Mean Curvature Flow and Isoperimetric Inequalities

Author: Manuel Ritoré,Carlo Sinestrari

Publisher: Springer Science & Business Media

ISBN: 3034602138

Category: Mathematics

Page: 114

View: 6602

Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
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Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations

Author: Giovanni Bellettini

Publisher: Springer

ISBN: 8876424296

Category: Mathematics

Page: 350

View: 4015

The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.
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Global Riemannian Geometry

Curvature and Topology

Author: Steen Markvorsen,Maung Min-Oo

Publisher: Springer Science & Business Media

ISBN: 9783764321703

Category: Mathematics

Page: 87

View: 7810

This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers.
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Moonwatch Only

60 Years of OMEGA Speedmaster

Author: Grégoire Rossier,Anthony Marquie

Publisher: Watchprint.com Sarl

ISBN: 9782940506170

Category:

Page: 566

View: 1759

-A new edition of this definitive book, marking the 60th anniversary of the Speedmaster -Includes new features and additional historical information "The OMEGA Speedmaster Professional - the Moonwatch - has done things that no other timepiece has done and it has been worn in places that only a few human beings have been." - Captain Eugene Cernan, last man on the moon "It is an indescribable reference work and a true must-have for every Speedmaster collector." - Forbes There are very few timepieces in the world that deserve a definitive and comprehensive book. The OMEGA Speedmaster Professional Moonwatch is one of them. Initially designed for automobile racing teams and engineers, the Omega Speedmaster embarked on a very different trajectory when NASA chose it to accompany astronauts heading for the Moon in 1965. Its involvement in the space adventure has propelled the Moonwatch to the top of the list of celebrated timepieces. After years of research and observation, the authors present a complete panorama of the Moonwatch in a systematic work that is both technical and attractive, making it the unparalleled reference book for this legendary watch. This new edition, marking the 60th anniversary of the Speedmaster, has been enriched with numerous new features and additional historical information. Contents: Foreword by Raynald Aeschlimann, President and CEO of OMEGA; Foreword by Captain Eugene Cernan, Commander of Apollo 17; Why a Speedmaster Moonwatch guide?; Part 1 - Speedmaster History; 1, Major Dates; 2, Speedmaster and NASA 25; Part 2 - Main Components and Accessories; 1, An Original Approach; 2, The Caliber; 3, The Caseband; 4, The Dial; 5, The Bezel; 6, The Hands; 7, The Caseback; 8, The Crown; 9, The Pushers; 10, The Glass; 11, The Bracelet; 12, The Presentation Box; 13, The Documents; Part 3 - The Models; 1, Introduction; 2, Standard Production; 3, Special and Limited Series; 4, Personalized Models and Special Projects; 5, The Alaska Project; Part 4 - 60 Years of Innovation; Part 5 - How to Start Collecting Speedmasters; 1, Budget; 2, Choosing a Model; 3, Sales Channels; Part 6 - Appendices; 1, Model Codes; 2, Tables & Bibliography; 3, Contributions; 4, Identification Aid
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Geometric Inequalities

Author: Yurii D. Burago,Viktor A. Zalgaller

Publisher: Springer Science & Business Media

ISBN: 3662074419

Category: Mathematics

Page: 334

View: 4260

A 1988 classic, covering Two-dimensional Surfaces; Domains on the Plane and on Surfaces; Brunn-Minkowski Inequality and Classical Isoperimetric Inequality; Isoperimetric Inequalities for Various Definitions of Area; and Inequalities Involving Mean Curvature.
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Social Network Data Analytics

Author: Charu C. Aggarwal

Publisher: Springer Science & Business Media

ISBN: 1441984623

Category: Computers

Page: 502

View: 6176

Social network analysis applications have experienced tremendous advances within the last few years due in part to increasing trends towards users interacting with each other on the internet. Social networks are organized as graphs, and the data on social networks takes on the form of massive streams, which are mined for a variety of purposes. Social Network Data Analytics covers an important niche in the social network analytics field. This edited volume, contributed by prominent researchers in this field, presents a wide selection of topics on social network data mining such as Structural Properties of Social Networks, Algorithms for Structural Discovery of Social Networks and Content Analysis in Social Networks. This book is also unique in focussing on the data analytical aspects of social networks in the internet scenario, rather than the traditional sociology-driven emphasis prevalent in the existing books, which do not focus on the unique data-intensive characteristics of online social networks. Emphasis is placed on simplifying the content so that students and practitioners benefit from this book. This book targets advanced level students and researchers concentrating on computer science as a secondary text or reference book. Data mining, database, information security, electronic commerce and machine learning professionals will find this book a valuable asset, as well as primary associations such as ACM, IEEE and Management Science.
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Fourier-Mukai Transforms in Algebraic Geometry

Author: Daniel Huybrechts

Publisher: Oxford University Press on Demand

ISBN: 0199296863

Category: Mathematics

Page: 307

View: 1418

This work is based on a course given at the Institut de Mathematiques de Jussieu, on the derived category of coherent sheaves on a smooth projective variety. It is aimed at students with a basic knowledge of algebraic geometry and contains full proofs and exercises that aid the reader.
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European Congress of Mathematics, Barcelona, July 10-14, 2000

Vol. 1

Author: Carles Casacuberta

Publisher: Springer Science & Business Media

ISBN: 9783764364175

Category: Mathematics

Page: 582

View: 4157

The Third European Congress of Mathematics (3ecm) took place from July 10th to July 14th, 2000 in Barcelona. It was organised by the Societat Catalana de Matematiques (Catalan Mathematical Society), under the auspices of the Euro­ pean Mathematical Society (EMS). As foreseen by the EMS and the International Mathematical Union, this Congress was a major event in World Mathematical Year 2000. In addition to reviewing outstanding research achievements, important aspects of the life of European mathematics were discussed. Mathematics is undergoing a period of rapid changes. Effective computation and applications in science and technology go ever more hand in hand with con­ ceptual developments. It was one of the aims of 3ecm to reflect this mutual enrich­ ment, while steering present and future trends of mathematical sciences. In fact, the motto of the Congress, Shaping the 21st Century, was meant to capture these views. Nearly 1400 people from 87 countries gathered together in the Palau de Con­ gressos of Barcelona in order to take part in the activities of the 3ecm scientific programme: Nine plenary lectures, thirty invited lectures in parallel sessions, lec­ tures given by EMS prize winners, ten mini-symposia on special topics, seven round tables, poster sessions, presentations of mathematical software and video exhibitions. Twenty events were satellites of 3ecm in various countries.
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Survival and Event History Analysis

A Process Point of View

Author: Odd Aalen,Ornulf Borgan,Hakon Gjessing

Publisher: Springer Science & Business Media

ISBN: 038768560X

Category: Mathematics

Page: 540

View: 2023

The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data. The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly from medicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. The book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics.
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Handbook of Tilting Theory

Author: Dieter Happel,Henning Krause

Publisher: Cambridge University Press

ISBN: 9780521680455

Category: Mathematics

Page: 472

View: 601

A handbook of key articles providing both an introduction and reference for newcomers and experts alike.
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The Chemistry of the Actinide and Transactinide Elements (Set Vol.1-6)

Author: Lester R. Morss,Norman Edelstein,Jean Fuger

Publisher: Springer Science & Business Media

ISBN: 9789400702110

Category: Science

Page: 4503

View: 3193

The fourth edition of "The Chemistry of the Actinide and Transactinide Elements" comprises all chapters in volumes 1 through 5 of the third edition (published in 2006) plus a new volume 6. To remain consistent with the plan of the first edition, “ ... to provide a comprehensive and uniform treatment of the chemistry of the actinide [and transactinide] elements for both the nuclear technologist and the inorganic and physical chemist,” and to be consistent with the maturity of the field, the fourth edition is organized in three parts. The first group of chapters follows the format of the first and second editions with chapters on individual elements or groups of elements that describe and interpret their chemical properties. A chapter on the chemical properties of the transactinide elements follows. The second group, chapters 15-26, summarizes and correlates physical and chemical properties that are in general unique to the actinide elements, because most of these elements contain partially-filled shells of 5f electrons whether present as isolated atoms or ions, as metals, as compounds, or as ions in solution. The third group, chapters 27-39, focuses on specialized topics that encompass contemporary fields related to actinides in the environment, in the human body, and in storage or wastes. Two appendices at the end of volume 5 tabulate important nuclear properties of all actinide and transactinide isotopes. Volume 6 (Chapters 32 through 39) consists of new chapters that focus on actinide species in the environment, actinide waste forms, nuclear fuels, analytical chemistry of plutonium, actinide chalcogenide and hydrothermal synthesis of actinide compounds. The subject and author indices and list of contributors encompass all six volumes.
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The Curve Shortening Problem

Author: Kai-Seng Chou,Xi-Ping Zhu

Publisher: CRC Press

ISBN: 1420035703

Category: Mathematics

Page: 272

View: 8897

Although research in curve shortening flow has been very active for nearly 20 years, the results of those efforts have remained scattered throughout the literature. For the first time, The Curve Shortening Problem collects and illuminates those results in a comprehensive, rigorous, and self-contained account of the fundamental results. The authors present a complete treatment of the Gage-Hamilton theorem, a clear, detailed exposition of Grayson's convexity theorem, a systematic discussion of invariant solutions, applications to the existence of simple closed geodesics on a surface, and a new, almost convexity theorem for the generalized curve shortening problem. Many questions regarding curve shortening remain outstanding. With its careful exposition and complete guide to the literature, The Curve Shortening Problem provides not only an outstanding starting point for graduate students and new investigations, but a superb reference that presents intriguing new results for those already active in the field.
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A Short Course on Operator Semigroups

Author: Klaus-Jochen Engel,Rainer Nagel

Publisher: Springer Science & Business Media

ISBN: 0387313419

Category: Mathematics

Page: 247

View: 7516

ThetheoryofstronglycontinuoussemigroupsoflinearoperatorsonBanach spaces, operator semigroups for short, has become an indispensable tool in a great number of areas of modern mathematical analysis. In our Springer Graduate Text EN00] we presented this beautiful theory, together with many applications, and tried to show the progress made since the pub- cation in 1957 of the now classical monograph HP57] by E. Hille and R. Phillips. However, the wealth of results exhibited in our Graduate Text seems to have discouraged some of the potentially interested readers. With the present text we o?er a streamlined version that strictly sticks to the essentials. We have skipped certain parts, avoided the use of sophisticated arguments, and, occasionally, weakenedtheformulationofresultsandm- i?ed the proofs. However, to a large extent this book consists of excerpts taken from our Graduate Text, with some new material on positive se- groups added in Chapter VI. We hope that the present text will help students take their ?rst step into this interesting and lively research ?eld. On the other side, it should provide useful tools for the working mathematician. Acknowledgments This book is dedicated to our students. Without them we would not be able to do and to enjoy mathematics. Many of them read previous versions when it served as the text of our Seventh Internet Seminar 2003/04. Here Genni Fragnelli, Marc Preunkert and Mark C. Veraar were among the most active readers. Particular thanks go to Tanja Eisner, Vera Keicher, Agnes Radl for proposing considerable improvements in the ?nal versi
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Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids

A Collection of Reprints of 14 Seminal Papers

Author: John M. Ball,David Kinderlehrer,Paulo Podio-Guidugli,Marshall Slemrod

Publisher: Springer Science & Business Media

ISBN: 3642599389

Category: Science

Page: 474

View: 9723

A traditional way to honor distinguished scientists is to combine collections of papers solicited from friendly colleagues into dedicatory volumes. To honor our friend and colleague Mort Gurtin on the occasion of his sixty-fifth birthday, we followed a surer path to produce a work of intrinsic and lasting scientific value: We collected pa pers that we deemed seminal in the field of evolving phase interfaces in solids, a field to which Mort Gurtin himself has made fundamental contributions. Our failure for lack of space to include in this volume every paper of major significance is mitigated by the ma gisterial introduction prepared by Eliot Fried, which assesses the contributions of nu merous works. We hope that this collection will prove useful and stimulating to both researchers and students in this exciting field. August 1998 JohnM. Ball David Kinderlehrer Paulo Podio-Guidugli Marshall Slemrod Contents Introduction: Fifty Years of Research on Evolving Phase Interfaces By Eliot Fried. 0 •••••••••••••••••••••••••••••••••••••••••••••••• 0 ••••• 1 I. Papers on Materials Science Surface Tension as a Motivation for Sintering By C. Herring 33 Two-Dimensional Motion of Idealized Grain Boundaries By W. W. Mullins 0 ••••••••••• 0 ••••••••••••••••••• 70 Morphological. Stability of a Particle Growing by Diffusion or Heat Flow By w. w. Mullins and R. F. Sekerka 75 Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics By J. D. Eshelby 82 The Interactions of Composition and Stress in Crystalline Solids By F. e. Larche and 1. W. Cahn 120 II.
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Introduction to Geometric Probability

Author: Daniel A. Klain,Gian-Carlo Rota

Publisher: Cambridge University Press

ISBN: 9780521596541

Category: Mathematics

Page: 178

View: 5677

The basic ideas of the subject and the analogues with enumerative combinatorics are described and exploited.
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Implementing Microsoft Dynamics AX 2012 with Sure Step 2012

Author: Andrew Birch

Publisher: Packt Publishing Ltd

ISBN: 1849687056

Category: Computers

Page: 234

View: 7861

Implementing Microsoft Dynamics AX 2012 with Sure Step 2012 is a guide that will help you better understand the principles of Sure Step Methodology and enable you to utilize these in a practical and pragmatic way when implementing Microsoft Dynamics AX 2012.If you are a Dynamics AX consultant, developer, or in a customer resources or sales role that requires guidance and knowledge of the AX business solution space, or the delivery of an AX business solution that meets or exceeds the expectations of your organization, then this book is ideal for you. Basic experience of Dynamics AX and Sure Step is required.
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Discrete and Computational Geometry

Author: Satyan L. Devadoss,Joseph O'Rourke

Publisher: Princeton University Press

ISBN: 9781400838981

Category: Mathematics

Page: 280

View: 7583

Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only). To obtain access, please e-mail: [email protected]
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Bosch Automotive Electrics and Automotive Electronics

Systems and Components, Networking and Hybrid Drive

Author: Robert Bosch GmbH

Publisher: Springer Science & Business Media

ISBN: 3658017848

Category: Technology & Engineering

Page: 521

View: 8126

This is a complete reference guide to automotive electrics and electronics. This new edition of the definitive reference for automotive engineers, compiled by one of the world's largest automotive equipment suppliers, includes new and updated material. As in previous editions different topics are covered in a concise but descriptive way backed up by diagrams, graphs, photographs and tables enabling the reader to better comprehend the subject. This fifth edition revises the classical topics of the vehicle electrical systems such as system architecture, control, components and sensors. There is now greater detail on electronics and their application in the motor vehicle, including electrical energy management (EEM) and discusses the topic of inter system networking within the vehicle. It also includes a description of the concept of hybrid drive a topic that is particularly current due to its ability to reduce fuel consumption and therefore CO2 emissions.This book will benefit automotive engineers and design engineers, automotive technicians in training and mechanics and technicians in garages. It may also be of interest to teachers/ lecturers and students at vocational colleges, and enthusiasts.​
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Harmonic and Geometric Analysis

Author: Giovanna Citti,Loukas Grafakos,Carlos Pérez,Alessandro Sarti,Xiao Zhong

Publisher: Birkhäuser

ISBN: 3034804083

Category: Mathematics

Page: 170

View: 581

This book contains an expanded version of lectures delivered by the authors at the CRM in Spring of 2009. It contains four series of lectures. The first one is an application of harmonic analysis and the Heisenberg group to understand human vision. The second and third series of lectures cover some of the main topics on linear and multilinear harmonic analysis. The last one is a clear introduction to a deep result of De Giorgi, Moser and Nash on regularity of elliptic partial differential equations in divergence form.
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Geometric Curve Evolution and Image Processing

Author: Frédéric Cao

Publisher: Springer Science & Business Media

ISBN: 9783540004028

Category: Mathematics

Page: 194

View: 7551

In image processing, "motions by curvature" provide an efficient way to smooth curves representing the boundaries of objects. In such a motion, each point of the curve moves, at any instant, with a normal velocity equal to a function of the curvature at this point. This book is a rigorous and self-contained exposition of the techniques of "motion by curvature". The approach is axiomatic and formulated in terms of geometric invariance with respect to the position of the observer. This is translated into mathematical terms, and the author develops the approach of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then draws a complete parallel with another axiomatic approach using level-set methods: this leads to generalized curvature motions. Finally, novel, and very accurate, numerical schemes are proposed allowing one to compute the solution of highly degenerate evolution equations in a completely invariant way. The convergence of this scheme is also proved.
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