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Author: Werner Schindler
Publisher: Springer Science & Business Media
ISBN: 9783540002352
Category : Mathematics
Languages : en
Pages : 184
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Book Description
Symmetries and invariance principles play an important role in various branches of mathematics. This book deals with measures having weak symmetry properties. Even mild conditions ensure that all invariant Borel measures on a second countable locally compact space can be expressed as images of specific product measures under a fixed mapping. The results derived in this book are interesting for their own and, moreover, a number of carefully investigated examples underline and illustrate their usefulness and applicability for integration problems, stochastic simulations and statistical applications.
Author: Werner Schindler
Publisher: Springer Science & Business Media
ISBN: 9783540002352
Category : Mathematics
Languages : en
Pages : 184
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Book Description
Symmetries and invariance principles play an important role in various branches of mathematics. This book deals with measures having weak symmetry properties. Even mild conditions ensure that all invariant Borel measures on a second countable locally compact space can be expressed as images of specific product measures under a fixed mapping. The results derived in this book are interesting for their own and, moreover, a number of carefully investigated examples underline and illustrate their usefulness and applicability for integration problems, stochastic simulations and statistical applications.
Author: Gabor Toth
Publisher: Springer
ISBN: 3319237330
Category : Mathematics
Languages : en
Pages : 289
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Book Description
This textbook treats two important and related matters in convex geometry: the quantification of symmetry of a convex set—measures of symmetry—and the degree to which convex sets that nearly minimize such measures of symmetry are themselves nearly symmetric—the phenomenon of stability. By gathering the subject’s core ideas and highlights around Grünbaum’s general notion of measure of symmetry, it paints a coherent picture of the subject, and guides the reader from the basics to the state-of-the-art. The exposition takes various paths to results in order to develop the reader’s grasp of the unity of ideas, while interspersed remarks enrich the material with a behind-the-scenes view of corollaries and logical connections, alternative proofs, and allied results from the literature. Numerous illustrations elucidate definitions and key constructions, and over 70 exercises—with hints and references for the more difficult ones—test and sharpen the reader’s comprehension. The presentation includes: a basic course covering foundational notions in convex geometry, the three pillars of the combinatorial theory (the theorems of Carathéodory, Radon, and Helly), critical sets and Minkowski measure, the Minkowski–Radon inequality, and, to illustrate the general theory, a study of convex bodies of constant width; two proofs of F. John’s ellipsoid theorem; a treatment of the stability of Minkowski measure, the Banach–Mazur metric, and Groemer’s stability estimate for the Brunn–Minkowski inequality; important specializations of Grünbaum’s abstract measure of symmetry, such as Winternitz measure, the Rogers–Shepard volume ratio, and Guo’s Lp -Minkowski measure; a construction by the author of a new sequence of measures of symmetry, the kth mean Minkowski measure; and lastly, an intriguing application to the moduli space of certain distinguished maps from a Riemannian homogeneous space to spheres—illustrating the broad mathematical relevance of the book’s subject.
Author: Sacha Friedli
Publisher: Cambridge University Press
ISBN: 1107184827
Category : Mathematics
Languages : en
Pages : 643
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Book Description
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Author:
Publisher: Elsevier
ISBN: 0080531407
Category : Technology & Engineering
Languages : en
Pages : 457
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Book Description
This volume provides an overview of modern acoustical techniques for the measurement of mechanical properties. Chapters include Fundamentals of Elastic Constants; Point Source/Point Receiver Methods; Laser Controlled Surface Acoustic Waves; Quantitative Acoustical Microscopy of Solids; Resonant Ultrasound Spectroscopy; Elastic Properties and Thermodynamics; Sound Speed as a Thermodynamic Property of Fluids; Noninvasive Determination of Sound Speed in Liquids; Introduction to the Elastic Constants of Gases; and Acoustic Measurement in Gases.
Author: Shusaku Tsumoto
Publisher: Springer
ISBN: 3540259295
Category : Computers
Languages : en
Pages : 871
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Book Description
In recent years rough set theory has attracted the attention of many researchers and practitioners all over the world, who have contributed essentially to its development and applications. Weareobservingagrowingresearchinterestinthefoundationsofroughsets, including the various logical, mathematical and philosophical aspects of rough sets. Some relationships have already been established between rough sets and other approaches, and also with a wide range of hybrid systems. As a result, rough sets are linked with decision system modeling and analysis of complex systems, fuzzy sets, neural networks, evolutionary computing, data mining and knowledge discovery, pattern recognition, machine learning, and approximate reasoning. In particular, rough sets are used in probabilistic reasoning, granular computing (including information granule calculi based on rough mereology), intelligent control, intelligent agent modeling, identi?cation of autonomous s- tems, and process speci?cation. Methods based on rough set theory alone or in combination with other - proacheshavebeendiscoveredwith awide rangeofapplicationsinsuchareasas: acoustics, bioinformatics, business and ?nance, chemistry, computer engineering (e.g., data compression, digital image processing, digital signal processing, p- allel and distributed computer systems, sensor fusion, fractal engineering), de- sion analysis and systems, economics, electrical engineering (e.g., control, signal analysis, power systems), environmental studies, informatics, medicine, mole- lar biology, musicology, neurology, robotics, social science, software engineering, spatial visualization, Web engineering, and Web mining.
Author: Hans G. Hornung
Publisher: Courier Corporation
ISBN: 048615047X
Category : Science
Languages : en
Pages : 80
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Book Description
Derived from a course in fluid mechanics, this text for advanced undergraduates and graduate students employs symmetry arguments to illustrate the principles of dimensional analysis. 2006 edition.
Author: D.J. Daley
Publisher: Springer Science & Business Media
ISBN: 0387955410
Category : Mathematics
Languages : en
Pages : 487
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Book Description
Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.
Author: Ctirad Uher
Publisher: CRC Press
ISBN: 1000513777
Category : Science
Languages : en
Pages : 352
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Book Description
Superconductivity and Magnetism in Skutterudites discusses superconducting and magnetic properties of a class of materials called skutterudites. With a brief introduction of the fundamental structural features of skutterudites, the book then provides a detailed assessment of the superconducting and magnetic properties, focusing particularly on the rare earth-filled skutterudites where a plethora of fascinating properties and ground states is realized due to interactions of the filler species with the framework ions. Such interactions underpin the exciting forms of superconductivity and magnetism, most notably realized in the exotic heavy fermion superconductor of composition PrOs4Sb12. The two main topics of superconductivity and magnetism are provided with a concise introduction of superconducting and magnetic properties so that a reader can appreciate and understand the main arguments in the text. This book would appeal to graduate students, postdoctoral students, and anyone interested in superconducting and magnetic properties of a large family of minerals called skutterudites. Key Features: • Gives a thorough account of the superconducting and magnetic properties of skutterudites. • Each topic is accompanied by introductory sections to assist in the understanding of the text. • Supported by numerous figures and all key references.
Author: Ray Fraser
Publisher: Heinemann
ISBN: 9780435017613
Category : Juvenile Nonfiction
Languages : en
Pages : 262
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Book Description
Green Impact Maths textbooks are intended for lower ability pupils in Year 7. It has been written to cater for weak readers. The emphasis is placed on helping the teacher ensure that pupils understand basic concepts, then encouraging them to progress and improve their performance.
Author: Markus Knauff
Publisher: MIT Press
ISBN: 0262045079
Category : Psychology
Languages : en
Pages : 879
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Book Description
The first reference on rationality that integrates accounts from psychology and philosophy, covering descriptive and normative theories from both disciplines. Both analytic philosophy and cognitive psychology have made dramatic advances in understanding rationality, but there has been little interaction between the disciplines. This volume offers the first integrated overview of the state of the art in the psychology and philosophy of rationality. Written by leading experts from both disciplines, The Handbook of Rationality covers the main normative and descriptive theories of rationality—how people ought to think, how they actually think, and why we often deviate from what we can call rational. It also offers insights from other fields such as artificial intelligence, economics, the social sciences, and cognitive neuroscience. The Handbook proposes a novel classification system for researchers in human rationality, and it creates new connections between rationality research in philosophy, psychology, and other disciplines. Following the basic distinction between theoretical and practical rationality, the book first considers the theoretical side, including normative and descriptive theories of logical, probabilistic, causal, and defeasible reasoning. It then turns to the practical side, discussing topics such as decision making, bounded rationality, game theory, deontic and legal reasoning, and the relation between rationality and morality. Finally, it covers topics that arise in both theoretical and practical rationality, including visual and spatial thinking, scientific rationality, how children learn to reason rationally, and the connection between intelligence and rationality.
