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Insulating the Vacuum. Calculating the Casimir force using the boundary integral method with von Neumann boundary conditions
(Master thesis; Mastergradsoppgave, 2016-08-15)
In 2012, a new method for calculating the Casimir force between compact objects was developed, expressing the force in terms of a boundary integral equation. The case of perfectly conducting objects with Dirichlet boundary conditions in two dimensions was treated by Isak Kilen. The method was later extended to three dimensions by Karl Øyvind Mikalsen.
The contribution of this thesis will be to ...
A complex contour based perfectly matched layer applied to a pattern generating model equation.
(Master thesis; Mastergradsoppgave, 2017-02-17)
The observable universe consists of several non equilibrium systems that generate spatiotemporal behaviour in the form of various patterns. As the elementary laws of physics and chemistry are unable to explain the pattern forming behaviour of such systems, scientists have turned to desktop experiments and model equations to gain further insight. The model equations that generate numerical solutions ...
On the Ewald-Oseen scattering formulation for linear and nonlinear transient wave scattering
(Master thesis; Mastergradsoppgave, 2017-05-16)
In this thesis work we develop and apply EOS formulation to three scattering problems:
two of them are 1D problems and one is 2D. The first chapter comprises EOS
formulations and numerical implementation for 1D scattering problems.
Also in this chapter we use different numerical methods to solve test problem and
choose the most stable and accurate method for solving of the given 1D problems.
...
Almost affine codes and matroids
(Master thesis; Mastergradsoppgave, 2017-05-15)
In this thesis we study various types of block codes, like linear, mutlti-linear, almost affine codes. We also look at how these codes can be described by associated matroids. In addition we look at flags (chains) of codes and see how their behavior can be described using demi-matroids. We also introduce weight polynomials for almost affine codes.
Homological methods applied to theory of codes and matroids
(Master thesis; Mastergradsoppgave, 2015-05-15)
In this thesis we first give a survey of linear error-correcting codes, and how many of their most important properties only depend on the matroids derived from their parity check matrices.
We also introduce the Stanley-Reisner ring associated to the simplicial complex of the independent sets of a matroid.
We then recall in particular how some important properties of linear codes, including their ...
Towers of Betti Numbers of Matroids and Weight Distribution of Linear Codes and their Duals
(Master thesis; Mastergradsoppgave, 2015-05-15)
The main notion behind the study of matroids is linear dependence. In this thesis, we give a survey of the concepts and properties of linear error-correcting codes over finite fields being dependent only on the matroids derived from these codes. In particular, the weight distributions of linear codes, and their extensions, over bigger fields are only dependent on the N-graded Betti numbers of these ...
Simplicial complexes, Demi-matroids, Flag of linear codes and pair of matroids.
(Master thesis; Mastergradsoppgave, 2015-05-15)
We first describe linear error-correcting codes, and show how many of their most important properties are determined by their associated matroids . We also introduce the simplicial complex of the independent sets of a matroid.
We then proceed to study flags of linear codes, and recall the definition of demi-matroids, and how such demi-matroids associated to flags can describe important properties ...
Symmetry transformation groups and differential invariants
(Master thesis; Mastergradsoppgave, 2014-11-15)
There exists a local classification of finite-dimensional Lie algebras of vector
fields in two complex dimensions. We lift the Lie algebras from this classification to three complex dimensions.
Hopf algebras and monoidal categories
(Master thesis; Mastergradsoppgave, 2007-06-14)
In this thesis we study the correspondence between categorical notions and bialgebra notions, and make a kind of dictionary and grammar book for translation between these notions. We will show how to obtain an antipode, and how to define braidings and quantizations. The construction is done in two ways. First we use the properties of a bialgebra to define a monoidal structure on (co)modules over ...
The use of elliptic curves in cryptography
(Master thesis; Mastergradsoppgave, 2007-06)
The use of elliptic curves in cryptography was suggested independently by Neal Koblitz and Victor Miller in 1985. Being a relatively new field, there is still a lot of ongoing research on the subject, but elliptic curve cryptography, or ECC for short, has already been implemented in real-life applications. Its strength was proved in 2003 when the U.S. National Security Agency adopted ECC for protecting ...