Luigi Monge's Books

Optimal Transportation and Applications

Lectures Given at the C.I.M.E. Summer School Held in Martina Franca, Italy, September 2-8, 2001

By: Luigi Ambrosio

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Optimal Transportation and Applications

Lectures Given at the C.I.M.E. Summer School Held in Martina Franca, Italy, September 2-8, 2001

By: Luigi Ambrosio

Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.

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Page Count

184

Publisher

Springer Science & Business Media

Published Date

ISBN 10

354040192X

ISBN 13

9783540401926

Calculus of Variations and Nonlinear Partial Differential Equations

Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, June 27 - July 2, 2005

By: Luigi Ambrosio,E. Mascolo

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Calculus of Variations and Nonlinear Partial Differential Equations

Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, June 27 - July 2, 2005

By: Luigi Ambrosio,E. Mascolo

With a historical overview by Elvira Mascolo

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Page Count

213

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Springer Science & Business Media

Published Date

ISBN 10

3540759131

ISBN 13

9783540759133

Modelling and Optimisation of Flows on Networks

Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle

By: Luigi Ambrosio,Alberto Bressan,Dirk Helbing,Axel Klar,Enrique Zuazua

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Modelling and Optimisation of Flows on Networks

Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle

By: Luigi Ambrosio,Alberto Bressan,Dirk Helbing,Axel Klar,Enrique Zuazua

In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. applied mathematicians, engineers, physicists, economists. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others. This book presents an extensive set of notes by world leaders on the main mathematical techniques used to address such problems, together with investigations into specific applications. The main focus is on partial differential equations in networks, but ordinary differential equations and optimal transport are also included. Moreover, the modeling is completed by analysis, numerics, control and optimization of flows in networks. The book will be a valuable resource for every researcher or student interested in the subject.

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Page Count

507

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Springer

Published Date

ISBN 10

3642321607

ISBN 13

9783642321603

Transport Equations and Multi-D Hyperbolic Conservation Laws

By: Luigi Ambrosio,Gianluca Crippa,Camillo De Lellis,Felix Otto,Michael Westdickenberg

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Transport Equations and Multi-D Hyperbolic Conservation Laws

By: Luigi Ambrosio,Gianluca Crippa,Camillo De Lellis,Felix Otto,Michael Westdickenberg

The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements. This volume provides an up-to-date overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. The captivating volume contains surveys of recent deep results and provides an overview of further developments and related open problems. Readers should have basic knowledge of PDE and measure theory.

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141

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Springer Science & Business Media

Published Date

ISBN 10

3540767819

ISBN 13

9783540767817

Gradient Flows

In Metric Spaces and in the Space of Probability Measures

By: Luigi Ambrosio,Nicola Gigli,Giuseppe Savare

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Gradient Flows

In Metric Spaces and in the Space of Probability Measures

By: Luigi Ambrosio,Nicola Gigli,Giuseppe Savare

The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.

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Page Count

333

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Springer Science & Business Media

Published Date

ISBN 10

376438722X

ISBN 13

9783764387228

Lectures on Optimal Transport

By: Luigi Ambrosio,Elia Brué,Daniele Semola

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Lectures on Optimal Transport

By: Luigi Ambrosio,Elia Brué,Daniele Semola

This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations.

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Page Count

250

Publisher

Springer Nature

Published Date

ISBN 10

3030721620

ISBN 13

9783030721626

KAM Stability and Celestial Mechanics

By: Alessandra Celletti,Luigi Chierchia

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KAM Stability and Celestial Mechanics

By: Alessandra Celletti,Luigi Chierchia

KAM theory is a powerful tool apt to prove perpetual stability in Hamiltonian systems, which are a perturbation of integrable ones. The smallness requirements for its applicability are well known to be extremely stringent. A long standing problem, in this context, is the application of KAM theory to ``physical systems'' for ``observable'' values of the perturbation parameters. The authors consider the Restricted, Circular, Planar, Three-Body Problem (RCP3BP), i.e., the problem of studying the planar motions of a small body subject to the gravitational attraction of two primary bodies revolving on circular Keplerian orbits (which are assumed not to be influenced by the small body). When the mass ratio of the two primary bodies is small, the RCP3BP is described by a nearly-integrable Hamiltonian system with two degrees of freedom; in a region of phase space corresponding to nearly elliptical motions with non-small eccentricities, the system is well described by Delaunay variables. The Sun-Jupiter observed motion is nearly circular and an asteroid of the Asteroidal belt may be assumed not to influence the Sun-Jupiter motion. The Jupiter-Sun mass ratio is slightly less than 1/1000. The authors consider the motion of the asteroid 12 Victoria taking into account only the Sun-Jupiter gravitational attraction regarding such a system as a prototype of a RCP3BP. for values of mass ratios up to 1/1000, they prove the existence of two-dimensional KAM tori on a fixed three-dimensional energy level corresponding to the observed energy of the Sun-Jupiter-Victoria system. Such tori trap the evolution of phase points ``close'' to the observed physical data of the Sun-Jupiter-Victoria system. As a consequence, in the RCP3BP description, the motion of Victoria is proven to be forever close to an elliptical motion. The proof is based on: 1) a new iso-energetic KAM theory; 2) an algorithm for computing iso-energetic, approximate Lindstedt series; 3) a computer-aided application of 1)+2) to the Sun-Jupiter-Victoria system. The paper is self-contained but does not include the ($\sim$ 12000 lines) computer programs, which may be obtained by sending an e-mail to one of the authors.

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Page Count

150

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821841696

ISBN 13

9780821841693

Public Transportation Quality of Service

Factors, Models, and Applications

By: Luigi Dell ́Olio,Angel Ibeas,Juan de Ona,Rocio de Ona

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Public Transportation Quality of Service

Factors, Models, and Applications

By: Luigi Dell ́Olio,Angel Ibeas,Juan de Ona,Rocio de Ona

Public Transportation Quality of Service: Factors, Models, and Applications is the first book to help researchers better understand the contributing factors that can improve public transportation perception among users. The book compiles in one place metrics currently dispersed in journal articles, government publications and book chapters. It critically analyzes currently available modeling methodologies such as the Ordered Logit/Probit model and Models of Structural Equations, highlighting their advantages and disadvantages. The book addresses models of desired quality, including the views of users and non-users, discussing the gap between desired and perceived quality. The book also examines data mining approaches such as decision trees and neural networks, showing how to involve the public in the decision-making process to create policies that encourage public transport demand. Measuring passenger's views on public transportation is of critical concern to promote wider transit use in cities around the world. - Includes insights from both theoretical and practical points of view for both researchers and practitioners - Features case studies in each chapter that apply models discussed - Helps readers develop and design their own studies for measuring quality of service - Shows how to include perceived quality in contracts - Provides access to the survey formulas and data to better enable implementation of models

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Page Count

244

Publisher

Elsevier

Published Date

ISBN 10

0081022794

ISBN 13

9780081022795

Lectures on Elliptic Partial Differential Equations

By: Luigi Ambrosio,Alessandro Carlotto,Annalisa Massaccesi

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Lectures on Elliptic Partial Differential Equations

By: Luigi Ambrosio,Alessandro Carlotto,Annalisa Massaccesi

The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.

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234

Publisher

Springer

Published Date

ISBN 10

8876426515

ISBN 13

9788876426513

Geometric And Algebraic Topological Methods In Quantum Mechanics

By: Luigi Mangiarotti,Gennadi A Sardanashvily,Giovanni Giachetta

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Geometric And Algebraic Topological Methods In Quantum Mechanics

By: Luigi Mangiarotti,Gennadi A Sardanashvily,Giovanni Giachetta

In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.

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Page Count

715

Publisher

World Scientific

Published Date

ISBN 10

9814481149

ISBN 13

9789814481144

Privatization South American Style

By: Luigi Manzetti

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Privatization South American Style

By: Luigi Manzetti

It also examines the apparently 'unconventional' methods at times used by the governments of Argentina, Brazil, and Peru to achieve privatization."--Jacket.

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402

Publisher

Oxford University Press, USA

Published Date

ISBN 10

0198294662

ISBN 13

9780198294665

Mathematical Aspects of Evolving Interfaces

Lectures given at the C.I.M.-C.I.M.E. joint Euro-Summer School held in Madeira Funchal, Portugal, July 3-9, 2000

By: Luigi Ambrosio,Klaus Deckelnick,Gerhard Dziuk,Masayasu Mimura,Vsvolod Solonnikov,Halil Mete Soner

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Mathematical Aspects of Evolving Interfaces

Lectures given at the C.I.M.-C.I.M.E. joint Euro-Summer School held in Madeira Funchal, Portugal, July 3-9, 2000

By: Luigi Ambrosio,Klaus Deckelnick,Gerhard Dziuk,Masayasu Mimura,Vsvolod Solonnikov,Halil Mete Soner

Interfaces are geometrical objects modelling free or moving boundaries and arise in a wide range of phase change problems in physical and biological sciences, particularly in material technology and in dynamics of patterns. Especially in the end of last century, the study of evolving interfaces in a number of applied fields becomes increasingly important, so that the possibility of describing their dynamics through suitable mathematical models became one of the most challenging and interdisciplinary problems in applied mathematics. The 2000 Madeira school reported on mathematical advances in some theoretical, modelling and numerical issues concerned with dynamics of interfaces and free boundaries. Specifically, the five courses dealt with an assessment of recent results on the optimal transportation problem, the numerical approximation of moving fronts evolving by mean curvature, the dynamics of patterns and interfaces in some reaction-diffusion systems with chemical-biological applications, evolutionary free boundary problems of parabolic type or for Navier-Stokes equations, and a variational approach to evolution problems for the Ginzburg-Landau functional.

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249

Publisher

Springer

Published Date

ISBN 10

3540391894

ISBN 13

9783540391890

Rheology

Volume 1: Principles

By: Giovanni Astarita,Giuseppe Marrucci,Luigi Nicolais

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Rheology

Volume 1: Principles

By: Giovanni Astarita,Giuseppe Marrucci,Luigi Nicolais

At the VIIth International Congress on Rheology, which was held in Goteborg in 1976, Proceedings were for the first time printed in advance and distributed to all participants at the time of the Congress. Although of course we Italians would be foolish to even try to emulate our Swedish friends as far as efficiency of organization is concerned, we decided at the very beginning that, as far as the Proceedings were concerned, the VIIIth International Congress on Rheology in Naples would follow the standards of time liness set by the Swedish Society of Rheology. This book is the result we have obtained. We wish to acknowledge the cooperation of Plenum Press in producing it within the very tight time schedule available. Every four years, the International Congress on Rheology represents the focal point where all rheologists meet, and the state of the art is brought up to date for everybody interested; the Proceedings represent the written record of these milestones of scientific progress in rheology. We have tried to make use of the traditions of having invited lectures, and of leaving to the organizing committee the freedom to choose the lecturers as they see fit, in order to collect a group of invited lectures which gives as broad as possible a landscape of the state of the art in every relevant area of rheology. The seventeen invited lectures are collected in the first volume of the proceedings.

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Page Count

420

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1468437402

ISBN 13

9781468437409

Wasn’t That a Mighty Day

African American Blues and Gospel Songs on Disaster

By: Luigi Monge

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Wasn’t That a Mighty Day

African American Blues and Gospel Songs on Disaster

By: Luigi Monge

Wasn’t That a Mighty Day: African American Blues and Gospel Songs on Disaster takes a comprehensive look at sacred and secular disaster songs, shining a spotlight on their historical and cultural importance. Featuring newly transcribed lyrics, the book offers sustained attention to how both Black and white communities responded to many of the tragic events that occurred before the mid-1950s. Through detailed textual analysis, Luigi Monge explores songs on natural disasters (hurricanes, floods, tornadoes, and earthquakes); accidental disasters (sinkings, fires, train wrecks, explosions, and air disasters); and infestations, epidemics, and diseases (the boll weevil, the jake leg, and influenza). Analyzed songs cover some of the most well-known disasters of the time period from the sinking of the Titanic and the 1930 drought to the Hindenburg accident, and more. Thirty previously unreleased African American disaster songs appear in this volume for the first time, revealing their pertinence to the relevant disasters. By comparing the song lyrics to critical moments in history, Monge is able to explore how deeply and directly these catastrophes affected Black communities; how African Americans in general, and blues and gospel singers in particular, faced and reacted to disaster; whether these collective tragedies prompted different reactions among white people and, if so, why; and more broadly, how the role of memory in recounting and commenting on historical and cultural facts shaped African American society from 1879 to 1955.

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Page Count

388

Publisher

Univ. Press of Mississippi

Published Date

ISBN 10

1496841794

ISBN 13

9781496841797

Polymer Processing and Properties

By: Gianni Astarita,Luigi Nicolais

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Polymer Processing and Properties

By: Gianni Astarita,Luigi Nicolais

During the First Conference of European Rheologists, which was held in Graz, Austria, in April 1982, the Provisional Committee of European Delegates to the Inter national Committee on Rheology held a meeting to discuss future European activities in the general area of rheol ogy. It was agreed, among other things, that the organ ization of meetings in Europe on specific topics related to rheology would be done in cooperation, so as to avoid conflicts of dates and/or subject areas. Any such meeting, if approved by the Provisional Committee, would be named a European Meeting; the European Societies of Rheology would help the organizers with distribution 6f circulars, membership lists, and any required technical assistance. One of the very first meetings organized within this procedural scheme has been the European Meeting on Polymer Processing and Properties, which was held in Capri, Italy, on June 13-16, 1983. This book constitutes the Proceedings of that meeting.

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Page Count

440

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Springer Science & Business Media

Published Date

ISBN 10

1461327814

ISBN 13

9781461327813

Book's by Luigi Monge

Optimal Transportation and Applications

Optimal Transportation and Applications

Calculus of Variations and Nonlinear Partial Differential Equations

Calculus of Variations and Nonlinear Partial Differential Equations

Modelling and Optimisation of Flows on Networks

Modelling and Optimisation of Flows on Networks

Transport Equations and Multi-D Hyperbolic Conservation Laws

Transport Equations and Multi-D Hyperbolic Conservation Laws

Gradient Flows

Gradient Flows

Lectures on Optimal Transport

Lectures on Optimal Transport

KAM Stability and Celestial Mechanics

KAM Stability and Celestial Mechanics

Public Transportation Quality of Service

Public Transportation Quality of Service

Lectures on Elliptic Partial Differential Equations

Lectures on Elliptic Partial Differential Equations

Geometric And Algebraic Topological Methods In Quantum Mechanics

Geometric And Algebraic Topological Methods In Quantum Mechanics

Privatization South American Style

Privatization South American Style

Mathematical Aspects of Evolving Interfaces

Mathematical Aspects of Evolving Interfaces

Rheology

Rheology

Wasn’t That a Mighty Day

Wasn’t That a Mighty Day

Polymer Processing and Properties

Polymer Processing and Properties

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