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The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book "e;5000 Jahre Geometrie,"e; in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering.Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first "e;Golden Age"e; in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries.Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometry in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times.The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history.From letters to the authors for the German language editionI hope it gets a translation, as there is no comparable work.Prof. J. Grattan-Guinness (Middlesex University London)"e;Five Thousand Years of Geometry"e; - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically!Prof. J.W. Dauben (City University of New York)An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ...The graphic design is also excellent.Prof. Z. Nadenik (Czech Technical University in Prague)

Those connected with drug research, be they in industry, in universities or in clinics, are aware of these problems, and, as a result of this awareness, are all the more in need of an aid which will assist them in ascertaining the current position and in fixing future goals.

This book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be applied to the study of parabolic problems. It presents known theorems from a novel perspective and teaches how to exploit basic techniques.

This elegantly written text includes a wealth of exercises for students as it weaves classical probability theory into the quantum framework. It deepens our understanding of classical and quantum views on the dynamics of systems subject to the laws of chance.

Ibuprofen is one of the most successful drugs used worldwide for the treatment of mild to moderate pain and various inflammatory conditions. Over the past 40 years, ibuprofen has been proven to be as safe or even safer and also as effective as the established non-steroidal anti-inflammatory drugs (NSAIDs) and the coxibs. This well-written book reviews the pharmacology, clinical uses and the various adverse effects of Ibuprofen, the disposition and unique modes of action in relation to clinical effects of the drug as well as various formulations. The use of combinations with other drugs (e.g. paracetamol, codeine, caffeine) are critically assessed and the impact of natural products and Chinese Medicines on the safety of ibuprofen.

This book is an introduction to several active research topics in Foliation Theory and its connections with other areas. It contains expository lectures showing the diversity of ideas and methods converging in the study of foliations. The lectures by Aziz El Kacimi Alaoui provide an introduction to Foliation Theory with emphasis on examples and transverse structures. Steven Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations: limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, Pesin Theory and hyperbolic, parabolic and elliptic types of foliations. The lectures by Masayuki Asaoka compute the leafwise cohomology of foliations given by actions of Lie groups, and apply it to describe deformation of those actions. In his lectures, Ken Richardson studies the properties of transverse Dirac operators for Riemannian foliations and compact Lie group actions, and explains a recently proved index formula. Besides students and researchers of Foliation Theory, this book will be interesting for mathematicians interested in the applications to foliations of subjects like Topology of Manifolds, Differential Geometry, Dynamics, Cohomology or Global Analysis.

This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts.Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolic equations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems with time-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Cauchy problems are constructed as oscillatory integrals by working in appropriate time-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lower order terms can change asymptotic properties and thus complements the exposition.

Bartel Leendert van der Waerden made major contributions to algebraic geometry, abstract algebra, quantum mechanics, and other fields. He liberally published on the history of mathematics. His 2-volume work Modern Algebra is one of the most influential and popular mathematical books ever written. It is therefore surprising that no monograph has been dedicated to his life and work. Van der Waerden's record is complex. In attempting to understand his life, the author assembled thousands of documents from numerous archives in Germany, the Netherlands, Switzerland and the United States which revealed fascinating and often surprising new information about van der Waerden. Soifer traces Van der Waerden's early years in a family of great Dutch public servants, his life as professor in Leipzig during the entire Nazi period, and his personal and professional friendship with one of the great physicists Werner Heisenberg. We encounter heroes and villains and a much more numerous group in between these two extremes. One of them is the subject of this book. Soifer's journey through a long list of archives, combined with an intensive correspondence, had uncovered numerous details of Van der Waerden's German intermezzo that raised serious questions and reproaches. Dirk van Dalen (Philosophy, Utrecht University)Professor Soifer's book implicates the anthropologists' and culture historians' core interest in the evolution of culture and in the progress of human evolution itself on this small contested planet. James W. Fernandez (Anthropology, University of Chicago)The book is fascinating. Professor Soifer has done a great service to the discipline of history, as well as deepening our understanding of the 20th century. Peter D. Johnson, Jr. (Mathematics, Auburn University)This book is an important contribution to the history of the twentieth century, and reads like a novel with an ever-fascinating cast of characters. Harold W. Kuhn (Mathematics, Princeton University)This is a most impressive and important book. It is written in an engaging, very personal style and challenges the reader's ability of moral and historical judgment. While it is not always written in the style of 'objective' professional historiography, it satisfies very high standards of scholarly documentation. Indeed the book contains a wealth of source material that allows the reader to form a highly detailed picture of the events and personalities discussed in the book. As an exemplar of historical writing in a broader sense it can compete with any other historical book.Moritz Epple (History of Mathematics, Frankfurt University)

This book is devoted to the relation between two different concepts of integrability: the complete integrability of complex analytical Hamiltonian systems and the integrability of complex analytical linear differential equations. For linear differential equations, integrability is made precise within the framework of differential Galois theory. The connection of these two integrability notions is given by the variational equation (i.e. linearized equation) along a particular integral curve of the Hamiltonian system. The underlying heuristic idea, which motivated the main results presented in this monograph, is that a necessary condition for the integrability of a Hamiltonian system is the integrability of the variational equation along any of its particular integral curves. This idea led to the algebraic non-integrability criteria for Hamiltonian systems. These criteria can be considered as generalizations of classical non-integrability results by Poincare and Liapunov, as well as more recent results by Ziglin and Yoshida. Thus, by means of the differential Galois theory it is not only possible to understand all these approaches in a unified way but also to improve them. Several important applications are also included: homogeneous potentials, Bianchi IX cosmological model, three-body problem, Henon-Heiles system, etc.The book is based on the original joint research of the author with J.M. Peris, J.P. Ramis and C. Simo, but an effort was made to present these achievements in their logical order rather than their historical one. The necessary background on differential Galois theory and Hamiltonian systems is included, and several new problems and conjectures which open new lines of research are proposed.

This book offers comprehensive information on the polymorphisms of genes encoding pattern recognition receptors (PRRs). Following a short description of the general role of PRRs in the immune system, the structure and function of Toll-like and NOD-like receptors are examined in detail. The main focus is on the role of inherited variation in PRRs and their correlation to cancer and cardiovascular diseases. A review of all epidemiological investigations is included, and a concept of genomic risk markers for the prevention of various diseases is also discussed.

There is now compelling evidence that the complexity of higher organisms correlates with the relative amount of non-coding RNA rather than the number of protein-coding genes. Previously dismissed as "e;junk DNA"e;, it is the non-coding regions of the genome that are responsible for regulation, facilitating complex temporal and spatial gene expression through the combinatorial effect of numerous mechanisms and interactions working together to fine-tune gene expression. The major regions involved in regulation of a particular gene are the 5' and 3' untranslated regions and introns. In addition, pervasive transcription of complex genomes produces a variety of non-coding transcripts that interact with these regions and contribute to regulation. This book discusses recent insights into the regulatory roles of the untranslated gene regions and non-coding RNAs in the control of complex gene expression, as well as the implications of this in terms of organism complexity and evolution.

Gamma-Glutamyl Transpeptidases (y-GTs) are members of the N-terminal nucleophile hydrolase superfamily, enzymes that cleave the y-glutamyl amide bond of glutathione to liberate cysteinylglycine. The released y-glutamyl group can be transferred to water (hydrolysis) or to amino acids or short peptides (transpeptidation). y-GT plays a key role in the gamma glutamyl cycle by regulating the cellular levels of the antioxidant glutathione, hence it is a critical enzyme in maintaining cellular redox homeostasis.y-GT is upregulated during inflammation and in several human tumors, and it is involved in many physiological disorders related to oxidative stress, such as Parkinson's disease and diabetes. Furthermore, this enzyme is used as a marker of liver disease and cancer. This book covers current knowledge about the structure-function relationship of y-GTs and gives information about applications of y-GTs in different fields ranging from clinical biochemistry to biotechnology and biomedicine.

The book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines. Moreover, these differential systems are symmetric with respect to the origin of coordinates. This class of systems driven by concrete applications is of interest in engineering, in particular in control theory and the design of electric circuits. By studying these particular differential systems we will introduce the basic tools of the qualitative theory of ordinary differential equations, which allow us to describe the global dynamics of these systems including the infinity. The behavior of their solutions, their parametric stability or instability and their bifurcations are described. The book is very appropriate for a first course in the qualitative theory of differential equations or dynamical systems, mainly for engineers, mathematicians, and physicists.

The essential question that fractal dimensions attempt to answer is about the scales in Nature. For a system as non-idealistic and complex as a protein, studying scale-invariance becomes particularly important.Fractal Symmetry of Protein Exterior investigates the diverse facets of the various scales at which we describe protein biophysical and biochemical phenomena. Although these ideas are entirely mathematical, mathematical expositions have been avoided, unless the use of some expressions becomes absolutely obligatory. A first chapter introduce into fractal dimensions, protein exteriors and to methods to study the roughness of surfaces. The main topics covered in the following chapters include: protein-protein interaction interfaces; protein surface-roughness and local shape as well as adhesion on protein and other rough biomolecular surfaces.

The essential question that fractal dimensions attempt to answer is about the scales in Nature. For a system as non-idealistic and complex as a protein, studying scale-invariance becomes particularly important.Fractal Symmetry of Protein Interior investigates the diverse facets of the various scales at which we describe protein biophysical and biochemical phenomena. Following a thorough introduction to fractal dimensions, fractal-dimension-based approaches, that have been employed to study protein interior biophysical properties, are described. The focus is on the question "e;which scales are scale-invariant?"e; Investigations related to scaling of biophysical and biochemical behaviors may one day help us to formulate a fundamental theory about protein biophysics; which, in turn, may help us to understand fundamental principles of proteins.

This book draws on an eight-year study carried out in the DOCG Prosecco area of Italy, a wine region known worldwide. It is unique in the sense that it is based on one of the most comprehensive investigations into terroir zoning ever performed in Italy.By drawing attention to the complex interrelations between environmental and human factors that influence the growth and production of the Glera grape, the study illustrates the distinct correlation between a wine and its 'terroir'.It shows that the morphology of the sites, the meso and microclimate, the soil, the grapevine planting density, the trellising system, the yield of the vineyard, and the vine water status in the summer lead to unique combinations of grape maturity, acidity, and aroma that ultimately influence the sensory properties of the wines produced. Furthermore, the book details numerous technical and agronomic considerations, specific to the "e;Glera"e; grape variety, for different production strategies, including a section on the impact of climate change on cv "e;Glera"e; phenology."e;The Power of the Terroir: the Case Study of Prosecco Wine"e; represents a valuable resource for anyone involved in studies or research activities in the fields of viticulture, climatology, agronomic sciences or soil sciences, but is also of interest to vine growers, professionals in the wine industry, and wine enthusiasts in general.

The notes in this volume correspond to advanced courses held at the Centre de Recerca Matematica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year.The notes by Laurent Berger provide an introduction to p-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory.The notes by Gebhard Bockle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and discussing in detail the theory of pseudo-representations and their deformations, local deformations at places l = p and local deformations at p which are flat. In the last section,the results of Bockle and Kisin on presentations of global deformation rings over local ones are discussed. The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients. The notes by Lassina Dembele and John Voight describe methods for performing explicit computations in spaces of Hilbert modular forms. These methods depend on the Jacquet-Langlands correspondence and on computations in spaces of quaternionic modular forms, both for the case of definite and indefinite quaternion algebras. Several examples are given, and applications to modularity of Galois representations are discussed. The notes by Tim Dokchitser describe the proof, obtained by the author in a joint project with Vladimir Dokchitser, of the parity conjecture for elliptic curves over number fields under the assumption of finiteness of the Tate-Shafarevich group. The statement of the Birch and Swinnerton-Dyer conjecture is included, as well as a detailed study of local and global root numbers of elliptic curves and their classification.

This book is an essay on the epistemology of classifications. Its main purpose is not to provide an exposition of an actual mathematical theory of classifications, that is, a general theory which would be available to any kind of them: hierarchical or non-hierarchical, ordinary or fuzzy, overlapping or non-overlapping, finite or infinite, and so on, establishing a basis for all possible divisions of the real world. For the moment, such a theory remains nothing but a dream. Instead, the authors essentially put forward a number of key questions. Their aim is rather to reveal the "e;state of art"e; of this dynamic field and the philosophy one may eventually adopt to go further. To this end they present some advances made in the course of the last century, discuss a few tricky problems that remain to be solved, and show the avenues open to those who no longer wish to stay on the wrong track. Researchers and professionals interested in the epistemology and philosophy of science, library science, logic and set theory, order theory or cluster analysis will find this book a comprehensive, original and progressive introduction to the main questions in this field.

This book presents recent results on nonlinear evolutionary fluid equations such as the compressible (radiative) magnetohydrodynamics (MHD) equations, compressible viscous micropolar fluid equations, the full non-Newtonian fluid equations and non-autonomous compressible Navier-Stokes equations. These types of partial differential equations arise in many fields of mathematics, but also in other branches of science such as physics and fluid dynamics.This book will be a valuable resource for graduate students and researchers interested in partial differential equations, and will also benefit practitioners in physics and engineering.

Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests. It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book. The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.

Differential equations with delay naturally arise in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, distributed networks, heat flows, neural networks, combustion, interaction of species, microbiology, learning models, epidemiology, physiology, and many others. This book systematically investigates the stability of linear as well as nonlinear vector differential equations with delay and equations with causal mappings. It presents explicit conditions for exponential, absolute and input-to-state stabilities. These stability conditions are mainly formulated in terms of the determinants and eigenvalues of auxiliary matrices dependent on a parameter; the suggested approach allows us to apply the well-known results of the theory of matrices. In addition, solution estimates for the considered equations are established which provide the bounds for regions of attraction of steady states. The main methodology presented in the book is based on a combined usage of the recent norm estimates for matrix-valued functions and the following methods and results: the generalized Bohl-Perron principle and the integral version of the generalized Bohl-Perron principle; the freezing method; the positivity of fundamental solutions. A significant part of the book is devoted to the Aizerman-Myshkis problem and generalized Hill theory of periodic systems. The book is intended not only for specialists in the theory of functional differential equations and control theory, but also for anyone with a sound mathematical background interested in their various applications.