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On the Topology of Isolated Singularities in Analytic Spaces
The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry.
Numerical Continuation Methods for Dynamical Systems : Path following and boundary value problems
The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.
Neural Networks : Computational Models and Applications
Neural Networks: Computational Models and Applications covers a wealth of important theoretical and practical issues in neural networks, including the learning algorithms of feed-forward neural networks, various dynamical properties of recurrent neural networks, winner-take-all networks and their applications in broad manifolds of computational intelligence: pattern recognition, uniform approximation, constrained optimization, NP-hard problems, and image segmentation. By presenting various computational models, this book is developed to provide readers with a quick but insightful understanding of the broad and rapidly growing areas in the neural networks domain. Besides laying down fundamentals on artificial neural networks, this book also studies biologically inspired neural networks. Some typical computational models are discussed, and subsequently applied to objection recognition, scene analysis and associative memory. The studies of bio-inspired models have important implications in computer vision and robotic navigation, as well as new efficient algorithms for image analysis.
Negotiations with Asymmetrical Distribution of Power : Conclusions from Dispute Resolution in Network Industries
In many ways, complex negotiations shape the business arena of regulated network markets. In general, negotiating partners are not equal with regard to their various sources and instruments of power. This book unfolds a differentiated and, at the same time, applicable framework for analyzing and managing negotiations. It creatively combines power and negotiations theories. In addition, it illustrates the findings in a very inspiring way by investigating negotiation episodes in network industries such as telecommunications and railways. Thus, this book is highly relevant for all those wanting to better understand the complex political processes and outcomes in regulated industries, but also for those bearing practical responsibility in regulatory and government affairs and wanting to improve their management performance.
MSCs and Innovative Biomaterials in Dentistry
Presents the modern concepts of mesenchymal stem cells (MSCs) and biomaterials as they pertain to the dental field. The book is organized around three main topics: MSCs biology, advanced biomaterials, and clinical applications. The chapters present basic information on stem cell biology and physiology, modern biomaterials that improve bone tissue regeneration, the biomatrices like platelet-rich fibrin (PRF) used to functionalize the biomaterials surface, the strategic and safe intraoral seats of harvesting, the new sources for MSCs, as well as the future perspectives and new challenges in these exciting fields.
Molecular advances in dental pulp tissue engineering
Recent advances in regenerative medicine and tissue engineering aim to restore the dentin–pulp complex using stem cells, growth factors and tailored scaffolds to achieve biological regeneration within the root canal. This Special Issue highlights scientific advances in pulp regeneration, bridging the gap between research and clinical application.
Modern Differential Geometry in Gauge Theories : Maxwell Fields ; Vol. I
Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author’s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate unexpected potential applications .Volume 1, the focus is on Maxwell fields. All the basic concepts of this mathematical approach are formulated and used thereafter to describe elementary particles, electromagnetism, and geometric prequantization. Maxwell fields are fully examined and classified in the language of sheaf theory and sheaf cohomology.
Misleading marketing communication : Assessing the impact of potentially deceptive food labelling on consumer behaviour
Presenting four complementary experimental studies targeting recurrent grey-zone scenarios on the Danish food market, the book illustrates the potential of the so-called ShopTrip test paradigm which simulates and registers real-life e-shopping behaviour as it unfolds while yielding new types of data against which opposing assessments of potential misleadingness can be matched. The results are discussed in the light of possible paths of theoretical explanation and implications for future regulative practices, including companies’ self-regulation.
Microwave-Assisted Synthesis of Heterocycles
This book is Volume I of a new series by Springer entitled Topics in Heterocyclic Chemistry. At present, there are six such monographs in this series, the overall scope of which is to cover "current trends in heterocyclic chemistry". Given the importance of heterocylic natural products and heterocyclic scaffolds in the realm of medicinal chemistry and drug discovery, an up-todate series on this subject is well warranted, and a survey of the recent impact of microwave-assisted synthesis on this venerable field is both timely and needed
Metric Structures for Riemannian and Non-Riemannian Spaces
The first stages of the new developments were presented in Gromov's course in Paris, which turned into the famous "Green Book" by Lafontaine and Pansu (1979). The present English translation of that work has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices—by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures—as well as an extensive bibliography and index round out this unique and beautiful book.
Metal Catalyzed Cascade Reactions
Transition metal-catalyzed cascade reactions are an elegant approach to complex molecular scaffolds. Besides their esthetics and increase in structural complexity, they have also become mechanistic challenges for the combination of organometallic elementary steps. As a consequence, cascade reactions have revolutionized synthetic strategies and conceptual thinking. The authors highlight cyclization via carbopalladation and acylpalladation and Heck-pericyclic sequences. They discuss p-allyl palladium-based cascade reactions, Michael-type additions as an entry to transition-metal-promoted cyclizative transformations, and sequential or consecutive palladium-catalyzed processes, and show Pauson-Khand cascades, metal-catalyzed cyclizations of acyclic precursors, as well as cascade and sequential ruthenium-catalyzed transformations. Therefore, the reader finds overview of an exciting and highly dynamic field of a new and innovative methodological concept
Medical Retina
Although the treatment of retinal diseases remains one of the most challenging fields in ophthalmology, the standard of knowledge has improved substantially over the past few years. The insight into basic mechanisms of disease has been expanded and novel diagnostic and therapeutic strategies have been developed, bridging the gap between laboratory and clinical science.
Isomonodromic Deformations and Frobenius Manifolds : An Introduction
The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the seventies in the theory of singularities of holomorphic functions. Motivated by physical considerations, further development of the theory has opened new perspectives on, and revealed new links between, many apparently unrelated areas of mathematics and physics. Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations and ends with applications to recent research questions related to mirror symmetry.
Invariant Manifolds for Physical and Chemical Kinetics
By bringing together various ideas and methods for extracting the slow manifolds the authors show that it is possible to establish a more macroscopic description in nonequilibrium systems. The book treats slowness as stability. A unifying geometrical viewpoint of the thermodynamics of slow and fast motion enables the development of reduction techniques, both analytical and numerical. Examples considered in the book range from the Boltzmann kinetic equation and hydrodynamics to the Fokker-Planck equations of polymer dynamics and models of chemical kinetics describing oxidation reactions. Special chapters are devoted to model reduction in classical statistical dynamics, natural selection, and exact solutions for slow hydrodynamic manifolds. The book will be a major reference source for both theoretical and applied model reduction. Intended primarily as a postgraduate-level text in nonequilibrium kinetics and model reduction, it will also be valuable to PhD students and researchers in applied mathematics, physics and various fields of engineering.
Interphases and Mesophases in Polymer Crystallization III
In polymer crystallization the challenge is to identify and clarify the transformations by which chain molecules pass from a disordered, molten state to the ordered supra-molecular organization known as the semi-crystalline state. The subject is highly relevant in terms of both basic science and technology; it is indeed clear that many modern applications require complete control of the structure and the morphology of polymers from macroscopic dimensions down to below the nanoscale. As a simple example, making the crystallites in a polymer fiber equally oriented and reducing the number of chain folds (or hairpins) therein, usually turn out to be very favorable requisites for mechanical performance . .This series presents critical reviews of the present and future trends in polymer and biopolymer science including chemistry, physical chemistry, physics and material science. It is adressed to ali scientists at universities and in industry who wish to keep abreast of advances in the topics covered
Innovative bioceramics in translational medicine II : Surgical applications
Highlights the latest advances in innovative bioceramics applied in the highly interdisciplinary area referred to as “translational medicine”. This volume predominantly written by surgeons in the fields of craniomaxillofacial, orthopedics, and spinal surgery, examines the translation of innovative bioceramics and bioceramics-based composite from the laboratory to a personalized surgical environment for the repair of damaged and diseased bone tissues.
Holomorphic Morse Inequalities and Bergman Kernels
The main analytic tool is the analytic localization technique in local index theory developed by Bismut-Lebeau. The book includes the most recent results in the field and therefore opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are included, e.g., an analytic proof of the Kodaira embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, a compactification of complete Kähler manifolds of pinched negative curvature, the Berezin-Toeplitz quantization, weak Lefschetz theorems, and the asymptotics of the Ray-Singer analytic torsion.
H-infinity control for nonlinear descriptor systems
The authors present a study of the H-infinity control problem and related topics for descriptor systems, described by a set of nonlinear differential-algebraic equations. They derive necessary and sufficient conditions for the existence of a controller solving the standard nonlinear H-infinity control problem considering both state and output feedback. One such condition for the output feedback control problem to be solvable is obtained in terms of Hamilton–Jacobi inequalities and a weak coupling condition; a parameterization of output feedback controllers solving the problem is also provided. All of these results are then specialized to the linear case. The derivation of state-space formulae for all controllers solving the standard H-infinity control problem for descriptor systems is proposed. Among other important topics covered are balanced realization, reduced-order controller design and mixed H2/H-infinity control.
Handbook of Normal Frames and Coordinates
This book provides the first comprehensive and complete overview on results and methods concerning normal frames and coordinates in differential geometry, with emphasis on vector and differentiable bundles. The book can be used as a reference manual, for reviewing the existing results and as an introduction to some new ideas and developments. Virtually all essential results and methods concerning normal frames and coordinates are presented, most of them with full proofs, in some cases using new approaches.All classical results are expanded and generalized in various directions. For example, normal frames and coordinates are defined and investigated for different kinds of derivations, in particular for (possibly linear) connections on manifolds, with or without torsion, in vector bundles and on differentiable bundles; they are explored also for (possibly parallel) transports along paths in vector bundles. Theorems of existence, uniqueness and, possibly, holonomicity of normal frames and coordinates are proved; mostly, the proofs are constructive and some of their parts can be used independently for other tasks.
Groupes et algèbres de Lie : Chapitre 9, Groupes de Lie réels compacts = Lie groups and algebras : Chapter 9, Compact real Lie groups
Nicolas BOURBAKI's Elements of Mathematics aim to provide a rigorous, systematic and un-prerequisite presentation of mathematics from their foundations. This ninth chapter of the Book on Groups and Lie Algebras, ninth Book of the treatise, includes the paragraphs, Compact Lie Algebras ; Maximum tori of compact Lie groups; Compact fromes of complex semi-simple Lie algebras; Root system associated with a compact group; Conjugation classes; Integration into compact Lie groups; Irreducible representations of connected compact Lie groups; Fourier transformation; Operation of compact Lie groups on manifolds.
