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Showing result 1 - 5 of 6 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. 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

  4. 3. Worm simulation of Hausdorff dimension of critical loop fluctuations

    University essay from KTH/Fysik

    Author : Simon Rydell; [2018]
    Keywords : ;

    Abstract : .... READ MORE

  5. 4. Lebesgue points, Hölder continuity and Sobolev functions

    University essay from Matematiska institutionen

    Author : John Karlsson; [2009]
    Keywords : Lebesgue point; Hausdorff dimension; Hausdorff measure; Hölder continuity; Maximal function; Poincaré inequality; Sobolev space; Uniform continuity;

    Abstract : This paper deals with Lebesgue points and studies properties of the set of Lebesgue points for various classes of functions. We consider continuous functions, L1 functions and Sobolev functions. In the case of uniformly continuous functions and Hölder continuous functions we develop a characterization in terms of Lebesgue points. READ MORE

  6. 5. Fractal Geometry, Graph and Tree Constructions

    University essay from Institutionen för matematik och matematisk statistik

    Author : Tommy Löfstedt; [2008]
    Keywords : ;

    Abstract : In the 18th and 19th centuries the branch of mathematics that would later be known as fractal geometry was developed. It was the ideas of Benoˆıt Mandelbrot that made the area expand so rapidly as it has done recently, and since the publication of his works there have for fractals, and most commonly the estimation of the fractal dimension, been found uses in the most diverse applications. READ MORE