الصفحة 5
الصفحة 5
C*-algebras and Elliptic Theory
This volume contains the proceedings of the conference on "C*-algebras and Elliptic Theory" held in Bedlewo, Poland, in February 2004. It consists of original research papers and expository articles focussing on index theory and topology of manifolds.The collection offers a cross-section of significant recent advances in several fields, the main subject being K-theory (of C*-algebras, equivariant K-theory). A number of papers is related to the index theory of pseudodifferential operators on singular manifolds (with boundaries, corners) or open manifolds. Further topics are Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others.
Braid Groups
Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory of braids stems from their attractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces. In this presentation the authors thoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow representations of the braid groups, the Alexander--Conway and Jones link polynomials, connections with the representation theory of the Iwahori--Hecke algebras, and the Garside structure and orderability of the braid groups.
Bionanotechnology : Proteins to Nanodevices
Bionanotechnology is the key integrative technology of the 21st century and aims to use the knowledge, gathered from the natural construction of cellular systems, for the advancement of science and engineering. Investigating the topology and communication processes of cell parts can lead to invention of novel biological devices with exciting applications. Though microscale to nanoscale research offers an excellent space for the development of futuristic technologies, a number of challenges must be overcome. Due to paucity of a dedicated literature on the protein based nanodevices we bring you this monograph that combines collective research works of scientists probing into this fascinating universe of bionanotechnology. The monograph has been written with an aim of surveying engineering design principles of biomolecular nanodevices, prototype nanodevices based on redox proteins, bacteriorhodopsins and natural fibers, and touching upon the future developments in the field.
Biologically Inspired Approaches to Advanced Information Technology ; 2nd International Workshop, BioADIT 2006, Osaka, Japan 26-27, 2006, Proceedings
This book contains 30 articles and three abstracts of invited talks presented at The Second International Workshop on Biologically Inspired Approaches for Advanced Information Technology,The workshop is intended to provide an e?ective forum for original research results in the ?eld of bio-inspired approaches to advanced information technologies. It also serves to foster the connection between biological paradigms and solutions to building the next-generation information systems.
Axiom of Choice
AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom, shunned by some, used indiscriminately by others. This treatise shows paradigmatically that:Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC).Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games).Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.
Analytical and Numerical Approaches to Mathematical Relativity
This book contains a representative collection of surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods. This book addresses graduate students and specialist researchers alike.
An Undergraduate Primer in Algebraic Geometry
This book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors and linear series, Riemann–Roch and Riemann–Hurwitz Theorems.The approach in this book is purely algebraic. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The prerequisites consist of the knowledge of basics in affine and projective geometry, basic algebraic concepts regarding rings, modules, fields, linear algebra, basic notions in the theory of categories, and some elementary point–set topology.
An Invitation to Morse Theory
This treatment of Morse Theory focuses on applications and is intended for a graduate course on differential or algebraic topology. This is the first textbook to include topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory.
An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile.
An Introduction to Structural Optimization
This textbook gives an introduction to all three classes of geometry optimization problems of mechanical structures: sizing, shape and topology optimization. The style is explicit and concrete, focusing on problem formulations and numerical solution methods. The treatment is detailed enough to enable readers to write their own implementations. On the book's homepage, programs may be downloaded that further facilitate the learning of the material covered.
An Introduction to Manifolds
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology.
Algorithmic topology and classification of 3-manifolds
This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology. The book is intended to combine the pedagogical approach of a graduate textbook with the completeness and reliability of a research monograph.
Algebraic Geometry and Geometric Modeling
Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically. Geometric Modeling uses every day, in order to solve practical and difficult problems, digital shapes based on algebraic models. In this book, we have collected articles bridging these two areas. The confrontation of the different points of view results in a better analysis of what the key challenges are and how they can be met. We focus on the following important classes of problems: implicitization, classification, and intersection. The combination of illustrative pictures, explicit computations and review articles will help the reader to handle these subjects.
Algebraic Cycles, Sheaves, Shtukas, and Moduli : Impanga Lecture Notes
The articles in this volume are devoted to: - moduli of coherent sheaves. - principal bundles and sheaves and their moduli. - new insights into Geometric Invariant Theory. - stacks of shtukas and their compactifications. - algebraic cycles vs. commutative algebra. - Thom polynomials of singularities. - zero schemes of sections of vector bundles.
Algebra 3 : Homological Algebra and Its Applications
Includes algebra, deals with important topics in homological algebra, including abstract theory of derived functors, sheaf co-homology, and an introduction to etale and l-adic co-homology. It contains four chapters which discuss homology theory in an abelian category together with some important and fundamental applications in geometry, topology, algebraic geometry (including basics in abstract algebraic geometry), and group theory.
Advances in Geometric Modeling and Processing ; 5th International Conference, GMP 2008, Hangzhou, China, April 23-25, 2008. Proceedings
This book constitutes the refereed proceedings of the 5th International Conference on Geometric Modeling and Processing, GMP 2008, held in Hangzhou, China, in April 2008.
Advanced studies in biometrics : Summer School on biometrics, Alghero, Italy, June 2-6, 2003. Revised Selected Lectures and Papers
This book originates from an international summer school on biometrics, held in Alghero, Italy, in June 2003. The seven revised tutorial lectures by leading researchers introduce the reader to biometrics-based person authentication, fingerprint recognition, gait recognition, various aspects of face recognition and face detection, topologies for biometric recognition, and hand detection. Also included are the four best selected student papers, all dealing with face recognition.
Ad-Hoc Networking Towards Seamless Communications
Ad-Hoc Networking Towards Seamless Communications is dedicated to an area that attracts growing interest in academia and industry and concentrates on wireless ad hoc networking paradigm. The persistent efforts to acquire the ability to establish dynamic wireless connections from anywhere to anyone with any device without prerequisite imbedded infrastructure move the communications boundaries towards ad-hoc networks. Recently, ad hoc networking has attracted growing interest due to advances in wireless communications, and developed framework for running IP based protocols. The expected degree of penetration of these networks will depend on the successful resolution of the key features.
Active Sensor Planning for Multiview Vision Tasks
Describes some effective strategies to generate a sequence of viewing poses and sensor settings for optimally completing a perception task. Several methods are proposed to solve the problems in both model-based and nonmodel-based vision tasks. For model-based applications, the method involves determination of the optimal sensor placements and a shortest path through these viewpoints for automatic generation of a perception plan.
A Taste of Topology
The present book grew out of notes for an introductory topology course at the University of Alberta. It provides a concise introduction to set-theoretic topology (and to a tiny little bit of algebraic topology). Great care has been devoted to the selection of examples that are not self-serving, but already accessible for students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis.
