University, Diss., 2004--Kassel. / Download lizenzpflichtig.

Universiẗat, Diss., 2005--Karlsruhe.

The notion of fulfilment of a formula by a sequence of numbers, an approximation of truth due to Kripke, is presented and subsequently formalised in the weak arithmetic theory IΣ1, in some detail. After a number of technical results connecting the formalised notion to the meta-theoretical one a version of Gödel’s Incompleteness Theorem, that no consistent, recursively axiomatisable, Σ2-sound extension T of Peano arithmetic is complete, is shown by construction of a true Π2-sentence and a model of T where it is false, yielding its independence from T. These results are then generalised to a more general notion of fulfilment, proving that IΣ1 has no complete, consistent, recursively axiomatisable, Σ2-sound extensions by a similar construction of an independent sentence. This generalisation comes at the cost of some naturality, however, and an explicit falsifying model will only be obtained under additional assumptions. The aim of the thesis is to reproduce in some detail the notions and results developed by Kripke and Quinsey and presented by Quinsey and Putnam. In particular no novel results are obtained.

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In this thesis, we consider hom-associative algebras, which is an algebra with multiplication that is not necessarily commutative nor associative, but obeys a twisted version of associativity by a linear homomorphism. We will give some conditions for associativity, which helps us determine commuting elements. Under other conditions, such as different types of unitality conditions, we can also state some results regarding commuting elements in the general, non-associative case.

I detta arbete har lösningar till ekvationen xn+yn= 1 i en ändlig kropp av primtalsordning studerats. Både konkreta lösningar för vissa givna förutsättningar samt resultat gällande antalet lösningar har varit målet för dessa studier. I uppsatsen redovisas även de metoder som använts för att nå nämnda resultat. Eftersom ekvationen kan studeras för en oändlig mängd kroppar presenteras inget heltäckande resultat. Vissa resultat är dock generella under premissen att antingen kroppen eller ekvationen fixeras för något primtal p respektive exponent n. För sådana specialfall presenteras flera exempel. Huvudresultatet i arbetet visar att det alltid finns många icke-triviala lösningar för ekvationen över stora ändliga kroppar.

We classify plethories over fields of characteristic zero, thus answering a question of Borger-Wieland and Bergman-Hausknecht. All plethories over characteristic zero fields are linear, in the sense that they are free plethories on a bialgebra. For the proof we need some facts from the theory of ring schemes where we extend previously known results. We also classify plethories with trivial Verschiebung over a perfect field of non-zero characteristic and indicate future work. / <p>QC 20151117</p>

This thesis is constituted of two articles, both related to Hilbert functions and h-vectors. In the first paper, we deal with h-vectorsof reduced zero-dimensional schemes in the projective plane, and, in particular, with the problem of finding the possible h-vectors for the union of two sets of points of given h-vectors. In the second paper, we generalize the Green’s Hyperplane Restriction Theorem to the case of modules over the polynomial ring. / <p>QC 20131114</p>

In this thesis, we will investigate the rapidly developing eld of computergraphics by giving an insight into the calculations behind the most im-portant topics in perspectives, shading and distance. We will delve intofrequently used shading algorithms and perspective transforms in areas ofcomputer science, architecture and photography, such as pseudo sh-eyelenses and wide-angle lenses.

The purpose of the study is to investigate how people, in a situation of ongoing environmental and climate change, problematize Swedish forestry. Based on the discourses and logics that are expressed, the focus is on how the resistance is made through notions of the Swedish forest, social categories, nature and man's place in nature. The analysis shows how scientific knowledge and cultural knowledge from the participants' imaginary worlds interact in the crisis discourse the group creates about the Swedish forest. In the social reality of the crisis discourse, it becomes central to make other people "wake up" and see how forestry and the majority's way of life threatens not only the forest but all life on earth. The discussions can be described as a negotiation over what is "natural" as well as what and who is imagined to be part of "nature". Paradoxically, man is articulated both as part of ecological systems and as an "unnatural" intruder in nature: like a pest.