Mastergradsoppgaver i matematikk
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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 ... 
Extensions of groups and modules
(Master thesis; Mastergradsoppgave, 2010)The main goal of this thesis is to build up detailed constructions and give complete proofs for the extension functors of modules and groups, which we define using cohomology functors. Further, we look at the relations ... 
Kompleksiteten til noen kryptologisk viktige algoritmer
(Master thesis; Mastergradsoppgave, 19900404)Denne hovedfagsoppgaven har som mål å sammenligne teoretisk og praktisk kompleksitet til algoritmer som har stor kryptologisk betydning. Et av målene er å avsløre den skjulte konstanten bak Onotasjonen, slik at algoritmene ... 
Distributing a private key generator in Ad hoc Networks
(Master thesis; Mastergradsoppgave, 20090515)A Mobile Ad hoc Network (MANET) is a wireless network that does not rely on a fixed infrastructure. These characteristics make algorithms that route network traffic particularly vulnerable to attack. Mechanisms used to ... 
Light induced forces on dielectric nanospheres
(Master thesis; Mastergradsoppgave, 20080215)Waves that are reflected and refracted by material bodies also transfer momentum to these bodies. This means that the wave field induces a force on the bodies, and multiple reflections between bodies induce forces between ... 
Differential invariants of the 2D conformal Lie algebra action
(Master thesis; Mastergradsoppgave, 20080215)In this thises we consider the Lie algebra that corresponds to the Lie pseudogroup of all conformal transformations on the plane. This conformal Lie algebra is canonically represented as a Lie algebra of vector fields ... 
The use of elliptic curves in cryptography
(Master thesis; Mastergradsoppgave, 200706)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 ... 
Hopf algebras and monoidal categories
(Master thesis; Mastergradsoppgave, 20070614)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, ...