Category «Mathematics»

Lyapunov Exponents - download pdf or read online

By Ludwig Arnold, Volker Wihstutz

ISBN-10: 3540164588

ISBN-13: 9783540164586

Because the predecessor to this quantity (LNM 1186, Eds. L. Arnold, V. Wihstutz)appeared in 1986, major growth has been made within the thought and purposes of Lyapunov exponents - one of many key strategies of dynamical structures - and particularly, reported shifts in the direction of nonlinear and infinite-dimensional structures and engineering purposes are observable. This quantity opens with an introductory survey article (Arnold/Crauel) by way of 26 unique (fully refereed) examine papers, a few of that have partly survey personality. From the Contents: L. Arnold, H. Crauel: Random Dynamical Systems.- I.Ya. Goldscheid: Lyapunov exponents and asymptotic behaviour of the made of random matrices.- Y. Peres: Analytic dependence of Lyapunov exponents on transition probabilities.- O. Knill: the higher Lyapunov exponent of Sl (2, R) cocycles:Discontinuity and the challenge of positivity.- Yu.D. Latushkin, A.M. Stepin: Linear skew-product flows and semigroups of weighted composition operators.- P. Baxendale: Invariant measures for nonlinear stochastic differential equations.- Y. Kifer: huge deviationsfor random increasing maps.- P. Thieullen: Generalisation du theoreme de Pesin pour l' -entropie.- S.T. Ariaratnam, W.-C. Xie: Lyapunov exponents in stochastic structural mechanics.- F. Colonius, W. Kliemann: Lyapunov exponents of keep an eye on flows.

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Calculus of Thought: Neuromorphic Logistic Regression in - download pdf or read online

By Daniel M. Rice

Calculus of proposal: Neuromorphic Logistic Regression in Cognitive Machines is a must-read for all scientists a few extremely simple computation procedure designed to simulate big-data neural processing. This publication is galvanized by way of the Calculus Ratiocinator concept of Gottfried Leibniz, that is that desktop computation can be built to simulate human cognitive tactics, therefore keeping off challenging subjective bias in analytic options to sensible and medical problems.

The decreased blunders logistic regression (RELR) approach is proposed as the sort of "Calculus of Thought." This ebook stories how RELR's thoroughly automatic processing may possibly parallel vital features of particular and implicit studying in neural procedures. It emphasizes the truth that RELR is basically only a basic adjustment to already commonly used logistic regression, in addition to RELR's new functions that cross way past commonplace logistic regression in prediction and clarification. Readers will learn the way RELR solves probably the most easy difficulties in today’s immense and small info regarding excessive dimensionality, multi-colinearity, and cognitive bias in capricious results mostly regarding human behavior.

• presents a high-level creation and certain stories of the neural, statistical and laptop studying wisdom base as a beginning for a brand new period of smarter machines
• Argues that smarter computing device studying to deal with either rationalization and prediction with no cognitive bias should have a starting place in cognitive neuroscience and needs to include related particular and implicit studying ideas that take place within the brain
• bargains a brand new neuromorphic starting place for computer studying dependent upon the diminished blunders logistic regression (RELR) procedure and gives easy examples of RELR computations in toy difficulties that may be accessed in spreadsheet workbooks via a significant other web site

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Symmetry: A Mathematical Exploration by Kristopher Tapp PDF

By Kristopher Tapp

ISBN-10: 1461402980

ISBN-13: 9781461402985

This textbook is ideal for a math path for non-math majors, with the aim of encouraging powerful analytical considering and exposing scholars to dependent mathematical ideas.  It contains many subject matters in most cases present in sampler classes, like Platonic solids, Euler’s formulation, irrational numbers, countable units, variations, and an evidence of the Pythagorean Theorem.  All of those themes serve a unmarried compelling aim: realizing the mathematical styles underlying the symmetry that we discover within the actual global round us.

The exposition is enticing, specified and rigorous.  The theorems are visually inspired with intuitive proofs applicable for the meant audience.  scholars from all majors will benefit from the many attractive themes herein, and may come to raised savour the robust cumulative nature of arithmetic as those themes are woven jointly right into a unmarried interesting tale in regards to the ways that items may be symmetric.

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New PDF release: Das BUCH der Beweise

By Martin Aigner, Günter M. Ziegler, Karl H. Hofmann

ISBN-10: 3642022588

ISBN-13: 9783642022586

ISBN-10: 3642022596

ISBN-13: 9783642022593

Diese deutlich erweiterte dritte deutsche Auflage von "Das BUCH der Beweise" enthält fünf neue Kapitel, in denen es um Klassiker geht wie den "Fundamentalsatz der Algebra", um kombinatorisch-geometrische Zerlegungsprobleme, aber auch um Beweise aus letzter Zeit, etwa für die "Kneser-Vermutung" in der Graphentheorie.

Die Neuausgabe wartet auch mit weiteren Verbesserungen und Überraschungen auf - darunter ein neuer Beweis für "Hilberts drittes Problem".

Aus den Rezensionen der bisherigen Ausgaben:

"Ein prächtiges, äußerst sorgfältig und liebevoll gestaltetes Buch! Erdös hatte die Idee DES BUCHES, in dem Gott die perfekten Beweise mathematischer Sätze eingeschrieben hat. Das hier gedruckte Buch will eine "very modest approximation" an dieses BUCH sein.... Das Buch von Aigner und Ziegler ist gelungen ..." Mathematische Semesterberichte, November 1999

"Unermüdlich reiste Paul Erdös durch die Welt und stellte neue Theoreme auf. Jetzt haben zwei seiner Kollegen sein schönstes Werk vollendet: Das BUCH der Beweise - ein Feuerwerk mathematischer Geistesblitze. ......" Die Weltwoche 18. April 2002

"... Martin Aigner ... und Günter Ziegler referieren sympathisch einige dieser gottgefälligen Geistesblitze. ... Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch über das BUCH. Um sie genießen zu können, lohnt es sich, das bißchen Mathe nachzuholen, das wir vergessen haben oder das uns von der Schule vorenthalten wurde." Die Zeit, 13.August 1998

...Hier ist es additionally, das BUCH der Beweise in der wunderbaren model von Martin Aigner und Günter Ziegler ....Wer (wie ich) bislang vergeblich versucht hat, einen Blick ins BUCH zu werfen, wird begierig in Aigners und Zieglers BUCH der Beweise schmökern. ... www.mathematik.de, Mai 2002

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