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Geometry --- Fractals --- Mathematical analysis --- Congresses --- Fractals - Congresses. --- Mathematical analysis - Congresses. --- Fractals - Congresses --- Mathematical analysis - Congresses

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This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott,  Michał Rams, Pablo Shmerkin, and András Telcs.

Mathematics. --- Probability Theory and Stochastic Processes. --- Geometry. --- Measure and Integration. --- Distribution (Probability theory). --- Mathématiques --- Géométrie --- Distribution (Théorie des probabilités) --- Fractals -- Congresses. --- Stochastic processes -- Congresses. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Fractals --- Stochastic processes --- Measure theory. --- Probabilities. --- Distribution (Probability theory. --- Euclid's Elements --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Math --- Science --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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Statistical physics --- Analytical topology --- Geometry --- Mathematical physics --- Fractals --- Irreversible processes --- Congresses --- 517.987 <063> --- -Irreversible processes --- -Mathematical physics --- -Physical mathematics --- Physics --- Processes, Irreversible --- Dynamics --- Equilibrium --- Molecular dynamics --- Statistical mechanics --- Thermodynamics --- Nonequilibrium thermodynamics --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems--Congressen --- Mathematics --- -Measures. Representations of Boolean algebras. Metric theory of dynamic systems--Congressen --- 517.987 <063> Measures. Representations of Boolean algebras. Metric theory of dynamic systems--Congressen --- Fractals - Congresses --- Irreversible processes - Congresses --- Mathematical physics - Congresses

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This volume presents selected aspects of non-integer, or fractional order systems, whose analysis, synthesis and applications have increasingly become a real challenge for various research communities, ranging from science to engineering. The spectrum of applications of the fractional order calculus has incredibly expanded, in fact it would be hard to find a science/engineering-related subject area where the fractional calculus had not been incorporated. The content of the fractional calculus is ranged from pure mathematics to engineering implementations and so is the content of this volume. The volume is subdivided into six parts, reflecting particular aspects of the fractional order calculus. The first part contains a single invited paper on a new formulation of fractional-order descriptor observers for fractional-order descriptor continuous LTI systems. The second part provides new elements to the mathematical theory of fractional-order systems. In the third part of this volume, a bunch of new results in approximation, modeling and simulations of fractional-order systems is given. The fourth part presents new solutions to some problems in controllability and control of non-integer order systems, in particular fractional PID-like control. The fifth part analyzes the stability of non-integer order systems and some new results are offered in this important respect, in particular for discrete-time systems. The final, sixth part of this volume presents a spectrum of applications of the non-integer order calculus, ranging from bi-fractional filtering, in particular of electromyographic signals, through the thermal diffusion and advection diffusion processes to the SIEMENS platform implementation. This volume's papers were all subjected to stimulating comments and discussions from the active audience of the RRNR'2014, the 6th Conference on Non-integer Order Calculus and Its Applications that was organized by the Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland.

Engineering. --- Control. --- Complexity. --- Signal, Image and Speech Processing. --- Physics. --- Ingénierie --- Physique --- Dynamics -- Mathematics -- Congresses. --- Dynamics -- Mathematics. --- Fractals -- Congresses. --- Fractional calculus -- Congresses. --- Fractional calculus. --- Mechanical Engineering --- Engineering & Applied Sciences --- Mechanical Engineering - General --- Fractional calculus --- Dynamics --- Mathematics --- Dynamical systems --- Kinetics --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Construction --- Industrial arts --- Technology --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Calculus --- Control and Systems Theory. --- Control engineering. --- Computational complexity. --- Signal processing. --- Image processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Complexity, Computational --- Electronic data processing --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers