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This book collects the lecture notes of the Summer School on Convex Geometry, held in Cetraro, Italy, from August 30th to September 3rd, 2021. Convex geometry is a very active area in mathematics with a solid tradition and a promising future. Its main objects of study are convex bodies, that is, compact and convex subsets of n-dimensional Euclidean space. The so-called Brunn--Minkowski theory currently represents the central part of convex geometry. The Summer School provided an introduction to various aspects of convex geometry: The theory of valuations, including its recent developments concerning valuations on function spaces; geometric and analytic inequalities, including those which com...
This book presents the proceedings of the international conference Analytic Aspects in Convexity, which was held in Rome in October 2016. It offers a collection of selected articles, written by some of the world’s leading experts in the field of Convex Geometry, on recent developments in this area: theory of valuations; geometric inequalities; affine geometry; and curvature measures. The book will be of interest to a broad readership, from those involved in Convex Geometry, to those focusing on Functional Analysis, Harmonic Analysis, Differential Geometry, or PDEs. The book is a addressed to PhD students and researchers, interested in Convex Geometry and its links to analysis.
Integral geometry, known as geometric probability in the past, originated from Buffon's needle experiment. Remarkable advances have been made in several areas that involve the theory of convex bodies. This volume brings together contributions by leading international researchers in integral geometry, convex geometry, complex geometry, probability, statistics, and other convexity related branches. The articles cover both recent results and exciting directions for future research.
This commemorative book contains the 28 major articles that appeared in the 2008 Twentieth Anniversary Issue of the journal Discrete & Computational Geometry, and presents a comprehensive picture of the current state of the field. The articles in this volume, a number of which solve long-outstanding problems in the field, were chosen by the editors of DCG for the importance of their results, for the breadth of their scope, and to show the intimate connections that have arisen between discrete and computational geometry and other areas of both computer science and mathematics. Apart from the articles, the editors present an expanded preface, along with a set of photographs of groups and individuals who have played a major role in the history of the field during the past twenty years.
Written as a tribute to the mathematician Carlo Pucci on the occasion of his 70th birthday, this is a collection of authoritative contributions from over 45 internationally acclaimed experts in the field of partial differential equations. Papers discuss a variety of topics such as problems where a partial differential equation is coupled with unfavourable boundary or initial conditions, and boundary value problems for partial differential equations of elliptic type.
The control of greenhouse gas emissions continues to be a major global problem. It is inter-disciplinary, both in substance and approach, and covers technical, political and economic issues involving governments, industry and the scientific community. These proceedings contain 220 papers presented at the 5th International Conference on Greenhouse Gas Control Technologies (GHGT-5) held in August 2000 at Cairns, Queensland, Australia. The papers cover the capture of carbon dioxide, geological storage of carbon dioxide, ocean storage of carbon dioxide, storage of carbon dioxide with enhanced hydrocarbon recovery, utilisation of carbon dioxide, other greenhouse gases, fuel cells, alternative energy carriers, energy efficiency, life cycle assessments and energy modelling, economics, international and national policy, trading and accounting policy, social and community issues, and reducing emission from industry and power generation.
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Global environmental problems, especially global warming caused by the accelerative accumulation of carbon dioxide in the atmosphere, are of great importance for humans. The world's population is now approaching 6 billion, and is still increasing. Developments in communication systems and transportation tools have made the circulation of information, technologies and materials easier, which results in rapid economic growth, particularly in the East and Southeastern Asian countries. Increased affluence leads to an increased consumption of fossil fuels. Inevitably, this leads to an increase in carbon dioxide emission and environmentally hazardous materials which in turn precipitates climatic c...