Browsing Dept. of Mathematics  Master's degree by Title
Now showing items 92111 of 119

Ramanujan's congruences for the partition function
(Bilkent University, 2009)In this thesis, we study Ramanujan’s congruences for the partition function and some of their combinatorial interpretations. Our main tools are from the theory of theta function. 
Real monomial Burnside rings and a decomposition of the the tom Dieck map
(Bilkent University, 2009)This thesis is mainly concerned with a decomposition of the reduced tom Dieck map die : f A(RG) → B(G) × into two maps die+ and die− of the real monomial Burnside ring. The key idea is to introduce a real Lefschetz ... 
Recursion operators and classification of integrable nonlinear equations
(Bilkent University, 2012)Recursion operators, if they exist, of nonlinear partial differential equations map symmetries to symmetries of these equations. It is this property that the integrable nonlinear partial differential equations possess ... 
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 ... 
Representations of symmetric groups and structures of Lie algebra
(Bilkent University, 201708)The aim of this thesis construct structure of Free Lie Algebra L(V ) generated by nite dimensional vector space V and decompose into irreducible components of a given degree n. To splits into irreducible component, ... 
Reproducing kernel Hilbert spaces
(Bilkent University, 2005)In this thesis we make a survey of the theory of reproducing kernel Hilbert spaces associated with positive definite kernels and we illustrate their applications for interpolation problems of NevanlinnaPick type. Firstly ... 
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 ... 
Riemann boundary value problem
(Bilkent University, 2000) 
Schlesinger transformations of second discrete painleve equation
(Bilkent University, 2004) 
Schubert calculus, adjoint representation and moment polytopes
(Bilkent University, 2012)Let Hν denote the irreducible representation of the special unitary group SU(n) corresponding to Young diagram ν and let g = su(n) denote the Lie algebra of SU(n). One can show that Hν appears in the symmetric algebra ... 
Sectional curvature of standard static spacetimes
(Bilkent University, 2013)Curvature related geometric properties of warped product manifolds are given. The casual structure of Lorentzian warped products is reviewed. In particular, two wellknown examples of warped product spacetimes models, ... 
Simple functors of admissible linear categories
(Bilkent University, 2013)We review the notion of an admissible Rlinear category for a commutative unital ring R and we prove the classification theorem for simple functors of such a category by BarkerBoltje which states that there is a bijective ... 
Singularities of plane model of the modular curve Yo(l)
(Bilkent University, 1998) 
Smoothness of the green function for some special compact sets
(Bilkent University, 2010)Smoothness of the Green functions for some special compact sets, which are sequences of closed intervals with certain parameters, is described in terms of the function ϕ(δ) = 1 log 1 δ that gives the logarithmic measure ... 
Smoothness properties of Green's functions
(Bilkent University, 2014)Basic notions of potential theory are explained with illustrative examples. Many important properties, including the characteristic ones, of Green’s functions that are defined by the help of equilibrium measures are ... 
Some criteria of selfadjointness for unbounded operators in Hilbert spaces
(Bilkent University, 2013)This is a detailed presentation of some criteria of selfadjointness for unbounded operators in a Hilbert space, through operator Cauchy problems. We also include detailed preliminary results on unbounded linear operators ... 
SPTfunction and its properties
(Bilkent University, 2014)In this thesis, we survey some properties of the sptfunction. We start with providing some background information for qseries and the partition function p(n). Then we define the sptfunction and study its generating ... 
Stochastic analysis of shortrate modeling: which approach yields a better fit to data?
(Bilkent University, 201710)This thesis investigates the extent to which the two of the most common onefactor shortrate models are able to describe the market behavior of risk free Turkish treasuries for the post2005 period. The investigated ... 
Symplectic geometry and topology of spatial polygons in Euclidean and Minkowski spaces
(Bilkent University, 2000)In this work, we studied the relations between spatial polygons in Euclidean spaces and point configurations in projective line P'. We classi (i('d all nonsingular hexagon spa.ces and modified some methods to evaluate ( ... 
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 ...