In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.
Authored by leading scholars, this comprehensive, self-contained text presents a view of the state of the art in multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. Ordered in sections of gradually increasing degrees of difficulty, the text first covers linear Cauchy problems and linear initial boundary value problems, before moving on to nonlinear problems, including shock waves. The book finishes with a discussion of the application of hyperbolic PDEs to gas dynamics, culminating with the shock wave analysis for real fluids. With an extensive bibliography including classical and recent papers both in PDE analysis and in applications (mainly to gas dynamics), this text will be valuable to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.
Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.
This is a self-contained presentation that sets up the foundations of the modern theory of conservation laws and describes the physical models and mathematical methods leading to the Glimm scheme. The author then takes the reader to the current state of knowledge in the subject. With large numbers of exercises and full discussion of all the ideas this will be an ideal text for graduate courses in partial differential equations.
Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.
The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory. The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.
Authored by leading scholars, this comprehensive text presents a view of the multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. It is useful to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.
A clear and pedagogical introduction to classical integrable systems and their applications. It synthesizes the different approaches to the subject, providing a set of interconnected methods for solving problems in mathematical physics. Each method is introduced and explained, before being applied to particular examples.
The primary aim of this monograph is to achieve part of Beilinson’s program on mixed motives using Voevodsky’s theories of A1-homotopy and motivic complexes. Historically, this book is the first to give a complete construction of a triangulated category of mixed motives with rational coefficients satisfying the full Grothendieck six functors formalism as well as fulfilling Beilinson’s program, in particular the interpretation of rational higher Chow groups as extension groups. Apart from Voevodsky’s entire work and Grothendieck’s SGA4, our main sources are Gabber’s work on étale cohomology and Ayoub’s solution to Voevodsky’s cross functors theory. We also thoroughly develop the theory of motivic complexes with integral coefficients over general bases, along the lines of Suslin and Voevodsky. Besides this achievement, this volume provides a complete toolkit for the study of systems of coefficients satisfying Grothendieck’ six functors formalism, including Grothendieck-Verdier duality. It gives a systematic account of cohomological descent theory with an emphasis on h-descent. It formalizes morphisms of coefficient systems with a view towards realization functors and comparison results. The latter allows to understand the polymorphic nature of rational mixed motives. They can be characterized by one of the following properties: existence of transfers, universality of rational algebraic K-theory, h-descent, étale descent, orientation theory. This monograph is a longstanding research work of the two authors. The first three parts are written in a self-contained manner and could be accessible to graduate students with a background in algebraic geometry and homotopy theory. It is designed to be a reference work and could also be useful outside motivic homotopy theory. The last part, containing the most innovative results, assumes some knowledge of motivic homotopy theory, although precise statements and references are given.
This book, which is the proceedings of a conference held at Memorial University of Newfoundland, August 1983, contains 18 papers in algebraic topology and homological algebra by collaborators and associates of Peter Hilton. It is dedicated to Hilton on the occasion of his 60th birthday. The various topics covered are homotopy theory, $H$-spaces, group cohomology, localization, classifying spaces, and Eckmann-Hilton duality. Students and researchers in algebraic topology will gain an appreciation for Hilton's impact upon mathematics from reading this book.
This book links the latest advances in molecular genetics with the science and history of plant domestication, the evolution of plant breeding, and the implications of our new knowledge for the agriculture of today and the future.
Over the past 30 years the writings of Georges Bataille have had a profound influence on French intellectual thought, informing the work of Foucault, Derrida, and Barthes, among others. Against Architecture offers the first serious interpretation of this challenging thinker, spelling out the profoundly original and radical nature of Bataille's work.
This timely comparative study assesses the role of medical doctors in reforming publicly funded health services in England and Canada. Respected authors from health and legal backgrounds on both sides of the Atlantic consider how the high status of the profession uniquely influences reforms. With summaries of developments in models of care, and the participation of doctors since the inception of publicly funded healthcare systems, they ask whether professionals might be considered allies or enemies of policy-makers. With insights for future health policy and research, the book is an important contribution to debates about the complex relationship between doctors and the systems in which they practice.
Honoring the contributions of one of the field's leading experts, Lu Ting, this indispensable volume contains important new results at the cutting edge of research. A wide variety of significant new analytical and numerical results in critical areas are presented, including point vortex dynamics, superconductor vortices, cavity flows, vortex breakdown, shock/vortex interaction, wake flows, magneto-hydrodynamics, rotary wake flows, and hypersonic vortex phenomena.The book will be invaluable for those interested in the state of the art of vortex dominated flows, both from a theoretical and applied perspective.Professor Lu Ting and Joe Keller have worked together for over 40 years. In their first joint work entitled ?Periodic vibrations of systems governed by nonlinear partial differential equations?, perturbation analysis and bifurcation theory were used to determine the frequencies and modes of vibration of various physical systems. The novelty was the application to partial differential equations of methods which, previously, had been used almost exclusively on ordinary differential equations. Professsor Lu Ting is an expert in both fluid dynamics and the use of matched asymptotic expansions. His physical insight into fluid flows has led the way to finding the appropriate mathematical simplications used in the solutions to many difficult flow problems.
Reviewing the state-of-the-art research in the field of imagery, visuo-spatial memory, spatial representation and language, with special emphasis on their interactions, the volume addresses the issues in depth, presenting new evidence through contributions from both behavioural and neuroimaging studies.
The aim of this book is to present pedestrian injuries from a biomechanical perspective. We aim to give a detailed treatment of the physics of pedestrian impact, as well as a review of the accident databases and the relevant injury criteria used to assess pedestrian injuries. A further focus will be the effects on injury outcome of (1) pedestrian/vehicle position and velocity at impact and (2) the influence of vehicle design on injury outcome. Most of the content of this book has been published by these and other authors in various journals, but this book will provide a comprehensive treatment of the biomechanics of pedestrian impacts for the first time. It will therefore be of value to new and established researchers alike.
Death's Men is the classic bestselling story of the First World War as told by the soldiers themselves - reissued for the 2014 Centenary. Millions of British men were involved in the Great War of 1914-1918. But, both during and after the war, the individual voices of the soldiers were lost in the collective picture. Men drew arrows on maps and talked of battles and campaigns, but what it felt like to be in the front line or in a base hospital they did not know. Civilians did not ask and soldiers did not write. Death's Men portrays the humble men who were called on to face the appalling fears and discomforts of the fighting zone. It shows the reality of the First World War through the voices of the men who fought. 'A raw, haunting read that puts you directly into the shoes of the men who rushed to volunteer at the start of the war' Guardian 'An engrossing view of what it was like to live in the trenches, go on leave, get wounded, et cetera, and features voice after voice from the ranks' Telegraph Denis Winter was born in 1940 and read history at Pembroke College, Cambridge. Death's Men was first published in 1978, to critical and popular acclaim. This was followed by his book The First of the Few: Fighter Pilots of the First World War.
In this the authors obtain an isoperimetric characterization of relatively hyperbolicity of a groups with respect to a collection of subgroups. This allows them to apply classical combinatorial methods related to van Kampen diagrams to obtain relative analogues of some well-known algebraic and geometric properties of ordinary hyperbolic groups. There is also an introduction and study of the notion of a relatively quasi-convex subgroup of a relatively hyperbolic group and solve somenatural algorithmic problems.
From Diderot's monumental illustrated record of 18th-century European arts and sciences: elegant renderings of architectural landmarks; drawings and plans for windmills, bridges and boats; renderings of palatial interiors and furnishings; elevations and floor plans for many well-known European theaters; scenes of 18th-century craftsmen at work in the building trades; and much more.
To many, chance and art are antagonistic terms. But a number of 20th century artists have turned this notion on its head by attempting to create artworks based on randomness. Among those, three in particular articulated a well-argued and thorough theory of the radical use of chance in art: André Breton (writer), John Cage (composer) and François Morellet (visual artist). The implications of such a move away from established aesthetics are far-reaching, as much in conceptual as in practical terms, as this book hopes to make clear. Of paramount importance in this coincidentia oppositorum is the suggested possibility of a correlation between the artistic use of chance and a system of thought itself organised around chance. Indeed placing randomness at the centre of one’s art may have deeper philosophical consequences than just on the aesthetical level.
For more than thirty years, the poetry of Denis Knight has been praised by such figures as Bertrand Russell, Seamus Heaney and John Pilger. Now, this remarkable anthology brings together his best work, and spans a roaming life from his days as a WW2 soldier, through Canada and rural France, to his present home in the English countryside.
Supplément au Voyage de Bougainville" est une œuvre écrite par le philosophe et écrivain français Denis Diderot. Il a été rédigé dans la seconde moitié du XVIIIe siècle, mais il n'a pas été publié de son vivant en raison de ses aspects controversés. Ce texte est un dialogue entre deux personnages, un Tahitien et un Français, qui discutent des différences culturelles et des points de vue sur la société. L'œuvre explore la question de la moralité, de la civilisation et des rapports entre les cultures européennes et polynésiennes à l'époque de l'exploration. Denis Diderot était un des philosophes majeurs de l'époque des Lumières en France et l'un des principaux contributeurs de l'Encyclopédie. "Supplément au Voyage de Bougainville" s'inscrit dans le contexte de la philosophie des Lumières, remettant en question les préjugés et les valeurs de l'époque, tout en encourageant la tolérance et la compréhension interculturelle. Il est reconnu pour sa réflexion sur le relativisme culturel et la manière dont les sociétés européennes percevaient d'autres cultures lors de l'exploration du monde.
In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.
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