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Percolation theory is the study of an idealized random medium in two or more dimensions. The mathematical theory is mature, and continues to give rise to problems of special beauty and difficulty. Percolation is pivotal for studying more complex physical systems exhibiting phase transitions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. The book is intended for graduate students and researchers in probability and mathematical physics. Almost no specialist knowledge is assumed. Much new material appears in this second edition, including: dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.

Seafloor surveying with acoustic remote sensing has become a powerful tool for researchers and professionals seeking knowledge about the structure and behavior of the seafloor. In particular, sidescan sonar is proving to be the preeminent technique, but its data is often difficult to interpret due to the physics of acoustic remote sensing, and to the varied geological processes at play. This handbook not only presents all the fundamentals but also explains how to interpret sidescan sonar imagery and bathymetry. It fully explores the most recent advances, both in the technology and in the knowledge of marine structures, and provides deep insights for interpretation and decision-making. Broadly expanded and updated from the previous 1997 “Handbook of Seafloor Sonar Imagery”, this handbook is indispensable to oceanographers, resource exploiters, telecommunications engineers, and marine researchers of all kinds.

For a brief period during the latter part of World War II, Nevill F. Mott led a theoretical group at Fort Halstead in the United Kingdom that tackled scientific issues related to pressing war-time concerns. Among later awards and honors, Mott was knighted and a recipient of the Nobel Prize. While at Fort Halstead, he undertook an effort to theoretically describe the statistical fragmentation of munitions subjected to intense explosive loading. Mott`s original internal reports contain seminal theoretical concepts on the physics and statistics of dynamic fracture and fragmentation, which have provided the inspiration for numerous later modeling efforts and engineering formulae. Some of his most forward-looking thoughts on the micromechanical and molecular aspects of fracture are included in these publications. The present book surveys the theoretical analysis put forth by Mott with particular focus on his efforts to characterize the size and distribution of fragments resulting from a dynamic fragmentation event. Copies of the original internal reports of Mott and his co-workers are included. The book also pursues additional theoretical analysis with the intent of delving further into the physical ideas and unfinished analysis implicit in Mott`s original studies. This book will be of interest to all scientists and engineers concerned with the dynamic fracture and fragmentation of solid bodies subject to intense transient loads imparted by explosive detonation and high-velocity impact from both the historical and modern perspective.

This book covers the dominant theoretical approaches to the approximate solution of hard combinatorial optimization and enumeration problems. It contains elegant combinatorial theory, useful and interesting algorithms, and deep results about the intrinsic complexity of combinatorial problems. Its clarity of exposition and excellent selection of exercises will make it accessible and appealing to all those with a taste for mathematics and algorithms.Richard Karp,University Professor, University of California at BerkeleyFollowing the development of basic combinatorial optimization techniques in the 1960s and 1970s, a main open question was to develop a theory of approximation algorithms. In the 1990s, parallel developments in techniques for designing approximation algorithms as well as methods for proving hardness of approximation results have led to a beautiful theory. The need to solve truly large instances of computationally hard problems, such as those arising from the Internet or the human genome project, has also increased interest in this theory. The field is currently very active, with the toolbox of approximation algorithm design techniques getting always richer.It is a pleasure to recommend Vijay Vazirani's well-written and comprehensive book on this important and timely topic.I am sure the reader will find it most useful both as an introduction to approximability as well as a reference to the many aspects of approximation algorithms.Laszlo Lovasz, Senior Researcher, Microsoft Research

There is growing recognition of the need to address the fragility of digital information, on which our society heavily depends for smooth operation in all aspects of daily life. This has been discussed in many books and articles on digital preservation, so why is there a need for yet one more? Because, for the most part, those other publications focus on documents, images and webpages – objects that are normally rendered to be simply displayed by software to a human viewer. Yet there are clearly many more types of digital objects that may need to be preserved, such as databases, scientific data and software itself.David Giaretta, Director of the Alliance for Permanent Access,  and his contributors explain why the tools and techniques used for preserving rendered objects are inadequate for all these other types of digital objects, and they provide the concepts, techniques and tools that are needed. The book is structured in three parts. The first part is on theory, i.e., the concepts and techniques that are essential for preserving digitally encoded information. The second part then shows practice, i.e., the use and validation of these tools and techniques. Finally, the third part concludes by addressing how to judge whether money is being well spent, in terms of effectiveness and cost sharing.Various examples of digital objects from many sources are used to explain the tools and techniques presented. The presentation style mainly aims at practitioners in libraries, archives and industry who are either directly responsible for preservation or who need to prepare for audits of their archives. Researchers in digital preservation and developers of preservation tools and techniques will also find valuable practical information here. Researchers creating digitally encoded information of all kinds will also need to be aware of these topics so that they can help to ensure that their data is usable and can be valued by others now and in thefuture.To further assist the reader, the book is supported by many hours of videos and presentations from the CASPAR project and by a set of open source software.

This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"“… It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. […] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.”From the Reviews"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... "Notices of the AMS, August 1999"... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..."LMS Newsletter, January 1999"Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ..." SIGACT News, December 2011

In dem Band werden alle wichtigen operativen Eingriffe an Nageln Schritt fur Schritt beschrieben: in prazisen Texten und in aussagekraftigen Farbabbildungen. Besonderer Wert wird auf nagelschonende Verfahren gelegt. Mit Tipps und Tricks fur schwierige Falle.