Model theory of derivation spaces

Kasal, Özcan
In this thesis, the notion of the derivation spaces is introduced. In a suitable two-sorted language, the first order theory of these structures is studied. In particular, it is shown that the theory is not companionable. In the last section, the language is expanded by predicate symbols for a dependence relation. In this language it is shown that the extension of the corresponding theory has a model companion. It is shown that the model companion is a complete, unstable theory which does not eliminate quantifiers.


Isomorphism classes of elliptic curves over finite fields of characteristic two
Kırlar, Barış Bülent; Akyıldız, Ersan; Department of Mathematics (2005)
In this thesis, the work of Menezes on the isomorphism classes of elliptic curves over finite fields of characteristic two is studied. Basic definitions and some facts of the elliptic curves required in this context are reviewed and group structure of elliptic curves are constructed. A fairly detailed investigation is made for the isomorphism classes of elliptic curves due to Menezes and Schoof. This work plays an important role in Elliptic Curve Digital Signature Algorithm. In this context, those isomorphi...
Application of the boundary element method to parabolic type equations
Bozkaya, Nuray; Tezer-Sezgin, Münevver; Department of Mathematics (2010)
In this thesis, the two-dimensional initial and boundary value problems governed by unsteady partial differential equations are solved by making use of boundary element techniques. The boundary element method (BEM) with time-dependent fundamental solution is presented as an efficient procedure for the solution of diffusion, wave and convection-diffusion equations. It interpenetrates the equations in such a way that the boundary solution is advanced to all time levels, simultaneously. The solution at a requi...
Strictly singular operators and isomorphisms of Cartesian products of power series spaces
Djakov, PB; Onal, S; Terzioglu, T; Yurdakul, Murat Hayrettin (1998-01-02)
V. P. Zahariuta, in 1973, used the theory of Fredholm operators to develop a method to classify Cartesian products of locally convex spaces. In this work we modify his method to study the isomorphic classification of Cartesian products of the kind E-0(p)(a) x E-infinity(q) (b) where 1 less than or equal to p, q < infinity, p not equal q, a = (a(n))(n=1)(infinity) and b = (b(n))(n=1)(infinity) are sequences of positive numbers and E-0(p)(a), E(infinity)q(b) are respectively l(p)-finite and l(q)-infinite type...
On symplectic quotients of K3 surfaces
Cinkir, Z; Onsiper, H (Elsevier BV, 2000-12-18)
In this note, we construct generalized Shioda-Inose structures on K3 surfaces using cyclic covers and almost functoriality of Shioda-Inose structures with respect to normal subgroups of a given group of symplectic automorphisms.
Invariant subspaces for Banach space operators with an annular spectral set
Yavuz, Onur (2008-01-01)
Consider an annulus Omega = {z epsilon C : r(0) 0 such that parallel to p(T)parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} and parallel to p(r(0)T(-1))parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} for all polynomials p. Then there exists a nontrivial common invariant subspace for T* and T*(-1).
Citation Formats
Ö. Kasal, “Model theory of derivation spaces,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.