Mastergradsoppgaver i matematikk
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Almost affine codes and matroids
(Master thesis; Mastergradsoppgave, 20170515)In this thesis we study various types of block codes, like linear, mutltilinear, 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 ... 
On the EwaldOseen scattering formulation for linear and nonlinear transient wave scattering
(Master thesis; Mastergradsoppgave, 20170516)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 ... 
A complex contour based perfectly matched layer applied to a pattern generating model equation.
(Master thesis; Mastergradsoppgave, 20170217)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 ... 
Separable representations of the Poisson, Helmholtz and complex Helmholtz kernels
(Master thesis; Mastergradsoppgave, 20170215)For high accuracy applications of integral operators in higher dimensions the complexity of operation and storage usually grows exponentially with dimensions. One method that has proven successful for handling these ... 
Insulating the Vacuum. Calculating the Casimir force using the boundary integral method with von Neumann boundary conditions
(Master thesis; Mastergradsoppgave, 20160815)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 ... 
Modelling lasermatter interactions using resonant states
(Master thesis; Mastergradsoppgave, 20160512)Studying how light interacts with materials has become important for many technological applications from optical communication to developing of new materials. Therefore scientists have always tried to improve their ... 
High frequency financial time series prediction: machine learning approach
(Master thesis; Mastergradsoppgave, 20160513)Machine learning is a rapidly evolving subfield of computer science. It has enormous amount of applications. One of the application domains is financial data analysis. Machine learning was usually applied for analysis and ... 
Modelling the evolution of ideal, infinite domain patterns, on a finite domain using a Perfectly Matched Layer
(Master thesis; Mastergradsoppgave, 20160128)The SwiftHohenberg equation is an evolution equation which can produce a Pattern, or a patternlike picture, to be more precise. For example, it could be used to model some simple natural patterns, like stripes and rolls ... 
The Unidirectional Pulse Propagation Equation for Cylindrical Vector modes
(Master thesis; Mastergradsoppgave, 20150727)A new model for the unidirectional pulse propagation equations (UPPE) was developed by Per Jacobsen[1], this model is based on the assumption of cylindrical vector (CV) modes. The model will be strong for CV type electrical ... 
Arctic tipping points
(Master thesis; Mastergradsoppgave, 20150515)The Arctic is warming much faster than the entire planet, and this causes severe melting of sea ice. However, the climate of different regions of the Earth is interconnected, and changes in the amount of ice in the Arctic ... 
Tipping points and crises in financial markets
(Master thesis; Mastergradsoppgave, 20150515)Electricity spot markets and other financial markets are complex systems, and it is difficult to forecast their behaviour, especially uncontrolled and unmanageable situations, such as power crises and deflation of financial ... 
Simplicial complexes, Demimatroids, Flag of linear codes and pair of matroids.
(Master thesis; Mastergradsoppgave, 20150515)We first describe linear errorcorrecting 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 ... 
Homological methods applied to theory of codes and matroids
(Master thesis; Mastergradsoppgave, 20150515)In this thesis we first give a survey of linear errorcorrecting codes, and how many of their most important properties only depend on the matroids derived from their parity check matrices. We also introduce the StanleyReisner ... 
Towers of Betti Numbers of Matroids and Weight Distribution of Linear Codes and their Duals
(Master thesis; Mastergradsoppgave, 20150515)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 errorcorrecting codes over finite fields being dependent only on the matroids ... 
Symmetry transformation groups and differential invariants
(Master thesis; Mastergradsoppgave, 20141115)There exists a local classification of finitedimensional Lie algebras of vector fields in two complex dimensions. We lift the Lie algebras from this classification to three complex dimensions. 
Deforming the vacuum. On the physical origin and numerical calculation of the Casimir effect.
(Master thesis; Mastergradsoppgave, 20140514)A new method for calculating the Casimir force between compact objects was introduced in May 2012 by Per Jakobsen and Isak Kilen. In this method a regularization procedure is used to reduce the pressure to the solution of ... 
Numerical calculation of Casimir forces
(Master thesis; Mastergradsoppgave, 20120619)In this thesis a set of regularized boundary integral equation are introduced that can be used to calculate the Casimir force induced by a two dimensional scalar field. The boundary integral method is compared to the ... 
Local classification of 2dimensional solvable Lie algebra actions on the plane.
(Master thesis; Mastergradsoppgave, 201005)In the thesis the local classification of 2dimensional solvable Lie algebra action on the plane is given. Normal forms of such actions are found. The classification applied to classifcation of 2nd order differential ... 
Almost complex homogeneous spaces with semisimple isotropy
(Master thesis; Mastergradsoppgave, 201205)We classify the almost complex structures on homogeneous spaces M = G/H of real dimension less than or equal to 6 with semisimple isotropy group H. 
Matroids, demimatroids and chains of linear codes
(Master thesis; Mastergradsoppgave, 20101209)The central theme of this thesis is the study of matroids and related concepts such as linear codes and graphs. Demimatroids, structures which arise from a relaxation of the definition of a matroid are explored along with ...