Browsing Dept. of Mathematics  Ph.D. / Sc.D. by Title
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Asymptotics of extremal polynomials for some special cases
(Bilkent University, 201705)We study the asymptotics of orthogonal and Chebyshev polynomials on fractals. We consider generalized Julia sets in the sense of Br uckB uger and weakly equilibrium Cantor sets which was introduced in [62]. We give ... 
Bases in banach spaces of smooth functions on cantortype sets
(Bilkent University, 2013)We construct Schauder bases in the spaces of continuous functions C p (K) and in the Whitney spaces E p (K) where K is a Cantortype set. Here different Cantortype sets are considered. In the construction, local ... 
Canonical induction, Green functors, lefschetz invariant of monomial Gposets
(Bilkent University, 201906)Green functors are a kind of group functor, rather like Mackey functors, but with a further multiplicative structure. They are defined on a category whose objects are finite groups and whose morphisms are generated by ... 
Character sums, algebraic function fields, curves with many rational points and geometric Goppa codes
(Bilkent University, 1997)In this thesis we have found and studied fibre products of hyperelliptic and superelliptic curves with many rational points over finite fields. We have applied Goppa construction to these curves to get “good” linear ... 
Characteristic lie algebra and classification of semidiscrete models
(Bilkent University, 2009)In this thesis, we studied a differentialdifference equation of the following form tx(n + 1, x) = f(t(n, x), t(n + 1, x), tx(n, x)), (1) where the unknown t = t(n, x) is a function of two independent variables: discrete n ... 
Code construction on modular curves
(Bilkent University, 2003)In this thesis, we have introduced two approaches on code construction on modular curves and stated the problems step by step. Moreover, we have given solutions of some problems in road map of code construction. One of ... 
Codes on fibre products of ArtinSchreier and Kummer coverings of the projective line
(Bilkent University, 200208)In this thesis, we study smooth projective absolutely irreducible curves defined over finite fields by fibre products of ArtinSchreier and Kummer coverings of the projective line. We construct some curves with many rational ... 
Complete intersection monomial curves and nondecreasing Hilbert functions
(Bilkent University, 2008)In this thesis, we first study the problem of determining set theoretic complete intersection (s.t.c.i.) projective monomial curves. We are also interested in finding the equations of the hypersurfaces on which the ... 
Concrete sheaves and continuous spaces
(Bilkent University, 2015)In algebraic topology and differential geometry, most categories lack some good ”convenient” properties like being cartesian closed, having pullbacks, pushouts, limits, colimits... We will introduce the notion of continuous ... 
A conjecture on squarezero upper triangular matrices and Carlsson's rank conjecture
(Bilkent University, 201809)A wellknown conjecture states that if an elementary abelian pgroup acts freely on a product of spheres, then the rank of the group is at most the number of spheres in the product. Carlsson gives an algebraic version ... 
A correspondence of simple alcahestic group functors
(Bilkent University, 2008)Representation theory of finite groups associates two classical constructions to a group G, namely the representation ring of G and the Burnside ring of G. These rings share a special structure that comes from three ... 
Deformation classes of singular quartic surfaces
(Bilkent University, 201701)We study complex spatial quartic surfaces with simple singularities and give their classication up to equisingular deformation. Simple quartics are K3surfaces and as such they can be studied by means of the global Torelli ... 
Dilations of doubly invariant kernels valued in topologically ordered * spaces
(Bilkent University, 201807)An ordered *space Z is a complex vector space with a conjugate linear involution *, and a strict cone Z+ consisting of self adjoint elements. A topologically ordered *space is an ordered *space with a locally convex ... 
Distance between a maximum point and the zero set of an entire function
(Bilkent University, 2006)We obtain asymptotical bounds from below for the distance between a maximum modulus point and the zero set of an entire function. Known bounds (Macintyre, 1938) are more precise, but they are valid only for some maximum ... 
Essays in collective decision making
(Bilkent University, 201410)Four different problems in collective decision making are studied, all of which are either formulated directly in a gametheoretical context or are concerned with neighboring research areas. The rst two problems fall ... 
Essential cohomology and relative cohomology of finite groups
(Bilkent University, 2009)In this thesis, we study modp essential cohomology of finite pgroups. One of the most important problems on essential cohomology of finite pgroups is finding a group theoretic characterization of pgroups whose essential ... 
Extension operators for spaces of infinitely differentiable functions
(Bilkent University, 2005)We start with a review of known linear continuous extension operators for the spaces of Whitney functions. The most general approach belongs to PawÃlucki and Ple´sniak. Their operator is continuous provided that the ... 
Extension problem and bases for spaces of infinitely differentiable functions
(Bilkent University, 201704)We examine the Mityagin problem: how to characterize the extension property in geometric terms. We start with three methods of extension for the spaces of Whitney functions. One of the methods was suggested by B. S. Mityagin: ... 
Fusion systems in group representation theory
(Bilkent University, 2013)Results on the Mackey category MF corresponding to a fusion system F and fusion systems defined on ppermutation algebras are our main concern. In the first part, we give a new proof of semisimplicity of MF over C by ... 
Gibbs measures and phase transitions in onedimensional models
(Bilkent University, 2000)In this thesis we study the problem of limit Gibbs measures in onedimensional models. VVe investigate uniqueness conditions for the limit Gibbs measures for onedimensional models. VVe construct a onedimensional model ...