Recent Submissions

  • Asymptotics of extremal polynomials for some special cases 

    Alpan, Gökalp (Bilkent University, 2017-05)
    We study the asymptotics of orthogonal and Chebyshev polynomials on fractals. We consider generalized Julia sets in the sense of Br uck-B uger and weakly equilibrium Cantor sets which was introduced in [62]. We give ...
  • Extension problem and bases for spaces of infinitely differentiable functions 

    Merpez, Zeliha Ural (Bilkent University, 2017-04)
    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: ...
  • Monoid actions, their categorification and applications 

    Erdal, Mehmet Akif (Bilkent University, 2017-01)
    We study actions of monoids and monoidal categories, and their relations with (co)homology theories. We start by discussing actions of monoids via bi-actions. We show that there is a well-defined functorial reverse action ...
  • Deformation classes of singular quartic surfaces 

    Aktaş, Çisem Güneş (Bilkent University, 2017-01)
    We study complex spatial quartic surfaces with simple singularities and give their classication up to equisingular deformation. Simple quartics are K3-surfaces and as such they can be studied by means of the global Torelli ...
  • Concrete sheaves and continuous spaces 

    Özkan Recep (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 ...
  • Distance between a maximum point and the zero set of an entire function 

    Üreyen, Adem Ersin (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 

    Madran, Uğur (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 ...
  • Extension operators for spaces of infinitely differentiable functions 

    Altun, Muhammed (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 ...
  • Representations of functions harmonic in the upper half-plane and their applications 

    Gergün, Seçil (Bilkent University, 2003)
    In this thesis, new conditions for the validity of a generalized Poisson representation for a function harmonic in the upper half-plane have been found. These conditions differ from known ones by weaker growth restrictions ...
  • Code construction on modular curves 

    Kara, Orhun (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 ...
  • Recursion operator and dispersionless Lax representation 

    Zheltukhin, Kostyantyn (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 ...
  • Piatetski-shapir prime number theorem and chebotarev density theorem 

    Akbal, Yıldırım (Bilkent University, 2015-07)
    Let K be a nite Galois extension of the eld Q of rational numbers. In this thesis, we derive an asymptotic formula for the number of the Piatetski-Shapiro primes not exceeding a given quantity for which the associated ...
  • Essays in collective decision making 

    Derya, Ayşe Mutlu (Bilkent University, 2014-10)
    Four different problems in collective decision making are studied, all of which are either formulated directly in a game-theoretical context or are concerned with neighboring research areas. The rst two problems fall ...
  • Painleve test and the Painleve equations hierarchies 

    Jrad, Fahd (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 ...
  • Gibbs measures and phase transitions in one-dimensional models 

    Mallak, Saed (Bilkent University, 2000)
    In this thesis we study the problem of limit Gibbs measures in one-dimensional models. VVe investigate uniqueness conditions for the limit Gibbs measures for one-dimensional models. VVe construct a one-dimensional model ...
  • The solvability of PVI equation and second-order second-degree Painleve type equations 

    Sakka, Ayman (Bilkent University, 1998)
    A rigorous method was introduced by Fokas and Zhou for studying the Riernaiin-Hilhert problem associated with the Painleve II and IV. The same methodology has been applied to Painleve I, III and V. In this thesis, we ...
  • KO-rings and J-groups of lens spaces 

    Kırdar, Mehmet (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 .7-groups in terms of generators and relations. These computations ...
  • Character sums, algebraic function fields, curves with many rational points and geometric Goppa codes 

    Özbudak, Ferruh (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 ...
  • The quasi-equivalence problem and isomorphic classification of Whitney spaces 

    Arslan, Bora (Bilkent University, 1999)
    We proved that the quasi-equivalence 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 ...
  • Symmetries and boundary conditions of integrable nonlinear partial differential equations 

    Gürel, T Burak (Bilkent University, 1999)
    The solutions of initial-boundary 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 ...

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