Browsing Mastergradsoppgaver i matematikk by Title
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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 and see how their behavior can be described using demimatroids. We also introduce weight polynomials for almost affine codes. 
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. 
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 can dramatically affect the climate across the whole planet. Some scientists claim that a possible tipping point is the event of the icefree Arctic Ocean in summer. Certain ... 
A bidirectional pulse propagation model for extreme nonlinear optics: derivation and implementation.
(Master thesis; Mastergradsoppgave, 20200513)With growing capabilities of highintensity laser beams to generate ultrashort pulses of light, the simulation of pulse propagation in nonlinear media is expected to catch up with the frontline experimental setups. Among the challenges of nonlinear material response modeling is the ability to capture the backscatter effect  a phenomenon inherently elusive for the wellestablished methods of ... 
A boundary integral approach to the modeling of surface waves in a wave tank
(Master thesis; Mastergradsoppgave, 20200614)Boundary integral equations (BIEs) are used to model surface waves in a wave tank. Assuming an ideal fluid, the velocity of the fluid can be considered as a potential flow and be modeled by the Laplace equation on the domain. The domain in this case will be a section of a wave channel with an incoming wave from the right, a rigid bottom, a reflective wall on the right and a time varying surface that ... 
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 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 ... 
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 an integral equation defined on the boundaries of the objects. In this thesis the method is further developed by extending from a 2D to a 3D massless scalar field, subject to ... 
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 on R^2. We will find all possible representations of vector fields in R^3=J^0R^2 which projects to the canonical representation and find the algebra of scalar differential invariants ... 
Differential Invariants of Symplectic and Contact Lie Algebra Actions
(Master thesis; Mastergradsoppgave, 20200623)In this thesis we consider the equivalence problem for symplectic and conformal symplectic group actions on submanifolds and functions. We solve the equivalence problem for general submanifolds by means of computing differential invariants and describing all the invariants of the associated group action by appealing to the LieTresse theorem. 
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 protect against such attacks often depend on cryptographic keys. Since the nodes in a MANET have limited resources, designing methods for cryptographic key management is ... 
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 that appear between these and short exact sequences of modules, respectively groups. We calculate also several concrete cohomology groups, and build extensions that are described by ... 
The Four Faces of Hyperelliptic curves
(Master thesis; Mastergradsoppgave, 20200513)In this thesis we will look at elliptic and hyperelliptic curves. There are three abelian groups that are isomorphic to hyperelliptic curves. The Jacobian of hyperelliptic curves, the ideal class group and the form class group, will all be defined and given abelian group structure. We will give an algorithm for point addition and point doubling done exclusively in the jacobian of the curve. ... 
Group Cohomology and Extensions
(Master thesis; Mastergradsoppgave, 20190831)The goal of this thesis is to classify all extensions where the kernel has order p^s and the cokernel has order p^t, p is a prime, and 1 ≤ s,t ≤ 2. We determine (up to weak congruence) the different combinations of kernel, cokernel and operators, and for each case, calculate the second cohomology group. By comparing resolutions, we get an explicit correspondence between the second cohomology group ... 
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 forecasting of daily financial time series. Availability of high frequency financial data became another challenge with its own specifics and difficulties. Regressors, being 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 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 ... 
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, 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 ... 
Icealbedo tipping points in a diffusive energybalance model with land and ocean
(Mastergradsoppgave; Master thesis, 20210120)The icealbedo feedback is associated with the nonlinearity in the climate system, due to the sudden change in albedo between icefree and icecovered surfaces. This nonlinearity can potentially cause abrupt and dramatic shifts in the climate, referred to as tipping points. It is also believed that this mechanism has contributed significantly to the precipitous losses of Arctic sea ice, which have ... 
IndividualBased Modeling of COVID19 Vaccine Strategies
(Master thesis; Mastergradsoppgave, 20210601)COVID19 is a respiratory disease with influenzalike symptoms originating from Wuhan, China, towards the end of 2019. There has been developed multiple vaccines to contain the virus and to protect the most vulnerable people in society. In this thesis we look at two different vaccination strategies to prevent most deaths and years of life lost. We conclude that the safest and most consistent strategy ... 
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 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 ... 
Joint Invariants of Symplectic and Contact Lie Algebra Actions
(Master thesis; Mastergradsoppgave, 20200623)By restricting generating functions of infinitesimal symmetries of symplectic and contact vector spaces to quadratic forms, we obtain a finitedimensional Lie subalgebra, consisting of vector fields isomorphic to the linear symplectic or conformal symplectic algebra. This allows us to look for joint invariants of the diagonal action of g on product manifolds. We find an explicit recipe for creating ...