Browsing Dept. of Mathematics  Master's degree by Title
Now showing items 100119 of 119

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 ... 
Unified approach to transformations of Painleve equations
(Bilkent University, 1993)In this thesis, we iind the explicit form of some transformations associated with the second, third, fourth and fifth Painleve equations. These transformations are obtained by using the Schlesinger transformations associated ... 
Weingarten surfaces arising from soliton theory
(Bilkent University, 1999)In this work we presented a method for constructing surfaces in associated with the symmetries of GaussMainardiCodazzi equations. We show that among these surfaces the sphere has a unique role. Under constant gauge ... 
Which algebraic K3 surfaces cover an enriques surface
(Bilkent University, 201809)We partially determine the necessary and su cient conditions on the entries of the intersection matrix of the transcendental lattice of algebraic K3 surface with Picard number 18 (X) 19 for the surface to doubly ... 
Which algebraic K3 surfaces doubly cover an enriques surface: a computational approach
(Bilkent University, 201902)The relationship between K3 Surfaces and Enriques Surfaces is known to mathematicians for the last 30 years. We examined this relationship from a lattice theoretical point of view by looking at transcendental lattice of ... 
Widom Factors
(Bilkent University, 2014)In this thesis we recall classical results on Chebyshev polynomials and logarithmic capacity. Given a nonpolar compact set K, we define the nth Widom factor Wn(K) as the ratio of the supnorm of the nth Chebyshev ... 
Wiener disorder problem with observation control
(Bilkent University, 2012)Suppose that a Wiener process gains a known drift rate at some unobservable disorder time with some zeromodified exponential distribution. The process is observed only at some intervals that we control. Beginning and ... 
Zero curvature and Gel'fandDikii formalisms
(Bilkent University, 2004)In soliton theory, integrable nonlinear partial differential equations play an important role. In that respect such differential equations create great interest in many research areas. There are several ways to obtain ... 
Zero sets of analytic function spaces on the unit disk
(Bilkent University, 201807)We survey some known results on the zero sets of two families of analytic function spaces and another single space de ned on the unit disk in the complex plane. We investigate mostly the basic properties of the zero sets ...