolo)('.(l by VV(hss, 'labor ainl t biriK'vale (VV1X9) investigatc'd the Pa.inleve property of Ibirgers’ ty)e of ('(piarioiis, KdV type of equations and the KP ... 
On real Enriques surfaces
(Bilkent University, 1997) 
Conditions for uniqueness of limit Gibbs states
(Bilkent University, 1998)In this work we studied the problem of phase transitions in onedirnensional models with unique ground state. A model ha\dng two spins, one ground state and exhibiting phase transition is constructed.