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351	Fractal Sets: Dynamical, Dimensional and Topological Properties / Fraktalmängder: Dynamiska, Dimensionella och Topologiska Egenskaper Wang, Nancy January 2018 (has links) 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. Fractal dimension is a dimension which need not take integer values. In fractal geometry, a fractal dimension is a ratio providing an index of the complexity of fractal pattern with regard to how the local geometry changes with the scale at which it is measured. In recent years, fractal analysis is used increasingly in many areas of engineering and technology. Among others, fractal analysis is used in signal and image compression, computer and video design, neuroscience and fractal based cancer modelling and diagnosing. This study consists of two main parts. The first part of the study aims to understand the appearance of an irregular Cantor set generated by the chaotic dynamical system generated by the logistic function on the unit interval [0,1]. In order to understand this irregular Cantor set, we studied the topological properties of the Cantor Middle-thirds set and the generalised Cantor sets, all of which have zero length. The necessity to compare these sets with regard to their size led us to the second part of this paper, namely the dimension studies of fractals. More complex fractals were presented in the second part, three definitions of dimension were introduced. The fractal dimension of the irregular Cantor set generated by the logistic mapping was estimated and we found that the Hausdorff dimension has the widest scope and greatest flexibility in the fractal studies. / Fraktaler är ett relativt nytt ämne inom matematik som fick sitt stora genomslag först efter 60-talet. En fraktal är ett självliknande mönster med struktur i alla skalor. Några vardagliga exempel på fraktaler är spiralkaktus, romanescobroccoli, mänskliga hjärnan, blodkärlen och Sveriges fastlandskust. Bråktalsdimension är en typ av dimension där dimensionsindexet tillåts att anta alla icke-negativa reella tal. Inom fraktalgeometri kan dimensionsindexet betraktas som ett komplexitetsindex av mönstret med avseende på hur den lokala geometrin förändras beroende på vilken skala mönstret betraktas i. Under det senaste decenniet har fraktalanalysen använts alltmer flitigt inom tekniska och vetenskapliga tillämpningar. Bland annat har fraktalanalysen använts i signal- och bildkompression, dator- och videoformgivning, neurovetenskap och fraktalbaserad cancerdiagnos. Denna studie består av två huvuddelar. Den första delen fokuserar på att förstår hur en fraktal kan uppstå i ett kaotiskt dynamiskt system. För att vara mer specifik studerades den logistiska funktionen och hur denna ickelinjära avbildning genererar en oregelbunden Cantormängd på intervalet [0,1]. Vidare, för att förstå den oregelbundna Cantormängden studerades Cantormängden (eng. the Cantor Middle-Thirds set) och de generaliserade Cantormängderna, vilka alla har noll längd. För att kunna jämföra de olika Cantormängderna med avseende på storlek, leds denna studie vidare till dimensionsanalys av fraktaler som är huvudämnet i den andra delen av denna studie. Olika topologiska fraktaler presenterades, tre olika definitioner av dimension introducerades, bland annat lådräkningsdimensionen och Hausdorffdimensionen. Slutligen approximerades dimensionen av den oregelbundna Cantormängden med hjälp av Hausdorffdimensionen. Denna studie demonstrerar att Hausdorffdimensionen har större omfattning och mer flexibilitet för fraktalstudier. 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 Engineering and Technology Teknik och teknologier
352	Modeling Physical and Hydraulic Properties of Disordered Porous Media: Applications from Percolation Theory and Fractal Geometry Ghanbarian-Alavijeh, Behzad 30 May 2014 (has links) No description available. Environmental Science Petroleum Engineering Soil Sciences Hydrology Geology Geophysics Fluid Dynamics Environmental Engineering Agriculture Agricultural Engineering Civil Engineering Chemical Engineering Geophysical Geological Hydrologic Sciences Physics Theoretical Mathematics
353	Vnímání krásy - biologické vs. kulturní determinanty / Perception of beauty - biological vs. cultural determinants Obdržálková, Zita January 2013 (has links) This thesis deals with problems of biological and cultural determinants influencing perception of beauty. It attempts to find out if there is a common biological basis of perception of beauty or if beauty represents merely a sociocultural construct - product of a specific culture. With respect to biological determinants it concerns biological processes significantly influencing perception of beauty. In this context, these processes include probably innate evolutionary adaptations, effects of brain cognitive systems and neural correlates processing perceptions of beautiful objects. In connection with cultural determinants it presents studies emphasizing cross-cultural differences in perception of beauty. Further subject of the thesis is an aesthetic conception of subjective and objective beauty and related concept of beauty based on mathematical relations. In this connection, the creation of universally beautiful objects based on fixed mathematical rules as well as the possibility of exact measurement of beauty are discussed.
354	Chaos / Chaos Vogelová, Tereza January 2012 (has links) The existing world is becoming more disrupted and is falling apart. For its resurrection and restoration, a new way of thinking is necessary. This new type of thinking is needed to be able to open up its mind and to think about the process of thinking itself; it must understand what is happening in other systems, where processes seem to be taking place by themselves without any other visible interference. First Chaos is the title for an intermedia installation which contains 90 black and white photographs, both digital and analogue, all of which were taken between the years 2008 and 2012. Together, the photographs create one coherent piece – a kind of sculpture. They can evoke a "still film" with a non-linear, cyclical storyline, whilst the images can simultaneously function individually, without any connection to other photographs.
355	Feigenbaum Scaling Sendrowski, Janek January 2020 (has links) In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive. Feigenbaum Feigenbaum constant Feigenbaum point superstable self-similarity fractals final-state diagram logistic map period-doubling operator linearized period-doubling operator Cantor set Sharkovsky sequence Chebyshev interpolation stable manifold unstable manifold orbits fixed points scaling factor pitchfork bifurcation cobweb plot renormalization iterates one-hump map unimodal map bifurcation cascade Feigenbaum universality chaos theory spectrum generalized Feigenvalues bifurcation points superstable points fixed function universal function eigenvalues eigenvectors eigenfunctions universality conditions Schwarzian derivative Newton’s method power method Arnoldi’s method attractive fixed point repellent fixed point Banach fixed-point theorem collocation method functional analysis topology Mathematical Analysis Matematisk analys Other Mathematics Annan matematik Computational Mathematics Beräkningsmatematik

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