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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.
Nuclear Dynamics : Molecular Biology and Visualization of the Nucleus
The dynamics of nuclear structures described in this book furnish the basis for a comprehensive understanding of how the higher-order organization and function of the nucleus is established and how it correlates with the expression of a variety of vital activities such as cell proliferation and differentiation. The resulting volume creates an invaluable source of reference for researchers in the field.
Nonlinear Dimensionality Reduction
This book describes existing and advanced methods to reduce the dimensionality of numerical databases. For each method, the description starts from intuitive ideas, develops the necessary mathematical details, and ends by outlining the algorithmic implementation. Methods are compared with each other with the help of different illustrative examples. The purpose of the book is to summarize clear facts and ideas about well-known methods as well as recent developments in the topic of nonlinear dimensionality reduction. With this goal in mind, methods are all described from a unifying point of view, in order to highlight their respective strengths and shortcomings.
Network and Parallel Computing ; IFIP International Conference, NPC 2005, Beijing, China, November 30 - December 3, 2005, Proceedings
These proceedings contain the papers presented at the 2005 IFIP International Conference on Network and Parallel Computing (NPC 2005), held in Beijing, China, between November 30 and December 3, 2005. The goal of the conference was to establish an international forum for engineers and scientists to present their ideas and experiences in network and parallel computing. A total of 320 submissions were received in response to our Call for Papers. These papers were from the following countries or regions: Australia, Canada, China, France, Germany, Hong Kong, India, Iran, Italy, Japan, Korea, Lux- burg, Nepal, Netherlands, Taiwan, United Arab Emirates, and United States.
Nearrings and Nearfields ; Proceedings of the Conference on Nearrings and Nearfields, Hamburg, Germany July 27 - August 3, 2003
This present volume is the Proceedings of the 18th International Conference on Nearrings and Nearfields held at the Helmut-Schmidt-Universitat, Universitat der Bundeswehr Hamburg, from July 27-August 3, 2003. It contains the written versions of the lectures by the five invited speakers. These concern recent developments of planar nearrings, nearrings of mappings, group nearrings and loop-nearrings. One of them is a long and very substantial research paper "The Z-Constrained Conjecture". These are followed by 13 contributions reflecting the diversity of the subject of nearrings and related structures. Besides the purely algebriac structure theory, these papers show many connections of nearring theory with group theory, combinatorics, geometries, and topology, and all contain original research.
Multiple Integrals in the Calculus of Variations
From the reviews: "…the book contains a wealth of material essential to the researcher concerned with multiple integral variational problems and with elliptic partial differential equations. The book not only reports the researches of the author but also the contributions of his contemporaries in the same and related fields. The book undoubtedly will become a standard reference for researchers in these areas. …The book is addressed mainly to mature mathematical analysts. However, any student of analysis will be greatly rewarded by a careful study of this book."
Multimedia Content Analysis and Mining ; International Workshop, MCAM 2007, Weihai, China, June 30-July 1, 2007, Proceedings
The workshop gives a snapshot of the current wor- wide research in multimedia analysis. Through recent advances in computing, networking, and data storage, multimedia will create new interesting technical possibilities in a wide range of ?elds, such as entertainment, commerce, science, medicine, and public safety.
Motivic Homotopy Theory : Lectures at a Summer School in Nordfjordeid, Norway, August 2002
This book is based on lectures given at a summer school held in Nordfjordeid on the Norwegian west coast in August 2002. In the little town with the sp- tacular surroundings where Sophus Lie was born in 1842, the municipality, in collaboration with the mathematics departments at the universities, has established the “Sophus Lie conference center”. The purpose is to help or- nizing conferences and summer schools at a local boarding school during its summer vacation, and the algebraists and algebraic geometers in Norway had already organized such summer schools for a number of years. In 2002 a joint project with the algebraic topologists was proposed.
Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology
It covered an ample spectrum of subjects which are re ected in the present volume: Morse theory and related techniques in in nite dim- sional spaces, Floer theory and its recent extensions and generalizations, Morse and Floer theory in relation to string topology, generating functions, structure of the group of Hamiltonian difieomorphisms and related dynamical problems, applications to robotics and many others. We thank all our main speakers for their stimulating lectures and all p- ticipants for creating a friendly atmosphere
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.
Metric Spaces
This volume provides a complete introduction to metric space theory for undergraduates. It covers the topology of metric spaces, continuity, connectedness, compactness and product spaces, and includes results such as the Tietze-Urysohn extension theorem, Picard's theorem on ordinary differential equations, and the set of discontinuities of the pointwise limit of a sequence of continuous functions.
Measure, Topology, and Fractal Geometry
For the Second Edition of this highly regarded textbook, Gerald Edgar has made numerous additions and changes, in an attempt to provide a clearer and more focused exposition. The most important addition is an increased emphasis on the packing measure, so that now it is often treated on a par with the Hausdorff measure. The topological dimensions were rearranged for Chapter 3, so that the covering dimension is the major one, and the inductive dimensions are the variants. A "reduced cover class" notion was introduced to help in proofs for Method I or Method II measures. Research results since 1990 that affect these elementary topics have been taken into account. Some examples have been added, including Barnsley leaf and Julia set, and most of the figures have been re-drawn.
Mathematics of Surfaces XII ; 12th IMA International Conference, Sheffield, UK, September 4-6, 2007, Proceedings
This book constitutes the refereed proceedings of the 12th IMA International Conference on the Mathematics of Surfaces, held in Sheffield, UK in September 2007. The papers cover a range of ideas from underlying theoretical tools to industrial uses of surfaces.
Mathematics of Surfaces XI ; 11th IMA International Conference, Loughborough, UK, September 5-7, 2005, Proceedings
Constitutes the refereed proceedings of the 11th IMA International Conference on the Mathematics of Surfaces, held in Loughborough, UK in September 2005. Among the topics addressed are Voronoi diagrams, linear systems, curvatures on meshes, approximate parameterization, condition numbers, pythagorean hodographs, and more.
Mathematics and Culture II : Visual Perfection: Mathematics and Creativity
This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. This volume is devoted to the analysis of dynamical systems with emphasis on problems of uncertainty, whereas the second volume will be devoted to control. It combines features of a detailed introductory textbook with that of a reference source. The book contains many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions.
Mathematical Theory of Feynman Path Integrals : An Introduction
Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory.
Mathematical Survey Lectures 1943-2004
This collection traces the career of Beno Eckmann, whose work ranges across a broad spectrum of mathematical concepts from topology and differential geometry through homological algebra to group theory. One of our most influential living mathematicians, Eckmann has been associated for nearly his entire professional life with the Swiss Federal Institute of Technology Zurich (ETH), as student, lecturer, professor, and professor emeritus.
Mathematical Morphology : 40 Years On ; Proceedings of the 7th International Symposium on Mathematical Morphology, April 18-20, 2005
Mathematical Morphology is a speciality in Image Processing and Analysis, which considers images as geometrical objects, to be analyzed through their interactions with other geometrical objects. It relies on several branches of mathematics, such as discrete geometry, topology, lattice theory, partial differential equations, integral geometry and geometrical probability. It has produced fast and efficient algorithms for computer analysis of images, and has found applications in bio-medical imaging, materials science, geoscience, remote sensing, quality control, document processing and data analysis. This book contains the 43 papers presented at the 7th International Symposium on Mathematical Morphology, held in Paris on April 18-20, 2005. It gives a lively state of the art of current research topics in this field. It also marks a milestone, the 40 years of uninterrupted development of this ever-expanding domain.
Introduction to Symplectic Dirac Operators
One of the basic ideas in differential geometry is that the study of analytic properties of certain differential operators acting on sections of vector bundles yields geometric and topological properties of the underlying base manifold. Symplectic spinor fields are sections in an L^2-Hilbert space bundle over a symplectic manifold and symplectic Dirac operators, acting on symplectic spinor fields, are associated to the symplectic manifold in a very natural way. Hence they may be expected to give interesting applications in symplectic geometry and symplectic topology. These symplectic Dirac operators are called Dirac operators, since they are defined in an analogous way as the classical Riemannian Dirac operator known from Riemannian spin geometry. They are called symplectic because they are constructed by use of the symplectic setting of the underlying symplectic manifold. This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology,
Intelligent Information Technology ; 7th International Conference on Information Technology, CIT 2004, Hyderabad, India, December 20-23, 2004, Proceedings
Focused on the latest research findings on all topics in the area of information technology. Although the natural focus was on computer science issues, research results contributed from management, business and other disciplines formed an integral part. We received more than 200 papers from over 27 countries in the areas of com- tational intelligence, neural networks, mobile and adhoc networks, security, databases, software engineering, signal and image processing, and Internet and WWW-based computing. The programme committee, consisting of eminent researchers, academicians and practitioners, finally selected 43 full papers on the basis of reviewer grades. This proceedings contains the research papers selected for presentation at the c- ference and this is the first time that the proceedings have been published in the Lecture Notes in Computer Science (LNCS) series. The poster papers are being printed as a separate conference proceedings.
