The Callias Index Formula Revisited

The Callias Index Formula Revisited PDF

Author: Fritz Gesztesy

Publisher: Springer

Published: 2016-06-28

Total Pages: 192

ISBN-13: 3319299778

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These lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970’s, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hörmander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index.

Networks, Crowds, and Markets

Networks, Crowds, and Markets PDF

Author: David Easley

Publisher: Cambridge University Press

Published: 2010-07-19

Total Pages: 745

ISBN-13: 1139490303

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Are all film stars linked to Kevin Bacon? Why do the stock markets rise and fall sharply on the strength of a vague rumour? How does gossip spread so quickly? Are we all related through six degrees of separation? There is a growing awareness of the complex networks that pervade modern society. We see them in the rapid growth of the internet, the ease of global communication, the swift spread of news and information, and in the way epidemics and financial crises develop with startling speed and intensity. This introductory book on the new science of networks takes an interdisciplinary approach, using economics, sociology, computing, information science and applied mathematics to address fundamental questions about the links that connect us, and the ways that our decisions can have consequences for others.

Progress in Physics, vol. 4/2016

Progress in Physics, vol. 4/2016 PDF

Author: Dmitri Rabounski

Publisher: Infinite Study

Published:

Total Pages: 72

ISBN-13:

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The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics

Capital in the Twenty-First Century

Capital in the Twenty-First Century PDF

Author: Thomas Piketty

Publisher: Harvard University Press

Published: 2017-08-14

Total Pages: 817

ISBN-13: 0674979850

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What are the grand dynamics that drive the accumulation and distribution of capital? Questions about the long-term evolution of inequality, the concentration of wealth, and the prospects for economic growth lie at the heart of political economy. But satisfactory answers have been hard to find for lack of adequate data and clear guiding theories. In this work the author analyzes a unique collection of data from twenty countries, ranging as far back as the eighteenth century, to uncover key economic and social patterns. His findings transform debate and set the agenda for the next generation of thought about wealth and inequality. He shows that modern economic growth and the diffusion of knowledge have allowed us to avoid inequalities on the apocalyptic scale predicted by Karl Marx. But we have not modified the deep structures of capital and inequality as much as we thought in the optimistic decades following World War II. The main driver of inequality--the tendency of returns on capital to exceed the rate of economic growth--today threatens to generate extreme inequalities that stir discontent and undermine democratic values if political action is not taken. But economic trends are not acts of God. Political action has curbed dangerous inequalities in the past, the author says, and may do so again. This original work reorients our understanding of economic history and confronts us with sobering lessons for today.

Novikov Conjectures, Index Theorems, and Rigidity: Volume 1

Novikov Conjectures, Index Theorems, and Rigidity: Volume 1 PDF

Author: Steven C. Ferry

Publisher: Cambridge University Press

Published: 1995-11-23

Total Pages: 386

ISBN-13: 0521497965

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These volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'.

Narrative Discourse

Narrative Discourse PDF

Author: Gérard Genette

Publisher: Cornell University Press

Published: 1980

Total Pages: 292

ISBN-13: 9780801492594

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Genette uses Proust's Remembrance of Things Past as a work to identify and name the basic constituents and techniques of narrative. Genette illustrates the examples by referring to other literary works. His systemic theory of narrative deals with the structure of fiction, including fictional devices that go unnoticed and whose implications fulfill the Western narrative tradition.

Beyond Infinity

Beyond Infinity PDF

Author: Eugenia Cheng

Publisher: Profile Books

Published: 2017-03-09

Total Pages: 204

ISBN-13: 1782830812

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SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.

Class

Class PDF

Author: Paul Fussell

Publisher: Simon and Schuster

Published: 1992

Total Pages: 212

ISBN-13: 0671792253

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This book describes the living-room artifacts, clothing styles, and intellectual proclivities of American classes from top to bottom.