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This book is devoted to an important branch of the dynamical systems theory : the study of the fine (fractal) structure of Poincare recurrences -instants of time when the system almost repeats its initial state. The authors were able to write an entirely self-contained text including many insights and examples, as well as providing complete details of proofs. The only prerequisites are a basic knowledge of analysis and topology. Thus this book can serve as a graduate text or self-study guide for courses in applied mathematics or nonlinear dynamics (in the natural sciences). Moreover, the bo

Fractals. --- Poincaré series. --- Series, Poincaré --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology)

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The application of biosensors is expanding in different areas. These are portable and convenient devices that permit the rapid, accurate, and reliable detection of analytes of interest present either in the atmosphere or in aqueous or in liquid phases. The detection of glucose levels in blood for the effective management of diabetes is one. Though different biosensors have been designed for an increasing number of applications, the kinetics of binding (and dissociation) of analytes by the receptors on the biosensor surfaces has not been given enough attention in the open literature. This i

Biosensors --- Fractals. --- Pathogenic microorganisms --- Mathematics. --- Detection. --- Detection of pathogenic microorganisms --- Diagnostic microbiology --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Biodetectors --- Biological detectors --- Biological sensors --- Biomedical detectors --- Biomedical sensors --- Detectors --- Medical instruments and apparatus --- Physiological apparatus

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This book, combining analysis and tools from mathematical probability, focuses on a systematic and novel presentation of recent trends in pure and applied mathematics: the emergence of three fields, wavelets, signals and fractals. The unity of basis constructions and their expansions is emphasized as the starting point for the development of bases that are computationally efficient for use in several areas from wavelets to fractals. The book brings together tools from engineering and math, especially from signal- and image processing, and from harmonic analysis and operator theory. The presentation is aimed at graduate students, as well as users from a diverse spectrum of applications. Key features: • A hands-on approach for students, including tutorials and numerous exercises; • Excellent motivation throughout; • New pedagogical features: glossary of terms, their use in mathematics and in engineering, help for cross-audiences, image processing, visual presentation of key algorithms, structure and geometry of big matrix computations, explanation of uses of the theory in applications outside of mathematics; • Includes more than 50 figures with captions, illustrating the main ideas, plus engineering diagrams, graphic renditions of algorithms, and separate illustrations; • Separate sections in the book explain engineering terms to mathematicians, and operator theory to engineers; • Each chapter concludes with a helpful guide to the literature allowing students to follow up on the topics in the book. Palle E.T. Jorgensen is a Professor of Mathematics at the University of Iowa. This book is based in part on interdisciplinary courses that he has taught over the last several years, and on his work with his current and former students. His most recent book was written jointly with Ola Bratteli and is entitled Wavelets through a Looking Glass, ©2002 Birkhäuser Boston.

Fractals. --- Mathematical analysis. --- Probabilities. --- Wavelets (Mathematics) --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- 517.1 Mathematical analysis --- Mathematical analysis --- Wavelet analysis --- Harmonic analysis --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Probabilities --- Fractals --- Distribution (Probability theory. --- Global analysis (Mathematics). --- Mathematics. --- Engineering mathematics. --- Probability Theory and Stochastic Processes. --- Analysis. --- Applications of Mathematics. --- Mathematical and Computational Engineering. --- Signal, Image and Speech Processing. --- Information and Communication, Circuits. --- Engineering --- Engineering analysis --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Distribution functions --- Frequency distribution --- Characteristic functions --- Harmonic analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Signal processing. --- Image processing. --- Speech processing systems. --- Information theory. --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Communication theory --- Communication --- Cybernetics --- 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 --- Computer science --- Probability Theory. --- Mathematical and Computational Engineering Applications. --- Signal, Speech and Image Processing . --- Mathematical Applications in Computer Science. --- Data processing. --- Computer mathematics --- Electronic data processing

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This book introduces the reader to the notions, the techniques, and the theory of grammatical picture generation, a research field focusing on formal systems that describe sets of pictures by means of syntactic rules. The book presents important types of picture generators, using a tree-based approach to stress their common algorithmic basis, the treatment influenced by the theory of computation, and the theory of formal languages in particular. It guides the reader through the basics of the tree-based approach on to dedicated chapters on line-drawing languages, collage grammars, iterated function systems, grid picture languages, languages of fractals, and languages of coloured collages, while presenting results about (un)decidable, NP-complete, or efficiently solvable problems, normal forms, hierarchies of language classes, and related phenomena. In support, the book contains detailed exercises throughout. The book is of interest to researchers and graduate students in computer science and mathematics who are engaged with the theory and practice of picture-generating systems.

Fractals. --- Computer drawing. --- Image processing --- Digital techniques. --- Digital image processing --- Digital electronics --- Computer graphics --- Drawing --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Digital techniques --- Computer science. --- Information theory. --- Computer simulation. --- Computer graphics. --- Computer vision. --- Computer Applications. --- Theory of Computation. --- Mathematics of Computing. --- Simulation and Modeling. --- Computer Graphics. --- Image Processing and Computer Vision. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Communication theory --- Communication --- Cybernetics --- Informatics --- Science --- Application software. --- Computers. --- Computer science—Mathematics. --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Machine theory --- Calculators --- Cyberspace --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Computer software --- Optical equipment --- Informatique --- Computer science --- Langages formels --- Formal languages --- Formal languages. --- Automates abstraits