This master's thesis is focussed around investigating Massey products as tools for studying properties of links, in particular the Brunnian property. In the literature, there are only a few examples of the Massey product being used to study linking, none of which has any emphasis on links with the Brunnian property, except for computations for the Borromean rings. The result of the work is a number of thorough computations of Massey products in link complements, with the negative conclusion that the Massey product does not detect the Brunnian property.

Vi vil utforske bruken av adeler i matematisk fysikk.

This thesis is focused on solving the Darcy flow problem using divergence-free isogeometric methods, and comparing these results to the ones obtained using traditional finite element methods with Taylor Hood elements. A short introduction to B-splines is given, and a chapter is also about using repeated knots in the knot vectors to obtain a discontinuous basis for the finite element method. This can be useful when dealing with varying permeabilities.

In this thesis we have given an introduction to isogeometric finite element analysis on linear elasticity problems in 2D using non uniform rational B-splines (NURBS) as basis functions. We have studied the theory of B-splines and have derived the equations needed to perform linear elasticity stress analysis. An isogeometric finite element solver has been programmed in MATLAB. We have also analyzed the effect degenerated mappings have on the derivatives of the basis functions. We started by looking at a quadrilateral collapsing to a triangle, considering different parameterizations and their impact on the derivatives. We found that the derivatives were no longer in H^1 and that our basis was not a proper basis for finite element analysis. Our solution to this problem is to form a new set of basis functions by summing the basis functions at the singular points. Further we have applied this approach on a circular surface and an infinite plate with a circular hole.

We have compared the recently developed Multi-level binary replacement (MBR) design method for use in computer experiments, to the Latin hypercube design (LHD) and the Orthogonal array (OA) design. For means of comparison, we have suggested an algorithm for drawing permutations of the MBR design, so as to obtain what we have called a MBR based Latin hypercube design. In our comparison study, the main focus have been the design scores with respect to the root mean squared error (RMSE), Max and alias sum of squares criteria. We found that the MBR design generally performed good with respect to all criteria. It scored similarly to the OA design method and better than conventional Latin hypercube sampling. The score however varied with the number of samples and the set of design generators chosen for constructing the MBR design. The MBR design performed better for designs with a relatively high number of samples compared to the number of factors.

We prove that quasicrystals are universal sets of stable sampling in any dimension. Necessary and sufficient density conditions for stable sampling and interpolation sets in one dimension are studied in detail.

Using a simulation based model, with the Black-Scholes framework for equity andThe LIBOR Market Model for interest rates, we study market risk in multi assetclassportfolios, with static and dynamic weighting. The risk measures consideredare Value-at-Risk and Expected-Tail-Loss. The theoretical foundation is introducedand imperfections in the models and their assumptions are pointed out.The validity of the models and risk measures is tested using a backtesting procedureagainst data ranging from September 1999 to September 2009, with particularemphasis on the turbulent period of 2007 to September 2009. The results indicatethat the models perform slightly worse on the portfolio with the added complexityof a dynamic weighting regime. No evidence of the models performing lesssatisfactory under the latest financial turbulence is found.

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This thesis introduce a new parameterization of the model space in global inversion problems. The parameterization provides an explicit representation of the model space with a basis constrained on a priori information about the problem at hand. It is able to represent complex model structures with few parameters, and thereby enhancing the speed of the inversion, as the number of iterations needed to converge is heavily scaled with the number of parameters in stochastic, global inversion methods. A standard Simulated Annealing optimization routine is implemented, and further extended to be able to optimize for a dynamically varying number of variables. The method is applied on inversion of marine CSEM data, and inverts both synthetic and real data sets and is able to recover resistivity profiles that demonstrate good resemblance with provided well bore log data. The trans-dimensional, self-parameterizing Simulated Annealing algorithm which is introduced in this thesis proves to be superior to the regular algorithm with fixed parameter dimensions.

I denne oppgåva har eg studert avgansstudentar i fysikk sitt syn på studietida og framtida. Forskingsspørsmåla fokuserer på kva læringsaktivitetar studentane har likt, kva som har motivert dei gjennom studietida og kva ønskjer dei har for framtidig yrke. Vidare er det sett på kva verdiar som er viktige for dei vala studentane gjer, og korleis studentane har utvikla seg i løpet av eit fem år langt studie.Data er samla inn ved bruk av spørjeskjema, som vart sendt ut til studentane via e-post. Resultata viser at fysikkstudentane er ei gruppe som i stor grad let seg motivere og inspirere av eigne interesser og nysgjerrigheit. I studietida har dei sett pris på å kunne diskutere med likesinna, arbeide med oppgåveløysing og sjølvstudie. I framtida vil dei ha yrker som gjev dei moglegheit for å vidareutvikle kunnskapen og evnene dei har. Aller helst vil dei ha eit arbeid innanfor privat næringsliv eller forsking. Fysikkstudentane er ikkje redde for utfordringar. Dei har valt eit studie dei ser på som tidkrevjande og gjer val ut ifrå interesser, heller enn eit hensyn til relativ kostnad. Studentane har i løpet av studietida ikkje endra seg særleg mykje når det gjeld kva som motiverar dei, og kva faktorar som er avgjerande for val av arbeid. Deira nysgjerrigheit og sterke interessefokus har oppretthalde seg, og drive dei fram mot ei fullført mastergrad og eit yrke som gjev dei moglegheit til å utvikle seg vidare. Desse faktorane er dei same som studentane vektla ved studiestart. Faktorar som gjerne er knytt til status, som leiaransvar og høg inntekt, er imidlertid lite vektlagt av fysikkstudentane.