Browsing Dept. of Mathematics  Master's degree by Title
Now showing items 2645 of 119

Existence of basis in some Whitney spaces
(Bilkent University, 2003)Existence of basis in locally convex spaces has been a hot subject in functional analysis for more than 40 years. We will give some partial solutions to this wellknown problem. We will demonstrate two cases of Cantortype ... 
Explicit reciprocity laws
(Bilkent University, 2010)Quadratic reciprocity law was conjectured by Euler and Legendre, and proved by Gauss. Gauss made first generalizations of this relation to higher fields and derived cubic and biquadratic reciprocity laws. Eisenstein and ... 
The extension class of a subset complex
(Bilkent University, 2006) 
Extremal problems and bergman projections
(Bilkent University, 201707)Studying extremal problems on Bergman spaces is rather new and techniques used are usually specific to the problem to be solved. However, a 2014 paper by T. Ferguson developed a systematic method using Bergman projections ... 
Extreme behavior of lex ideals on Betti numbers
(Bilkent University, 2013)This paper mainly deals with the finitely generated graded modules of the polynomial ring k[x1, x2, ..., xn]. Free resolutions is an important tool to understand the structure of these modules. Betti numbers are an useful ... 
Factorization in Hardy and Nevanlinna classes
(Bilkent University, 1999)We find conditions under which the factors of a function belonging to Hardy or Nevanlinna class also belong to the corresponding class. The basis of our method is the theorem on the representation of a function harmonic ... 
Free actions on CWcomplexes and varieties of square zero matrices
(Bilkent University, 2011)Gunnar Carlsson stated a conjecture which gives a lower bound on the rank of a differential graded module over a polynomial ring with coefficients in algebraically closed field k when it has a finite dimensional homology ... 
Free actions on product of spheres at high dimensions
(Bilkent University, 2012) 
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 ...