Browsing Dept. of Mathematics  Master's degree by Title
Now showing items 120 of 126

Algebro geometric methods in coding theory
(Bilkent University, 1999)In this work, we studied a class of codes that, as a subspace, satisfy a certain condition for (semi)stability. We obtained the Poincare polynomial of the nonsingular projective variety which is formed by the equivalence ... 
Analysis on selfsimilar sets
(Bilkent University, 202008)Selfsimilar sets are one class of fractals that are invariant under geometric similarities. In this thesis, we study on selfsimilar sets. We give the deﬁnition of a selfsimilar set K and present the proof the existence ... 
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 ... 
Applications of duality for Hp spaces
(Bilkent University, 2006) 
Approximation of equilibrium measures by discrete measures
(Bilkent University, 2012)Basic notions of potential analysis are given. Equilibrium measures can be approximated by discrete measures by means of Fekete points and Leja sequences. We give the sets for which exact locations of Fekete points and ... 
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 ... 
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 ... 
Bâcklund transformations of Painleve equations and discrete equations of Painleve type
(Bilkent University, 2004)With the help of the Schlesinger transformations, we obtain the B¨acklund transformations of the classical continuous Painlev´e equations (PIIPVI). Then using these B¨acklund transformations we derived the corresponding ... 
Biset functors and brauer's induction theorem
(Bilkent University, 2014)We introduce two algebras on the endomorphism ring of the direct sum of character rings of groups from some collection. We prove the equality of these algebras to simplify a step in the proof of Brauer’s Induction Theorem. ... 
Blocks of quotients of mackey algebras
(Bilkent University, 2015)We review a theorem by Boltje and K¨ulshammer which states that under certain circumstances the endomorphism ring EndRG(RX) has only one block. We study the double Burnside ring, the Burnside ring and the transformations ... 
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 ... 
Canonical induction for trivial source rings
(Bilkent University, 2013)We discuss the canonical induction formula for some special Mackey functors by following the construction of Boltje. These functors are the ordinary and modular character rings and the trivial source rings. Making use ... 
Chain maps between Gruenberg resolutions
(Bilkent University, 201807)Let G be a finite group. For a given presentation of G = hFRi, Gruenberg gives a construction of a projective resolution for Z as a ZGmodule. This resolution, which is called Gruenberg resolution, only depends on the ... 
Characteristic bisets and local fusion subsystems
(Bilkent University, 201809)Fusion systems are categories that contain the plocal structure of a finite group. Bisets are sets endowed with two coherent group actions. We investigate the relation between fusion systems and bisets in this thesis. Fusion ... 
Classical Zariski pairs with nodes
(Bilkent University, 2008)In this thesis we study complex projective sextic curves with simple singularities. All curves constituting classical Zariski pairs, especially those with nodes, are enumerated and classified up to equisingular deformation. ... 
Cobordism calculations with Adams and James spectral sequences
(Bilkent University, 2010)Let ξn : Z/p → U(n) be an ndimensional faithful complex representation of Z/p and in : U(n)→O(2n) be inclusion for n ≥ 1. Then the compositions in ◦ ξn and jn ◦ in ◦ ξn induce fibrations on BZ/p where jn : O(2n) → O(2n ... 
Cohomological dimension and cubic surfaces
(Bilkent University, 2004)In this thesis we give necessary and sufficient conditions for a curve C on a given cubic surface Q so that Q − C is affine. We use this to give a simpler proof of cd(P 3 − C) = 1 by using Budach’s method for these ... 
Cohomology of semidirect products
(Bilkent University, 2012) 
Complete positivity in operator algebras
(Bilkent University, 2006)In this thesis we survey positive and completely positive maps defined on operator systems. In Chapter 3 we study the properties of positive maps as well as construction of positive maps under certain conditions. In ... 
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.