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The aim of this book is to show some applications of fractal analysis in the fields of sciences. The first chapter introduces the readers to the book, while the second chapter shows the methods and challenges of fractal analysis of time-series data sets. The third chapter demonstrates fractal geometry as an attractive choice for miniaturized planar microwave filter design. The fourth chapter presents fractal antennas for wearable applications. The objective of the fifth chapter is to show some Parrondian games in discrete dynamic systems, while the last chapter reveals fractal structures of carbon nanotube system arrays.
Fractal analysis. --- Fractals. --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Fractal geometric analysis --- Geometric analysis --- Physical Sciences --- Engineering and Technology --- Dynamical Systems Theory --- Mathematics --- Applied Mathematics
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This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions. Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.
Topology. --- Global analysis (Mathematics). --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Dimension theory (Topology) --- Topology
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Renowned scholars in the field of comparative and interreligious theology respond to Perry Schmidt-Leukel's novel approach to the understanding of religious diversity, using fractals (patterns found in science and nature). Conversation partners from multiple faith traditions include Alan Race, Paul Knitter, Francis Clooney, John Makransky, and Ephraim Meir.
Religions --- Religious pluralism. --- Fractals --- Relations. --- Miscellanea. --- Schmidt-Leukel, Perry. --- Religious pluralism --- 291.16 --- 291.16 Verhouding tussen de godsdiensten. Verdraagzaamheid. Interreligieuze dialoog --- Verhouding tussen de godsdiensten. Verdraagzaamheid. Interreligieuze dialoog --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Pluralism (Religion) --- Pluralism --- Religion --- Interreligious relations --- Relations among religions --- Relations --- Miscellanea --- Leukel, Perry Schmidt --- -Religions --- Interfaith relations. --- Fractals. --- -Religions - Relations. --- Fractals - Miscellanea.
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