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Street-Fighting Mathematics

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ISBN: 9780262265591 9780262514293 Year: Pages: 152 Language: English
Publisher: The MIT Press
Subject: Science (General)
Added to DOAB on : 2019-01-17 11:41:37
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An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation.In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Detection and characterization of inclusions in impedance tomography

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ISBN: 9783866446359 Year: Pages: VIII, 135 p. DOI: 10.5445/KSP/1000021838 Language: ENGLISH
Publisher: KIT Scientific Publishing
Subject: Computer Science
Added to DOAB on : 2019-07-30 20:01:57
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The topic of this work are two further developments of the Factorization method for electrical impedance tomography.We present a modification of this method that is capable of detecting mixed inclusions, i.e. both inclusions with a higher as well as inclusions with a lower conductivity than the background medium. In addition, we derive a new method to compute the conductivity inside inclusions after they have been localized.

Factorization methods for photonics and rough surfaces

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ISBN: 9783866442566 Year: Pages: VI, 156 p. DOI: 10.5445/KSP/1000008735 Language: ENGLISH
Publisher: KIT Scientific Publishing
Subject: Mathematics
Added to DOAB on : 2019-07-30 20:02:01
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This thesis investigates non-destructive testing problems for rough and periodic surfaces, where the task is to determine such structures from scattered waves. Such problems are non-linear and ill-posed. We are interested in the analysis of the Factorization method applied to this class of inverse scattering problems. This method does not attempt to solve a non-linear operator equation for the unknown object but computes a binary criterion characterizing points inside and outside the structure.

The factorization method for inverse scattering from periodic inhomogeneous media

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ISBN: 9783866445505 Year: Pages: X, 152 p. DOI: 10.5445/KSP/1000019400 Language: ENGLISH
Publisher: KIT Scientific Publishing
Subject: Mathematics
Added to DOAB on : 2019-07-30 20:01:59
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This book addresses the identification of the shape of penetrable periodic media by means of scattered time-harmonic waves. Mathematically, this is about the determination of the support of a function which occurs in the governing equations. Our theoretical analysis shows that this problem can be strictly solved for acoustic as well as for electromagnetic radiation by the so-called Factorization Method. We apply this method to reconstruct a couple of media from numerically simulated field data.

Forward and inverse problems of electrocardiography : clinical investigations

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Book Series: Karlsruhe transactions on biomedical engineering / Ed.: Universität Karlsruhe (TH) / Institute of Biomedical Engineering ISSN: 18645933 ISBN: 9783866442191 Year: Volume: 4 Pages: XVII, 196 p. DOI: 10.5445/KSP/1000007590 Language: ENGLISH
Publisher: KIT Scientific Publishing
Subject: Technology (General)
Added to DOAB on : 2019-07-30 20:02:00
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The non-invasive reconstruction of cardiac activity can significantly improve the quality of cardiac diagnostics. Two major approaches are considered. The model-based method consists in the optimization of an electrophysiological cardiac model until the measured and simulated ECGs are similar. The inverse problem of electrocardiography is solved to compute the cardiac sources distributions from body surface potential maps. The results and their interpretation are shown for several patients.

Network Structures of Cargo Airlines - An Empirical and a Modelling Approach

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ISBN: 9783866447967 Year: Pages: XX, 158 p. DOI: 10.5445/KSP/1000025525 Language: ENGLISH
Publisher: KIT Scientific Publishing
Subject: Business and Management
Added to DOAB on : 2019-07-30 20:02:02
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The development of efficient air freight networks is an upcoming challenge. The present book approaches this problem for cargo airlines by characterising and classifying their network structures and by developing a model for an airline's strategic network design. The book provides results which are of value for airline professionals (network efficiency analysis), policy makers (policy impact assessment) and researchers (cargo airline network design model).

Global Carbon Pricing

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ISBN: 9780262340397 9780262036269 Year: Pages: 268 Language: English
Publisher: The MIT Press
Subject: Environmental Sciences
Added to DOAB on : 2019-01-17 11:41:31
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Why the traditional “pledge and review” climate agreements have failed, and how carbon pricing, based on trust and reciprocity, could succeed.After twenty-five years of failure, climate negotiations continue to use a “pledge and review” approach: countries pledge (almost anything), subject to (unenforced) review. This approach ignores everything we know about human cooperation. In this book, leading economists describe an alternate model for climate agreements, drawing on the work of the late Nobel laureate Elinor Ostrom and others. They show that a “common commitment” scheme is more effective than an “individual commitment” scheme; the latter depends on altruism while the former involves reciprocity (“we will if you will”).The contributors propose that global carbon pricing is the best candidate for a reciprocal common commitment in climate negotiations. Each country would commit to placing charges on carbon emissions sufficient to match an agreed global price formula. The contributors show that carbon pricing would facilitate negotiations and enforcement, improve efficiency and flexibility, and make other climate policies more effective. Additionally, they analyze the failings of the 2015 Paris climate conference.ContributorsRichard N. Cooper, Peter Cramton, Ottmar Edenhofer, Christian Gollier, Éloi Laurent, David JC MacKay, William Nordhaus, Axel Ockenfels, Joseph E. Stiglitz, Steven Stoft, Jean Tirole, Martin L. Weitzman

Solving the inverse problem of electrocardiography in a realistic environment

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Book Series: Karlsruhe transactions on biomedical engineering / Ed.: Universität Karlsruhe (TH) / Institute of Biomedical Engineering ISSN: 18645933 ISBN: 9783866444867 Year: Volume: 9 Pages: X, 116 p. DOI: 10.5445/KSP/1000016052 Language: ENGLISH
Publisher: KIT Scientific Publishing
Subject: Technology (General)
Added to DOAB on : 2019-07-30 20:01:59
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Heart disease is a leading cause of death worldwide. Straightforward information about the cardiac electrophysiology can help to improve the quality of diagnosis of heart diseases. The inverse problem of electrocardiography and the intracardiac catheter measurement are two ways to get access to the electrophysiology in the heart. In this thesis six research topics related to these two techniques are included.

Lie and non-Lie Symmetries: Theory and Applications for Solving Nonlinear Models

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ISBN: 9783038425267 9783038425274 Year: Pages: XII, 414 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics
Added to DOAB on : 2017-10-25 13:19:05
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Since the end of the 19th century when the prominent Norwegian mathematician Sophus Lie created the theory of Lie algebras and Lie groups and developed the method of their applications for solving differential equations, his theory and method have continuously been the research focus of many well-known mathematicians and physicists. This book is devoted to recent development in Lie theory and its applications for solving physically and biologically motivated equations and models. The book contains the articles published in two Special Issue of the journal Symmetry, which are devoted to analysis and classification of Lie algebras, which are invariance algebras of real-word models; Lie and conditional symmetry classification problems of nonlinear PDEs; the application of symmetry-based methods for finding new exact solutions of nonlinear PDEs (especially reaction-diffusion equations) arising in applications; the application of the Lie method for solving nonlinear initial and boundary-value problems (especially those for modelling processes with diffusion, heat transfer, and chemotaxis).

Topological Groups: Yesterday, Today, Tomorrow

ISBN: 9783038422686 9783038422693 Year: Pages: VIII, 220 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics
Added to DOAB on : 2016-12-05 09:30:44
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In 1900, David Hilbert asked whether each locally euclidean topological group admits a Lie group structure. This was the fifth of his famous 23 questions which foreshadowed much of the mathematical creativity of the twentieth century. It required half a century of effort by several generations of eminent mathematicians until it was settled in the affirmative. These efforts resulted over time in the Peter-Weyl Theorem, the Pontryagin-van Kampen Duality Theorem for locally compact abelian groups, and finally the solution of Hilbert 5 and the structure theory of locally compact groups, through the combined work of Andrew Gleason, Kenkichi Iwasawa, Deane Montgomery, and Leon Zippin. For a presentation of Hilbert 5 see the 2014 book “Hilbert’s Fifth Problem and Related Topics” by the winner of a 2006 Fields Medal and 2014 Breakthrough Prize in Mathematics, Terence Tao.It is not possible to describe briefly the richness of the topological group theory and the many directions taken since Hilbert 5. The 900 page reference book in 2013 “The Structure of Compact Groups” by Karl H. Hofmann and Sidney A. Morris, deals with one aspect of compact group theory. There are several books on profinite groups including those written by John S. Wilson (1998) and by Luis Ribes and ‎Pavel Zalesskii (2012). The 2007 book “The Lie Theory of Connected Pro-Lie Groups” by Karl Hofmann and Sidney A. Morris, demonstrates how powerful Lie Theory is in exposing the structure of infinite-dimensional Lie groups.The study of free topological groups initiated by A.A. Markov, M.I. Graev and S. Kakutani, has resulted in a wealth of interesting results, in particular those of A.V. Arkhangelʹskiĭ and many of his former students who developed this topic and its relations with topology. The book “Topological Groups and Related Structures” by Alexander Arkhangelʹskii and Mikhail Tkachenko has a diverse content including much material on free topological groups. Compactness conditions in topological groups, especially pseudocompactness as exemplified in the many papers of W.W. Comfort, has been another direction which has proved very fruitful to the present day.

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