This book presents a one-stop reference to the empirical correlations used extensively in geotechnical engineering. Empirical correlations play a key role in geotechnical engineering designs and analysis. Laboratory and in situ testing of soils can add significant cost to a civil engineering project. By using appropriate empirical correlations, it is possible to derive many design parameters, thus limiting our reliance on these soil tests. The authors have decades of experience in geotechnical engineering, as professional engineers or researchers. The objective of this book is to present a critical evaluation of a wide range of empirical correlations reported in the literature, along with typical values of soil parameters, in the light of their experience and knowledge. This book will be a one-stop-shop for the practising professionals, geotechnical researchers and academics looking for specific correlations for estimating certain geotechnical parameters. The empirical correlations in the forms of equations and charts and typical values are collated from extensive literature review, and from the authors' database.

This volume contains the proceedings of the third Euroconference on Atomic Phys ics at Accelerators (APAC 2001), with the title Stored Particles and Fundamental Physics. It was held in Aarhus, Denmark, from September 8 to 13 at the Marselis Hotel located near the beach and the Marselis Woods outside Aarhus, but some of the activities took place at the Department of Physics, University of Aarhus. The conference was sponsored by the Commission of the European Union (Contract No. ERBFMMACT980469) and also by the Danish Research Foundation through ACAP (Aarhus Center for Atomic Physics). The meeting was focused on the application of storage rings for atomic physics, and there are two fairly small rings in Aarhus, ASTRID (Aarhus STorage Ring for Ions,Denmark) and ELISA (ELectrostatic Ion Storage ring, Aarhus). The research at these rings has contributed to the strong position of European Science in this field. Both rings are designed according to unique concepts. ASTRID is a dual purpose ring, which half the time stores electrons for the generation of low-energy synchrotron radiation. The storage of negative particles has also been a unique feature for the application of ASTRID as an ion storage ring.

As the nation's economic activities, security concerns, and stewardship of natural resources become increasingly complex and globally interrelated, they become ever more sensitive to adverse impacts from weather, climate, and other natural phenomena. For several decades, forecasts with lead times of a few days for weather and other environmental phenomena have yielded valuable information to improve decision-making across all sectors of society. Developing the capability to forecast environmental conditions and disruptive events several weeks and months in advance could dramatically increase the value and benefit of environmental predictions, saving lives, protecting property, increasing economic vitality, protecting the environment, and informing policy choices. Over the past decade, the ability to forecast weather and climate conditions on subseasonal to seasonal (S2S) timescales, i.e., two to fifty-two weeks in advance, has improved substantially. Although significant progress has been made, much work remains to make S2S predictions skillful enough, as well as optimally tailored and communicated, to enable widespread use. Next Generation Earth System Predictions presents a ten-year U.S. research agenda that increases the nation's S2S research and modeling capability, advances S2S forecasting, and aids in decision making at medium and extended lead times.

For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

This fantastic and deep book about how to use Sage for learning and doing mathematics at all levels perfectly complements the existing Sage documentation. It is filled with many carefully thought through examples and exercises, and great care has been taken to put computational functionality into proper mathematical context. Flip to almost any random page in this amazing book, and you will learn how to play with and visualize some beautiful part of mathematics. --- William A. Stein, CEO, SageMath, and professor of mathematics, University of Washington SageMath, or Sage for short, is an open-source mathematical software system based on the Python language and developed by an international community comprising hundreds of teachers and researchers, whose aim is to provide an alternative to the commercial products Magma, Maple, Mathematica, and MATLAB. To achieve this, Sage relies on many open-source programs, including GAP, Maxima, PARI, and various scientific libraries for Python, to which thousands of new functions have been added. Sage is freely available and is supported by all modern operating systems. Sage provides a wonderful scientific and graphical calculator for high school students, and it efficiently supports undergraduates in their computations in analysis, linear algebra, calculus, etc. For graduate students, researchers, and engineers in various mathematical specialties, Sage provides the most recent algorithms and tools, which is why several universities around the world already use Sage at the undergraduate level.