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Showing result 1 - 5 of 10 essays matching the above criteria.

  1. 1. A geometric approach to calculating the limit set of eigenvalues for banded Toeplitz matrices

    University essay from Lunds universitet/Matematik LTH

    Author : Teodor Bucht; [2023]
    Keywords : Toeplitz matrices; Banded Toeplitz matrices; Limit set; Eigenvalues; Mathematics and Statistics;

    Abstract : 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

  3. 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 statistik

    Author : Mats Karl Anders Wahlberg; [2022]
    Keywords : Banach; Tarski; Banach-Tarski; Banach-Tarski paradox; Hausdorff; Hausdorff paradox; paradox; measure; measure theory; axiom of choice; Banach; Tarski; Banach-Tarski; Banach-Tarskis paradox; Hausdorff; Hausdorffs paradox; paradox; mått; måtteori; urvalsaxiomet; valaxiomet;

    Abstract : 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

  4. 3. Fractal Sets: Dynamical, Dimensional and Topological Properties

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Nancy Wang; [2018]
    Keywords : logistic function; Cantor set; generalised Cantor Set; fat Cantor set; fractals; fractal dimension; von Koch snowflake; Sierpinski arrowhead curve; Sierpinski carpet; Menger sponge; topological dimension; box dimension; exterior measure; Hausdorff measure; Hausdorff dimension; logistisk funktion; Cantormängd; fet Cantormängd; generaliserade Cantormängd; fraktaler‚; bråktalsdimension; Kochsnöfling; Sierpinskismatta; Sierpinskispilspetskurva; Mengers tvättsvamp; topologiska dimension; lådräkningsdimension; yttre mått; Hausdorffmått; Hausdorffdimension;

    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

  5. 4. Multidimensional measures on Cantor sets

    University essay from Göteborgs universitet/Institutionen för matematiska vetenskaper

    Author : Palö Malin; [2013-06-24]
    Keywords : ;

    Abstract : 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

  6. 5. Clinical evaluation of atlas based segmentation for radiotherapy of prostate tumours

    University essay from Institutionen för fysik

    Author : Christoffer Granberg; [2011]
    Keywords : segmentation; registration; radiotherapy; atlas;

    Abstract : 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