This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.
This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School “Galois Theory of Difference Equations” in Santa Marta, Columbia, July 23–August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.
Originally published in 1993, this book opens a new and major line of interpretation, showing that Georg Simmel is the essential sociologist of the postmodern age. The authors trace the important contributions that Simmel's writings can make to current studies of intellectual ethics, textual methodology, sociological theory, philosophy of history and cultural theory
No member of the emergency room or trauma ward physician should be without this 4th edition of The Trauma Manual: Trauma and Acute Care Surgery. Designed to be used as a quick reference, this multidisciplinary pocket guide addresses all areas of trauma and emergency surgery with a list of key points at the end of each chapter. In addition to a new section on the intensive care unit and an extended section on surgical emergencies, this manual also covers GI hemorrhage, hernias, bowel obstruction, pancreatitis, biliary tract disease, and other surgical challenges faced by trauma and emergency surgery personnel. Organized in a chronological fashion following the usual events and phases of care after injury or acute surgical illness, this user-friendly manual is one guide every trauma surgeon, surgical resident, surgical critical care specialist, emergency medicine physician, and emergency or trauma nurse, will want to keep close by.
Cells, Aging, and Human Disease is the first book to explore aging all the way from genes to clinical application, analyzing the fundamental cellular changes which underlie human age-related disease. With over 4,000 references, this text explores both the fundamental processes of human aging and the tissue-by-tissue pathology, detailing both breaking research and current state-of-the-art clinical interventions in aging and age-related disease. Far from merely sharing a common onset late in the lifespan, age-related diseases are linked by fundamental common characteristics at the genetic and cellular levels. Emphasizing human cell mechanisms, the first section presents and analyzes our current knowledege of telomere biology and cell senescence. In superb academic detail, the text brings the reader up to date on telomere maintenance, telomerase dynamics, and current research on cell senescence--and the general model--cell senescence as the central component in human senescence and cancer. For each human malignancy, the chapter reviews and analyzes all available data on telomeres and telomerase, as well as summarizing current work on their clinical application in both diagnosis and cancer therapy. The second edition, oriented by organs and tissues, explores the actual physiological impact of cell senescence and aging on clinical disease. After a summary of the literature on early aging syndromes--the progerias--the text reviews aging diseases (Alzheimer's dementia, osteoarthritis, atherosclerosis, immune aging, presbyopia, sarcopenia, etc.) in the context of the tissues in which they occur. Each of the ten clinical chapters--skin, cardiovascular system, bone and joints, hematopoetic and immune systems, endocrine, CNS, renal, muscle, GI, and eyes--examines what we know of their pathology, the role of cell sensescence, and medical interventions, both current and potential.
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
The first book devoted to cluster algebras, this work contains chapters on Poisson geometry and Schubert varieties; an introduction to cluster algebras and their main properties; and geometric aspects of the cluster algebra theory, in particular on its relations to Poisson geometry and to the theory of integrable systems.
Provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the 'even case', where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of 'noncharacteristic 2 type'.
If you have a child in school, you may have heard stories of long-dormant diseases suddenly reappearing—cases of measles, mumps, rubella, and whooping cough cropping up everywhere from elementary schools to Ivy League universities because a select group of parents refuse to vaccinate their children. Between Hope and Fear tells the remarkable story of vaccine-preventable infectious diseases and their social and political implications. While detailing the history of vaccine invention, Kinch reveals the ominous reality that our victories against vaccine-preventable diseases are not permanent—and could easily be undone. In the tradition of John Barry’s The Great Influenza and Siddhartha Mukherjee’s The Emperor of All Maladies, Between Hope and Fear relates the remarkable intersection of science, technology, and disease that has helped eradicate many of the deadliest plagues known to man.
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