Browsing Dept. of Mathematics  Ph.D. / Sc.D. by Issue Date
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Integrability and Poisson structures of three dimensional dynamical systems and equations of hydrodynamic type
(Bilkent University, 1992)We show that the Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1form. We shall take advantage of this fact and use the theory of foliations in ... 
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 ... 
Some exact solutions of colliding waves, black holes and their thermodynamical properties in Dilaton gravity
(Bilkent University, 1998)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 ... 
The solvability of PVI equation and secondorder seconddegree Painleve type equations
(Bilkent University, 1998)A rigorous method was introduced by Fokas and Zhou for studying the RiernaiinHilhert problem associated with the Painleve II and IV. The same methodology has been applied to Painleve I, III and V. In this thesis, we ... 
KOrings and Jgroups of lens spaces
(Bilkent University, 1998)In this thesis, we make the explicit computation of the real A'theory of lens spaces and making use of these results and Adams conjecture, we describe their .7groups in terms of generators and relations. These computations ... 
Symmetries and boundary conditions of integrable nonlinear partial differential equations
(Bilkent University, 1999)The solutions of initialboundary value problems for integrable nonlinear partial differential equations have been one the most important problems in integrable systems on one hand, and on the other hand these kind ... 
Monomial curves and the CohenMacaulayness of their tangent cones
(Bilkent University, 1999)In this thesis, we show that in affine /space with / > 4, there are monomial curves with arbitrarily large minimal number of generators of the tangent cone and still having CohenMacaulay tangent cone. In order to prove ... 
The quasiequivalence problem and isomorphic classification of Whitney spaces
(Bilkent University, 1999)We proved that the quasiequivalence property holds in a subclass of the class of stable nuclear Frechet, Kothe spaces. Also we considered the isomorphic classification of spaces of Whitney functions on some special ... 
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 ... 
Painleve test and the Painleve equations hierarchies
(Bilkent University, 2001)Recently there has been a considerable interest in obtaining higher order ordinary differential equations having the Painleve property. In this thesis, starting from the first, the second and the third Painleve transcendents ... 
On sections and tails of power series
(Bilkent University, 2002)The thesis is devoted to the study of connections between properties of a power series and properties of its sections and tails. Power series having sections or tails with multiply positive coefficients are considered ... 
Recursion operator and dispersionless Lax representation
(Bilkent University, 2002)We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a dispersionless Lax representation. We consider a polynomial and rational Lax function. We give several ... 
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 ... 
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 ... 
Representations of functions harmonic in the upper halfplane and their applications
(Bilkent University, 2003)In this thesis, new conditions for the validity of a generalized Poisson representation for a function harmonic in the upper halfplane have been found. These conditions differ from known ones by weaker growth restrictions ... 
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 ... 
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 ... 
Modular vector invariants
(Bilkent University, 2006)Vector invariants of finite groups (see the introduction for definitions) provides, in general, counterexamples for many properties of the invariant theory when the characteristic of the ground field divides the group ... 
Solution surfaces and surfaces from a variotional principle
(Bilkent University, 2007)In this thesis, we construct 2surfaces in R 3 and in three dimensional Minkowski space (M3). First, we study the surfaces arising from modified Kortewegde Vries (mKdV), SineGordon (SG), and nonlinear Schr¨odinger ... 
The Pauli principe, representation theory, and geometry of flag varieties
(Bilkent University, 2008)According to the Pauli exclusion principle, discovered in 1925, no two identical electrons may occupy the same quantum state. In terms of electron density matrix this amounts to an upper bound for its eigenvalues by 1. ...