Blar i tittel Mastergradsoppgaver i matematikk

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    • Individual-Based Modeling of COVID-19 Vaccine Strategies 

      Skagseth, Håvard Mikal (Master thesis; Mastergradsoppgave, 2021-06-01)
      COVID-19 is a respiratory disease with influenza-like 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 

      Utheim, Marius (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 ...

    • Joint Invariants of Symplectic and Contact Lie Algebra Actions 

      Andreassen, Fredrik (Master thesis; Mastergradsoppgave, 2020-06-23)
      By restricting generating functions of infinitesimal symmetries of symplectic and contact vector spaces to quadratic forms, we obtain a finite-dimensional 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 ...

    • Killing Tensors in Koutras-McIntosh Spacetimes 

      Steneker, Wijnand (Mastergradsoppgave; Master thesis, 2022-05-15)
      This thesis is concerned with the (non)existence of Killing Tensors in Koutras-McIntosh spacetimes. Killing tensors are of particular interest in general relativity, because these correspond to conserved quantities for the geodesic motion. For instance, Carter found such a conserved quantity in the Kerr metric which he used to explicitly integrate the geodesic equations. The equation defining ...

    • Kompleksiteten til noen kryptologisk viktige algoritmer 

      Brattli, Tore (Master thesis; Mastergradsoppgave, 1990-04-04)
      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 O-notasjonen, slik at algoritmene kan sammenlignes på et reelt grunnlag. I tillegg er det sett på sammenheng mellom sikkerhet, størrelsen på tall, asymptotisk og praktisk kompleksitet. Spesielt algoritmer som ...

    • Light induced forces on dielectric nanospheres 

      Lundamo, Trine (Master thesis; Mastergradsoppgave, 2008-02-15)
      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 them. Light is an electromagnetic wave phenomenon, and the waves carry energy and momentum. Hence, any object that is scattering and refracting light is also acted upon by a ...

    • Local classification of 2-dimensional solvable Lie algebra actions on the plane. 

      Gustad, Christian O'cadiz (Master thesis; Mastergradsoppgave, 2010-05)
      In the thesis the local classification of 2-dimensional 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 equations that are solvable in quadratures.

    • Mathematics of Viral Infections: A Review of Modeling Approaches and A Case-Study for Dengue Dynamics 

      Yong, Chung Han (Master thesis; Mastergradsoppgave, 2018-09-20)
      In this thesis we use mathematical models to study the mechanisms by which diseases spread. Transmission dynamics is modelled by the class of SIR models, where the abbreviation stands for susceptible (S), infected (I) and recovered (R). These models are also called compartmental models, and they serve as the basic mathematical framework for understanding the complex dynamics of infectious diseases. ...

    • Matroids, demi-matroids and chains of linear codes 

      Martin, James Aloysius (Master thesis; Mastergradsoppgave, 2010-12-09)
      The central theme of this thesis is the study of matroids and related concepts such as linear codes and graphs. Demi-matroids, structures which arise from a relaxation of the definition of a matroid are explored along with related themes. Finally we examine the fact that some results in coding theory are essentially consequences of results for demi-matroids.

    • Modelling high intensity laser pulse propagation in air using the modified Korteweg-de Vries equation 

      Rørnes, Bjarne (Master thesis; Mastergradsoppgave, 2018-06-01)
      Ultrafast laser pulse experiments and applications are entering a phase that challenges the validity of mathematical models utilised to model longer pulses in nonlinear optics. This thesis aims to propose a possible mathematical model for high intensity laser pulse propagation in air through a multiple scales expansion of Maxwell’s equations and discuss a method on how to solve the corresponding ...

    • Modelling laser-matter interactions using resonant states 

      Juhász, Dávid (Master thesis; Mastergradsoppgave, 2016-05-12)
      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 understanding of these effects. The primary goal has always been to microscopically describe the pertinent processes. This paper provides a brief introduction into the interactions of ...

    • Modelling the evolution of ideal, infinite domain patterns, on a finite domain using a Perfectly Matched Layer 

      Antrushin, Andrey (Master thesis; Mastergradsoppgave, 2016-01-28)
      The Swift-Hohenberg equation is an evolution equation which can produce a Pattern, or a pattern-like picture, to be more precise. For example, it could be used to model some simple natural patterns, like stripes and rolls that one may observe in a Rayleigh-Benard convection experiment. But for any pattern formation obtained by an evolution equation to look ideal, we have to consider this equation ...

    • Modern climate-economic models and climate policies 

      Grabovskaia, Sofiia (Master thesis; Mastergradsoppgave, 2018-05-15)
      The problem of climate change is one of the most discussed problems nowadays. The global warming has an unquestionable influence on the economic growth of the different countries, and, consequently, on the whole world economics. The climate economics thus is an actual topic to study. Moreover, it is important to predict how the climate will change over the next century and which resulting outcomes ...

    • Murnaghan-Nakayama Rule The Explanation and Usage of the Algorithm 

      Sandal, Elias (Mastergradsoppgave; Master thesis, 2023-05-15)
      Character values are not the easiest to calculate, so it is important to find good algorithms that can help ease these calculations. In the 20th century, the two mathematicians Murnaghan and Nakayama developed a rule that calculates character values for partitions on some computations. This rule has later been given the name The Murnaghan-Nakayama rule, after these two authors. The Murnaghan-Nakayama ...

    • Numerical calculation of Casimir forces 

      Kilen, Isak Ragnvald (Master thesis; Mastergradsoppgave, 2012-06-19)
      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 functional integral method and mode summation where possible. Comparisons are done for the case of two parallel plates, two concentric circles and two adjacent circles. The results ...

    • On elementary particles as representations of the Poincaré group 

      Martínez Marín, Pau (Master thesis; Mastergradsoppgave, 2023-08-14)
      This thesis is concerned with the definition of elementary particles as irreducible projective unitary representations of the Poincaré group. During the contents of this work, we will introduce the relevant prerequisites and results. Concerning differential geometry, we will discuss smooth manifolds, Lie groups and Lie algebras. About quantum mechanics, we will introduce Hilbert spaces and the basic ...

    • On the effects of symmetry in the energy balance on a sphere 

      Samuelsberg, Aksel (Mastergradsoppgave; Master thesis, 2022-05-15)
      Simple climate models have gathered much attention as they have suggested the possibility of abrupt climate change associated with tipping points. Several simple climate models are found to have multiple equilibria, but in most cases similar equilibria do not appear or become too difficult to find in complex, fully coupled earth system models. In this thesis, we investigate a simple climate model, ...

    • On the Ewald-Oseen scattering formulation for linear and nonlinear transient wave scattering 

      Kuzmina, Anastasiia (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. ...

    • Real Plane Algebraic Curves 

      González García, Pedro (Master thesis; Mastergradsoppgave, 2021-06-18)
      This master thesis studies several properties of real plane algebraic curves, focusing on the case of even degree. The question of the relative positions of the connected components of real plane algebraic curves originates in Hilbert's sixteenth problem which, despite its prominence, is still open in the case of higher degree curves. The goal of this thesis is an exposition of fundamental ...

    • Separable representations of the Poisson, Helmholtz and complex Helmholtz kernels 

      Bjørgve, Magnar (Master thesis; Mastergradsoppgave, 2017-02-15)
      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 difficulties are the separation of the integral kernels as linear combinations of products of one-dimensional kernels, commonly referred to as separation of variables. In this ...