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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 $-1<\alpha\leqq0$. In the special case $\alpha=0$ the operator inequality obtained coincides with t
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.
This work investigates crew opinions about manual intervention on board submarines and planned new solutions on the new submarine, the A26. The planned solutions include an unmanned aft and the installation of water mist instead of Halon 1301 as fire suppression system. Literature, survey and interviews were used to gather information. The crew routines and previous fire incidents were determined.
This report evaluates a first response with water against an underventilated fire with imminent risk of backdraft occurrence. The report is based on a literature review followed by 35 experiments conducted in a shipping container. A fire in a wood-based fuel was forced to become underventilated after which a hatch was opened and the outcome was studied. In some of the experiments a known amount of
In the wake of the state government of Western Australia presenting a plan to develop a liquefied natural gas precinct, a campaign was sparked, drawing Aboriginal peoples, community members, ‘outsiders’ and environmental groups to vocally question the intentions of the proponents through on-site blockades and the social media. This thesis presents a case study of arguments and motivations for peop
Economic sanctions are defined as the exercise of pressure by one state to bring about a change in political behaviour of another state. Traditional economic sanctions are directed at the entire population of the sanctioned country while targeted sanctions are directed at the State’s government and/or individuals. Iran has become a sanction target first in 1979, which was imposed by United States
