Essays about: "Hausdorff measure"
Showing result 1 - 5 of 10 essays containing the words Hausdorff measure.
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1. A geometric approach to calculating the limit set of eigenvalues for banded Toeplitz matrices
University essay from Lunds universitet/Matematik LTHAbstract : This thesis is about the limiting eigenvalue distribution of n × n Toeplitz matrices as n → ∞. The two classical questions we want to answer are: what is the limit set of the eigenvalues, and what is the limiting distribution of the eigenvalues. Our main result is a new approach to calculate the limit set Λ(b) for a Laurent polynomial b, i.e. READ MORE
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2. The Banach-Tarski Paradox : How I Learned to Stop Worrying and Love the Axiom of Choice
University essay from Umeå universitet/Institutionen för matematik och matematisk statistikAbstract : This thesis presents the strong and weak forms of the Banach-Tarski paradox based on the Hausdorff paradox. It provides modernized proofs of the paradoxes and necessary properties of equidecomposable and paradoxical sets. READ MORE
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3. Fractal Sets: Dynamical, Dimensional and Topological Properties
University essay from KTH/Skolan för teknikvetenskap (SCI)Abstract : Fractals is a relatively new mathematical topic which received thorough treatment only starting with 1960's. Fractals can be observed everywhere in nature and in day-to-day life. To give a few examples, common fractals are the spiral cactus, the romanesco broccoli, human brain and the outline of the Swedish map. READ MORE
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4. Multidimensional measures on Cantor sets
University essay from Göteborgs universitet/Institutionen för matematiska vetenskaperAbstract : Cantor sets in R are common examples of sets on which Hausdorff measures can be positive and finite. However, there exists Cantor sets on which no Hausdorff measure is supported and finite. READ MORE
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5. Clinical evaluation of atlas based segmentation for radiotherapy of prostate tumours
University essay from Institutionen för fysikAbstract : Abstract Background Semi-automated segmentation using deformable registration of atlases consisting of pre-segmented patient images can facilitate the tedious task of delineating structures and organs in patients subjected to radiotherapy planning. However, a generic atlas based on a single patient may not function well enough due to the anatomical variation between patients. READ MORE