الصفحة 1
الصفحة 1
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 Mathematics
Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis.
Number Theory ; Vol. II : Analytic and Modern Tools
The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects.
Number Theory ; Vol. I : Tools and Diophantine Equations
The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects.
Number Fields and Function Fields – Two Parallel Worlds
These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives.
Nonsmooth Analysis
The book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts (tangent and normal cones) and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and finally presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed; this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. The presentation is rigorous, with detailed proofs. Each chapter ends with bibliographic notes and exercises.
NonlinearWaves and Solitons on Contours and Closed Surfaces
The present volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems.
Nonlinear Problems of Elasticity
This second edition is an enlarged, completely updated, and extensively revised version of the authoritative first edition. It is devoted to the detailed study of illuminating specific problems of nonlinear elasticity. The mathematical tools from nonlinear analysis are given self-contained presentations where they are needed. This book begins with chapters on (geometrically exact theories of) strings, rods, and shells, and on the applications of bifurcation theory and the calculus of variations to problems for these bodies. The book continues with chapters on tensors, three-dimensional continuum mechanics, three-dimensional elasticity, large-strain plasticity, general theories of rods and shells, and dynamical problems. Each chapter contains a wealth of interesting, challenging, and tractable exercises.
Nonlinear and Optimal Control Theory : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy June 19–29, 2004
The lectures gathered in this volume present some of the different aspects of Mathematical Control Theory. Adopting the point of view of Geometric Control Theory and of Nonlinear Control Theory, the lectures focus on some aspects of the Optimization and Control of nonlinear, not necessarily smooth, dynamical systems. Specifically, three of the five lectures discuss respectively: logic-based switching control, sliding mode control and the input to the state stability paradigm for the control and stability of nonlinear systems. The remaining two lectures are devoted to Optimal Control: one investigates the connections between Optimal Control Theory, Dynamical Systems and Differential Geometry, while the second presents a very general version, in a non-smooth context, of the Pontryagin Maximum Principle.
Non-Euclidean Geometries : János Bolyai Memorial Volume
Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics. This book is intended for those who teach, study, and do research in geometry and history of mathematics. Cultural historians, physicists, and computer scientists will also find it an important source of information.
Noncommutative Geometry and Number Theory : Where Arithmetic meets Geometry and Physics
This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local Lfactors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.
Nexus Network Journal 9,2 : Architecture and Mathematics
This volume is dedicated to "Mechanics in Architecture", that is, the science of structural mechanics, including the behaviour of structures, internal forces, and deformation, as well as the development of new structural systems to resist thrusts as a result of new architectural forms. It is a field of enquiry that examines a particular aspect of the relationships between architecture and the mathematical sciences. Some of the papers in this issue were presented at the Nexus 2006 conference during a special session dedicated to mechanics. Other research papers focus on an eighteenth-century Belgian pyramid, aspects of "fractal" architecture, and properties of a family of irrational values. The issue also includes a description and evaluation of a university-level course in architecture and mathematics, Rachel Fletcher's Geometer's Angle column, and book reviews.
Nexus Network Journal 9,1 : Architecture and Mathematics
This issue is dedicated to various kinds of patterns in architecture. Buthayna Eilouti and Amer Al-Jokhadar address patterns in shape grammars in the ground plans of Mamluk madrasas, religious schools. Giulio Magli goes back further in history, to the age of Greek colonies in Italy before they were conquered by the Romans, to examine patterns in urban design. In Traditional Patterns in Pyrgi of Chios: Mathematics and Community Charoula Stathopoulou examines the geometric patterns that decorate the buildings of the town of Pyrgi, on the Greek island of Chios. Curve Fitting is a study of ways to construct a function so that its graph most closely approximates the pattern given by a set of points.
Nexus Network Journal : Leonardo da Vinci : Architecture and Mathematics
The quintessential Renaissance Man, Leonardo da Vinci was well aware of the fundamental importance of mathematics for architecture. This issue of the Nexus Network Journal examines Leonardo’s knowledge of theoretical mathematics, explores how he used concepts of geometry in his designs for architectural projects, and reports on a real-life construction project using Leonardo’s principles. Authors include Sylvie Duvernoy, Kim Williams, Rinus Roelofs, Biagio Di Carlo, Mark Reynolds, João Pedro Xavier, Vesna Petresin, Christopher Glass, and Jane Burry. To complete the issue Rachel Fletcher writes her Geometer’s Angle column on "Dynamic Symmetry", Michael Ostwald reviews A Theory of General Ethics by Warwick Fox, Sarah Clough Edwards reviews Inigo Jones and the Classical Tradition by Christy Anderson, and Sylvie Duvernoy reviews Architecture and Mathematics in Ancient Egypt by Corinna Rossi.
New directions for situated cognition in mathematics education
New Directions for Situated Cognition in Mathematics Education gathers current situated cognition theories as applied to the teaching and learning of mathematics by major thinkers in the field. Arranged to be read cover to cover or by the individual chapter, this unique volume examines situated cognition in all levels and contexts of math instruction, in traditional school settings, in adult education, at home, on the job, or on the street. Well-known authorities explore beyond traditional concepts of good practice and the relationship between knowledge and the learner while synthesizing insights from related perspectives, including semiotics, activity theory, ardinas practice, and Moll’s concept of funds of knowledge.
New Approaches to Circle Packing in a Square : With Program Codes
This book summarizes results achieved in solving the circle packing problem over the past few years, providing the reader with a comprehensive view of both theoretical and computational achievements. Typically illustrations of problem solutions are shown, elegantly displaying the results obtained.Beyond the theoretically challenging character of the problem, the solution methods developed in the book also have many practical applications. Direct applications include cutting out congruent two-dimensional objects from an expensive material, or locating points within a square in such a way that the shortest distance between them is maximal.
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.
Nearest Neighbor Search : A Database Perspective
Modern applications are both data and computationally intensive and require the storage and manipulation of voluminous traditional (alphanumeric) and nontraditional data sets (images, text, geometric objects, time-series). Examples of such emerging application domains are: Geographical Information Systems (GIS), Multimedia Information Systems, CAD/CAM, Time-Series Analysis, Medical Information Sstems, On-Line Analytical Processing (OLAP), and Data Mining. These applications pose diverse requirements with respect to the information and the operations that need to be supported. From the database perspective, new techniques and tools therefore need to be developed towards increased processing efficiency. This monograph explores the way spatial database management systems aim at supporting queries that involve the space characteristics of the underlying data, and discusses query processing techniques for nearest neighbor queries. It provides both basic concepts and state-of-the-art results in spatial databases and parallel processing research, and studies numerous applications of nearest neighbor queries.
Neanderthals Revisited : New Approaches and Perspectives
This volume presents cutting-edge research by leading scientists re-examining the major debates in Neanderthal research with the use of innovative state-of-the art methods and exciting new theoretical approaches.Topics addressed include the re-evaluation of Neanderthal anatomy, inferred adaptations and habitual activities, developmental patterns, phylogenetic relationships, and the Neanderthal extinction; new methods include computer tomography, 3D geometric morphometrics, ancient DNA and bioenergetics. The diverse contributions offer fresh insights and advances in Neanderthal and modern human origins research.
Multiplicative Invariant Theory
Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far.. Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori.
