Browsing Dept. of Mathematics  Master's degree by Title
Now showing items 3453 of 119

Geodesic connectedness and completeness of twice warped products
(Bilkent University, 201709)We introduce the semiRiemannian geometry. We give some results about Riemannian and Lorentzian manifolds. We explained the Lorentzian causality. We focus on the causality of spacetimes. We de ne the Lorentzian distance. ... 
Geodesics of threedimensional walker manifolds
(Bilkent University, 201607)We review some basic facts of Lorentzian geometry including causality and geodesic completeness. We depict the properties of curves and planes in threedimensional Minkowski space. We deffne the Walker manifolds, that is, ... 
Geometric characterization of extension property for model compact sets
(Bilkent University, 2000) 
Geometry and matrix spectral problems
(Bilkent University, 2002)The aim of this thesis is to give a survey and applications of some recent work of Klyachko, Knutson and Tao that characterizes eigenvalues of sum of Hermitian matrices and decomposition of tensor products of representations of ... 
The geometry of tangent bundle and its applications
(Bilkent University, 2003)In this thesis, we first give a brief summary of the Riemannian Geometry which is the extension of Euclidean Geometry. Later we introduce the Finsler Geometry and the geometry of tangent bundle. Finally we give the ... 
Green correspondence for Mackey functors
(Bilkent University, 2008)The Green corespondence for modules of group algebras was introduced by Green in 1964. A version for Mackey functors was introduced by Sasaki in 1982. Sasaki’s characterization of Mackey functor correspondence was based ... 
Groebner basis approach in graphtheoretical problems
(Bilkent University, 201606)In the study of graphs, it is often desirable to know about the colorability properties of a given graph or whether it is planar or if it contains a Hamiltonian cycle. We consider such problems and describe corresponding ... 
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 ...