The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.
Consistently lauded for its comprehensiveness and full-color color presentation, the latest edition of Rheumatology by Marc C. Hochberg, MD, MPH et al. continues the tradition of excellence of previous editions. Designed to meet the needs of the practicing clinician, it provides extensive, authoritative coverage of rheumatic disease from basic scientific principles to practical points of clinical management in a lucid, logical, user-friendly manner. Find the critical answers you need quickly and easily thanks to a consistent, highly user-friendly format covering all major disorders of the musculoskeletal system in complete, self-contained chapters. Get trusted perspectives and insights from chapters co-authored by internationally renowned leaders in the field, 25% of whom are new to this edition. Track disease progression and treat patients more effectively with the most current information, including 22 new chapters on genetic findings, imaging outcomes, and cell and biologic therapies as well as rheumatoid arthritis and SLE. Incorporate the latest findings about pathogenesis of disease; imaging outcomes for specific diseases like RA, osteoarthritis, and spondyloarthropathies; cell and biologic therapies; and other timely topics.
The mental well-being of children and adults is shockingly poor. Marc Brackett, author of Permission to Feel, knows why. And he knows what we can do. "We have a crisis on our hands, and its victims are our children." Marc Brackett is a professor in Yale University’s Child Study Center and founding director of the Yale Center for Emotional Intelligence. In his 25 years as an emotion scientist, he has developed a remarkably effective plan to improve the lives of children and adults – a blueprint for understanding our emotions and using them wisely so that they help, rather than hinder, our success and well-being. The core of his approach is a legacy from his childhood, from an astute uncle who gave him permission to feel. He was the first adult who managed to see Marc, listen to him, and recognize the suffering, bullying, and abuse he’d endured. And that was the beginning of Marc’s awareness that what he was going through was temporary. He wasn’t alone, he wasn’t stuck on a timeline, and he wasn’t “wrong” to feel scared, isolated, and angry. Now, best of all, he could do something about it. In the decades since, Marc has led large research teams and raised tens of millions of dollars to investigate the roots of emotional well-being. His prescription for healthy children (and their parents, teachers, and schools) is a system called RULER, a high-impact and fast-effect approach to understanding and mastering emotions that has already transformed the thousands of schools that have adopted it. RULER has been proven to reduce stress and burnout, improve school climate, and enhance academic achievement. This book is the culmination of Marc’s development of RULER and his way to share the strategies and skills with readers around the world. It is tested, and it works. This book combines rigor, science, passion and inspiration in equal parts. Too many children and adults are suffering; they are ashamed of their feelings and emotionally unskilled, but they don’t have to be. Marc Brackett’s life mission is to reverse this course, and this book can show you how.
Penalising a process is to modify its distribution with a limiting procedure, thus defining a new process whose properties differ somewhat from those of the original one. We are presenting a number of examples of such penalisations in the Brownian and Bessel processes framework. The Martingale theory plays a crucial role. A general principle for penalisation emerges from these examples. In particular, it is shown in the Brownian framework that a positive sigma-finite measure takes a large class of penalisations into account.
The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.
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