In this thesis we implement and employ a simplex spline basis developed by Cohen, Lyche, and Riesenfeld for the space of C1 quadratic splines on the Powell–Sabin 12-split of a triangle. A matrix recursion is used for ...

Given a non-principal ultrafilter, we define and prove properties of ultralimits of measure spaces (including σ-algebras, filtrations and measures), random variables and discrete-time stochastic processes. Among other ...

This thesis investigates cubic hypersurfaces and their Fano schemes. After introducing the Fano schemes through low-dimensional examples, we move on to investigate cubic fourfolds. For the cubic fourfolds, we give complete ...

In this thesis, we consider the mod 2 homology of Q≥0S0 as an E∞ space and show the following. The homologies H*Q≥0S0 and H*C∞S0 are isomorphic as free commutative /2-algebras. The homology H*Q≥0S0 is generated as an ...

The recent results on non-uniqueness of the Euler equations, all based on the theory developed in the papers by Camillo De Lellis and László Székelyhidi Jr., are believed to be connected to the theory of turbulent fluid ...

In this master thesis we will prove Dirichlet's theorem on primes in arithmetic progressions. The theorem states that there are an infinite number of primes in every primitive residue class modulo any positive number q, ...

In this thesis we begin by looking at polynomials of m n x n matrices invariant under simultaneous conjugation. Thereafter we connect the invariant polynomials to simple representations of noncommutative plane curves, ...

A Heron triangle is a triangle with integer sides and integer area. A rational triangle is a triangle with rational sides and area. We will set out to prove van Luijks Theorem, that there exist infinitely many non-similar ...

In this thesis we give an introduction to the Minimal Model Program and the Morrison-Kawamata cone conjecture. We then present some known results on anticanonical hypersurfaces building up to the result proven by Kollár ...

The main goal of this thesis is to reproduce the article [SW16] by Sims and Williams, categorising the primitive ideal space of the class of Deaconu- Renault groupoid C*-algebras generated by N_0^k-actions. We go through ...

In this thesis, we study what can be said about Fermat's Last Theorem using only elementary methods. We will study the work of Sophie Germain and Niels Henrik Abel, both who worked with Fermat’s Last Theorem in the early ...

In this thesis we consider sextactic points on plane algebraic curves and a 2-Hessian curve that identifies these points. This curve was first established by Cayley, and we prove that Cayley's 2-Hessian is wrong. Moreover, ...

We consider the bidomain model of cardiac electrophysiology. Departing from a discrete cellular model we derive the bidomain equations by homogenization. Using two-scale convergence we provide a rigorous homogenization ...

Målet ved denne artikkelen er å analysere forholdet mellom vri- og flyttespill og symmetrigruppen. Vi skal se sammenhengen mellom gruppeteori og mange populære spill, spesielt når man vil løse spillene

In this thesis we study the construction of wavelets for the Cuntz--Krieger $C^{\ast}$-algebras as developed by M. Marcolli and A. Paolucci in [MP11]. We identify and correct some errors in the construction, as well as ...

In this thesis we will study the phase space, Ph(A), for an associative k-algebra A. The phase space can be considered as a noncommutative tangent bundle. We will derive algebraic notions of points, curves, tangent vectors ...

The study of generic quartic symmetroids in projective 3-space dates back to Cayley, but little is known about the special specimens. This thesis sets out to survey the possibilities in the non-generic case. We prove that ...

This thesis aims to study the risk measure Conditional Value-at-Risk and analyse an optimization problem of maximizing expected return subject to this risk measure. The analysis include performing Fourier-Motzkin eliminations ...

In this thesis, we consider applications of directed algebraic topology in optimization theory, by representing directed graphs as directed topological spaces. We review the classical max-flow min-cut theorem and a ...

Denne oppgaven studerer Reed-Solomon-koder og ser på hvordan dekoding av disse kan relateres til å finne potenssumdekomposisjoner av polynomer, hvilket kan tolkes geometrisk som å finne et sekantplan til den rasjonale ...

Parallellaksiomet er det eneste aksiomet der hyperbolsk geometri skiller seg fra euklidsk. Mens det i euklidsk geometri er en unik linje som går gjennom et gitt punkt og er parallell med en gitt linje, finnes det i hyperbolsk ...

In their article, "Continuity of the Spectrum of a Field of Self-Adjoint Operators", Beckus and Bellissard discuss the following problem: Given a family of bounded, self-adjoint linear operators indexed by a parameter t ...

Målet med denne masteroppgaven er å se på teorien som ligger til grunn for en rangeringsmodell kalt Offense-Defense Modellen. Jeg skriver om matriseskaleringer og dobbeltstokastiske matriser som ender med Sinkhorn-Knopp ...

Denne oppgaven er skrevet i faget MAT5930L, som er det siste faget i Lektorprogrammet ved UiO. Emnet er Euklids Elementer. Vi ser på noen av proposisjonene i de tre første bøkene av Elementer. Her fokuserer vi på hvordan ...

This thesis studies a relationship between solving optimal stopping problems and solving the weak variational inequalites. We prove a theorem that presents conditions under which the weak variatonal inequalities have a ...

En polytop er et legeme i det euklidske rom som avgrenses av et endelig antall hyperplan. Vi kan legge på ulike begrensninger på polytopene og få et ulikt utvalg polytoper. I denne avhandlingen ser vi på polytoper av ulik ...

A detailed study of computable iterations of Gödel-sentences, both in normal recursion and generalisations to other recursive theories.

In 1862, substituting for professor O. J. Broch, Ludvig Sylow gives the first lectures ever given on the field of Galois theory in Norway, at the University of Christiania. He lectures on, amongst other things, what he ...

Punktene på en elliptisk kurve danner en gruppe. Hvis vi kaller origo i gruppa for Q, er et n-torsjonspunkt et punkt P som er slik at nP=Q. Mengden n-torsjonspunkter danner en abelsk gruppe. Alle 3-torsjonspunktene på en ...

An examination of the abridged notation introduced by Salmon for plane geometry. Culminating in its use to prove the theorems of Brianchon and Pascal, Steiner's theorem on Pascal's Hexagon and Steiner's solution of the ...

The first part of the thesis concerns the problem of ranking in general. We take a closer look at the two ranking methods; Elo rating and Colley rating. The former is used to rate and rank chess players, whereas the latter ...

One of the puzzlingly hard problems in \emph{Computer Aided Geometric Design} and \emph{Approximation Theory} is that of finding the dimension of the spline space of $C^r$ piecewise polynomials of degree $n$ over a planar ...

In this thesis we compute the K_2-homology of B^3\Z=K(\Z,3) following Ravenel-Wilson, and exhibit all ring spectrum maps from \Sigma^\infty B^3\Z_+ to K_2. We define the complex oriented theory K_n as a quotient of Lubin-Tate ...

In elliptic curve cryptography, the choice of the elliptic curve is important for security. This is because there exist elliptic curves where certain shortcuts can be made that breaks the security of elliptic curve ...

The thesis solves the problem of finding the local-risk minimizing strategies in an incomplete market of electricity and fuels where there is a time-change. This is done under two methodologies: in the classical sense and ...

In this thesis we will consider Markov operators on cones . More precisely, we let X equipped with certain norm be a real Banach space, K in X be a closed, normal cone with nonempty interior, e in Int (K) be an order unit. ...

We define various notions of rank of a polynomial, and study them via apolarity. We treat the notion of natural rank in particular depth, and classify ternary forms of degree at most four and quaternary forms of degree at ...

In 1968 John Milnor published his now classic "Singular points of complex hypersurfaces". In this he proved the following theorem: Let f be a holomorphic function from n-dimensional complex space to one-dimensional complex ...

By a result due to F. Forstnerič, injective holomorphic maps defined and close to the identity on a certain neighborhood of the intersection of A and B (where (A,B) is a Cartan pair in a complex manifold X) admit compositional ...

When we inspect a disease, the social structure may be important for how a disease spread. The people with many friends, may face a bigger risk for infection than a person with few friends. The social network we may represent ...

In this master’s thesis we define a pricing model for futures contracts by using Lévy processes in an infinite dimensional Hilbert space H. The elements in H are assumed to be absolutely continuous functions on the positive ...

Symplektisk teori er i historisk matematisk perspektiv en relativt ny gren innen matematikken. Denne oppgaven viser holomorfe resultater innen symplektisk teori. Den er delt inn i to kapitler, et om symplektisk lineær ...

The European Trading Scheme (ETS) has been implemented as a way of reducing emissions of greenhouse gasses. In this scheme European Union emission allowances (EUAs) are traded during the so called trading period. In the ...

Let G(d,n) be the Grassmannian parametrizing d-dimensional linear subspaces in an n-dimensional vector space V. It is a projective scheme embedded in P^N for N = (n,d) − 1 via its Plücker embedding. Let L be a distributive ...

Mathematics in climate research is rarely mentioned in the everyday conversations or in the media when talking about climate changes. This thesis therefore focus on the central role mathematics plays in climate research, ...

In this thesis, we shall apply methods developed by Bertrand Deroin to solve the tangential Cauchy-Riemann equations on positive line bundles over compact hyperbolic Riemann surface laminations. In particular, we shall ...

I denne oppgaven utvikles det en endelig elemente Newton's metode løsningsalgoritme for fluid-strukture vekselvirkning med en arbitrary Lagrangian Eulerian formulering. Denne algoritme implementeres som en softwarepakke ...

Til enhver kvatratisk (reel eller kompleks) matrise A kan man tilordne dens eksponentialmatrise e^{At}. Eksponentialmatriser spiller en viktig rolle ved løsningen av enkelte differensialligninger og i mange andre anvendelser. ...

Vi innfører nødvendig teori i algebra og algebraisk geometri til å definere dihedral homologi av en algebra og utvide definisjonen til skjemaer. Vi viser også et resultat om hvordan dihedral homologi oppfører seg med hensyn ...

Spline functions are a form of piecewise polynomials with many diverse uses and applications across several fields of study. A particular application concerns approximation of other continuous functions. Although many such ...

The topic of this thesis is linear optimization in relation to doubly stochastic matrices, which constitute the Birkhoff polytope. This polytope is closely related to the concept of majorization, which will be defined and ...

The theme of this thesis is duality methods in mathematical - nance. This is a hot topic in the eld of mathematical nance, and there is currently a lot of research activity regarding this subject. However, since it is ...

En modell for diffusjon av nevrotransmittere (glutamat) med en enkel reaktive randbetingelse. Eksistens og entydighet av løsninger, stabilitetsestimater.

We give a summary of the TTE-approach to computable anlysis, as background for a discussion about Borel complexity on represented spaces. We study the hyperspace A(X) of closed subsets of a separable metric space X, and ...

The background for this thesis is the work on broccoli curves by Gathmann, Markwig and Schroeter. In their paper, broccoli curves are introduced in order to give a tropical proof of the invariance of tropical Welschinger ...

In this thesis we study thwe phase space Ph(A) for an associative algebra A, with k algebraically closed (when needed we will assume k=C). The phase space has a universal property analogous to that of the module of Kähler ...

It is an open problem whether the isomorphism class of a finite p-group is determined by its group ring over a field of characteristic p. In this thesis we present the theory of Jennings, which gives invariants of the group ...

Given an associative k-algebra A for a field k, we want to give a local description of the moduli space of indecomposable left A-modules. The tool for this will be deformation theory and homological algebra. The goal of ...

The second World War (WWII) involved most of the world's nations and lasted from 1939-1945. Several countries were occupied during this period. One of these countries was Norway, which was occupied during a five year period ...

Vi betrakter en gruppevirkning av G på en mengde X. Opgaven omhandler C*-algebraer relatert til den uniforme Roe-algebraen. Vi bruker konstruksjoner fra kryssprodukter av C*-algebraer til å konstruere en analog til den ...

In this thesis we show a reflection theorem for K2. We compare the 3-rank of K2 of the ring of integers of ℚ(√-3D) to the 3-rank of K2 of the ring of integers of ℚ(√-3D) and find that they differ by at most 2. We also show ...

The thesis studies certain mathematical aspects of model selection, statistical estimation theory and probability using stochastic process tools.<br> The paper “The copula information criterion” is the paper with most ...

This thesis studies two aspects of polynomial interpolation theory. The first part sets forth explicit formulas for the coefficients of polynomial interpolants to implicit functions. A formula for the higher-order derivatives ...

This thesis studies an approximate solution, called relaxation approximation, to a 2x2 triangular system of hyperbolic conservation laws. The system of interest is first approximated by a particular set of smooth functions. ...

Gauss-Bonnets teorem relaterer den geometriske strukturen til en flate til dens eulerkarakteristikk, en topologisk invariant. Dette teoremet forutsetter at flaten ikke inneholder noen singulariteter. I denne oppgaven vil ...