Browsing Dept. of Mathematics  Master's degree by Title
Now showing items 4160 of 119

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. 
The Hirota direct method
(Bilkent University, 2005)The search for integrability of nonlinear partial differential and difference equations includes the study on multisoliton solutions. One of the most famous method to construct multisoliton solutions is the Hirota ... 
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 ... 
Homotopy colimits and decompositions of function complexes
(Bilkent University, 201607)Given a functor F : C→ GSp, the homotopy colimit hocolimCF is defined as the diagonal space of simplicial replacement of F. Let G be a finite group and F be a family of subgroups of G, the classifying space EFG can be taken ... 
Hyperdeterminants, entangled states, and invariant theory
(Bilkent University, 2013)In [1] and [2], A. Klyachko connects quantum entanglement and invariant theory so that entangled state of a quantum system can be explained by invariants of the system. After representing states in multidimensional ... 
Incremental hash functions
(Bilkent University, 2014)Hash functions are one of the most important cryptographic primitives. They map an input of arbitrary finite length to a value of fixed length by compressing the input, that is why, they are called hash. They must run ... 
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 ... 
Interpolating bases in the spaces of C(formula)functions on cantortype sets
(Bilkent University, 2006)In this work by using the method of local interpolat ions suggested in [9] we construct topological bases in the spaces of CPfunctions defined on uniformly perfect compact sets of Cantor type. Elements of the basis are ... 
Invariant rings of modular Pgroups
(Bilkent University, 2013)We consider a finite group acting as linear substitutions on a polynomial ring and study the corresponding ring of invariants. Computing the invariant ring and finding its ring theoretical properties is a classical ... 
Investigation of homogeneous and inhomogeneous percolation models in two dimensions
(Bilkent University, 2007)In this thesis, we consider some models of percolation in two dimensional spaces. We study some numerical equalities and inequalities for the critical probability, together with a general method for establishing strict ... 
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 ... 
Kuroda's class number formula
(Bilkent University, 2007)In number theory theory, the class number of a field is a significant invariant. All over the time, people have come up with formulas for some cases and in this thesis I will discuss a proof of a class number formula for ... 
The lattice of periods of a group action and its topology
(Bilkent University, 2006)In this thesis, we study the topology of the poset obtained by removing the greatest and least elements of lattice of periods of a group action. For a Gset X where G is a finite group, the lattice of periods is defined ... 
Lebesgueradonnikodym decompositions for operator valued completely positice maps
(Bilkent University, 2014)We discuss the notion of RadonNikodym derivatives for operator valued completely positive maps on C*algebras, first introduced by Arveson [1969], and the notion of absolute continuity for completely positive maps, ... 
Limiting Gibbs measures in some one and two dimensional models
(Bilkent University, 2005)We give the definitions of finite volume Gibbs measure and limit Gibbs states. In one dimensional Ising model with arbitrary boundary conditions we calculate correlation functions in explicit way. In one dimension, ... 
Limiting Gibbs measures of some models of classical statistical mechanics
(Bilkent University, 2002)We consider some models of classical statistical mechanics with their random perturbations and investigate the phase diagrams of this models. By using uniqueness theorem we prove the absence of phase transitions in this models. 
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 ... 
Linear topological structure of spaces of Whitney functions defined on sequences of points
(Bilkent University, 2002)In this work we consider the spaces of Whitney functions defined on convergent sequences of points.By means of linear topological invariants we analyze linear topological structure of these spaces .Using diametral dimension ... 
Logarithmic dimension and bases in whitney spaces
(Bilkent University, 2006)In generalization of [3] we will give the formula for the logarithmic dimension of any Cantortype set. We will demonstrate some applications of the logarithmic dimension in Potential Theory. We will construct a polynomial ... 
Lζ modules and a theorem of Jon Carlson
(Bilkent University, 2004)In this thesis, we study Lζ modules, and using some exact sequences involving Lζ modules, we give an alternative proof to a theorem by Jon Carlson which says that any ZGmodule is a direct summand of a module which has ...