The basic theory of semisimple Lie algebras and their representations is studied in detail. In particular it is shown that every irreducible module V (λ) is uniquely determined up to isomorphism by its highest weight λ. Then the problem of decomposing a tensor product of two finite dimensional modules into a direct sum of irreducible modules is considered. It is shown that for λ fixed, the decompo

Med hjälp av tredimensionella datorsimulationer har vi studerat utfallen från kollisioner mellan planeter. Målet med projektet var att utreda beroendet av kollisionsparametrar som till exempel avståndet vid närmaste passage, hastighet och planeternas massor. Vi kom fram till att planeterna kan bli gravitationellt bundna efter kollisionerna på grund av energiförluster som gör att de eventuellt kollUsing three-dimensional smoothed particle hydrodynamics (SPH) simulations, we have studied the outcomes from collisions between Jupiter-like planets. Planet models have been generated from polytropic profiles using a polytropic index of n=1 and each planet is represented by 15,000 particles. The dependency on a range of parameters specifying the point of closest approach, velocity at infinity and

In the 19th century E. Mathieu discovered and studied five multiply transitive permutation groups. The grops are called the Mathieu groups and it turned out that all five are simple. In this thesis these remarkable groups are constructed, with special focus on the largest Mathieu group M24. All maximal subgroups of M24 will be described and classied. It is also shown that the other Mathieu groups

We consider the scale of standard weighted Bergman spaces in the unit disc. We show that in this scale of spaces the shift operator satisfies a certain operator identity. By duality arguments this operator identity leads to an operator inequality for the Bergman shift operator in the parameter range $-1

Sturm's oscillation theorem says that the zeros of the nth eigenfunction of a Sturm-Liouville problem with separated boundary conditions divides the domain into n connected pieces. We present a proof of this theorem which partly uses a variational characterization of the eigenfunctions. We also show how the variational characterization can be adapted to study some properties of the eigenvalues

Imaging of stellar surfaces in visible wavelengths is one of the current frontiers in astronomy. With a few exceptions, stars can not be seen in visible light as anything but point objects with current technology. Being able to properly image stars would open up the door to a vast field of new discoveries, permitting direct studies of phenomena such as rotationally deformed stars, circumstellar di

This paper consists of two parts. In the first part the following problem is presented (see [1]): a king invites n couples for dinner at his round table with 2n+1 seats. For each couple there is an in advance prescribed distance between 1 and n at which the two spouses of the couple have to be seated from each other. We show that there is a solution to the king’s problem for every choice of distan

A Poisson integral formula for a weighted Laplacian in the unit disc Beskrivning: In this paper a counterpart of the classical Poisson integral formula is found for a weighted Laplace differential operator in the unit disc. In the process the corresponding Dirichlet boundary value problem is solved for arbitrary continuous boundary data. The associated power series expansions are calculated and in

Digital watermarking is done by adding a piece of data to a signal, which depending on the target media type, may be a picture, audio or video signal. The purpose of this additional signal is to provide a consistent signature linked to the original source which then remains through the act of copying. This allows the author to obstruct the act of theft by adding this signal to his or her creation.

In order to study the influence of the weather on the snowmelt in the Tarfala Valley, a survey of the runoff from the snow in the valley, was performed in May and June 1988, at the Tarfala Research Station. The aim of the survey was to find a simple numerical model that corresponds well to the runoff from the snow and to identify reasons for deviating runoff in different places. The survey was bas

Följande arbete utgör en 10 poängs-uppsats vid Naturgeografiska institutionen, Lunds universitet. Syftet med studien var att undersöka vilken skoglig information en Landsat TM scen innehåller avseende vissa skogliga beståndsvariabler. En skogsfastighet utanför Oskarshamn i Småland utgjorde undersökningsområde. Fastigheten består av cirka 1300 ha produktiv skogsmark indelat i 198 avdelningar. Lands

Undersökningen har visat att koncentrationer av luftföroreningar i bl a gatumiljö är avhängiga olika meteorologiska parametrar. Sålunda finns tydliga samband mellan koncentration och vindhastighet. Mellan koncentration och nederbörd respektive luftfuktighet finns någon typ av samband. De olika parametrarna påverkas i olika hög grad av omlandets och stadens morfologi. Rapporten redogör dels generel

Lönebildningen är en central samhällsprocess med avgörande betydelse för såväl den enskilde löntagaren, arbetsgivarna, arbetsmarknadens parter och staten. Den genererar förutsättningarna för bland annat sysselsättningen och den internationella konkurrenskraften. I en tvärvetenskaplig kontext av arbetsrätt med inslag av statsvetenskap, ekonomisk historia och arbetsmarknadsekonomi åskådliggörs en ko

In this essay the encyclopedia Kvinnan och hemmet from 1951 is examined by using Yvonne Hirdman’s theoretical framework of the gender system and its two principles and as a methodical approach the hermeneutic circle is used. The purpose of this essay is to analyze which female and male ideals that are to be found in Kvinnan och hemmet and how these ideals are described in relation to each other. T