On the finite perimeter sets of sub-Lorentzian metric spaces

Çetin, Günseli
In this thesis, inspired by the recent progress on sub-Riemannian geometry, a method of determining the finite perimeter sets of sub-Lorentzian manifolds independent of the original metric structure is suggested and a possible version of Riesz Representation theorem is discussed.


On the arithmetic operations over finite fields of characteristic three with low complexity
AKLEYLEK, SEDAT; Özbudak, Ferruh; Özel, Claire Susanna (2014-03-15)
In this paper, the Hermite polynomial representation is adapted as a new way to represent certain finite fields of characteristic three. We give the multiplication method to multiply two elements of F-3n in the Hermite polynomial representation with subquadratic computational complexity by using a divide-and-conquer idea. We show that in some cases there is a set of irreducible binomials in the Hermite polynomial representation to obtain modular reduction with a lower addition complexity than the standard p...
On maximal curves and linearized permutation polynomials over finite fields
Özbudak, Ferruh (Elsevier BV, 2001-08-08)
The purpose of this paper is to construct maximal curves over large finite fields using linearized permutation polynomials. We also study linearized permutation polynomials under finite field extensions.
BASKAL, S; ERIS, A; SATIR, A (1994-12-19)
The symmetries and associated conservation laws of the SO(2,1) invariant non-linear sigma model equations in 1+1 dimensions are investigated. An infinite family of generalized local symmetries is presented and the uniqueness of these solutions is discussed.
On multiplication in finite fields
Cenk, Murat; Özbudak, Ferruh (2010-04-01)
We present a method for multiplication in finite fields which gives multiplication algorithms with improved or best known bilinear complexities for certain finite fields. Our method generalizes some earlier methods and combines them with the recently introduced complexity notion (M) over cap (q)(l), which denotes the minimum number of multiplications needed in F-q in order to obtain the coefficients of the product of two arbitrary l-term polynomials modulo x(l) in F-q[x]. We study our method for the finite ...
Investigation of nonplanar perfectly matched absorbers for finite-element mesh truncation
Kuzuoğlu, Mustafa (1997-03-01)
In this paper, we present a detailed theoretical and numerical investigation of the perfectly matched layer (PML) concept as applied to the problem of mesh truncation in the finite-element method (FEM), We show that it is possible to extend the Cartesian PML concepts involving half-spaces to cylindrical and spherical geometries appropriate for closed boundaries in two and three dimensions by defining lossy anisotropic layers in the relevant coordinate systems, By using the method of separation of variables,...
Citation Formats
G. Çetin, “On the finite perimeter sets of sub-Lorentzian metric spaces,” M.S. - Master of Science, Middle East Technical University, 2022.