Using the Borsuk-Ulam Theorem / Lectures on Topological Methods in Combinatorics and Geometry, Matousek Jiri, BjÃ¶rner A., Ziegler G.M.

Àâòîð: Edited by B?la Bollob?s Íàçâàíèå: Combinatorics, Geometry and Probability ISBN: 0521607663 ISBN-13(EAN): 9780521607667 Èçäàòåëüñòâî: Cambridge Academ Ðåéòèíã: Öåíà: 8314 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: Paul Erdos was one of the greatest mathematicians of this century, known the world over for his brilliant ideas and stimulating questions. On the date of his 80th birthday a conference was held in his honour at Trinity College, Cambridge. Many leading combinatorialists attended. Their subsequent contributions are collected here. The areas represented range from set theory and geometry, through graph theory, group theory and combinatorial probability, to randomised algorithms and statistical physics. Erdos himself was able to give a survey of recent progress made on his favourite problems. Consequently this volume, consisting of in-depth studies at the frontier of research, provides a valuable panorama across the breadth of combinatorics as it is today.

Îïèñàíèå: This book is based on two series of lectures given at a summer school on algebraic combinatorics at the Sophus Lie Centre in Nordfjordeid, Norway, in June 2003, one by Peter Orlik on hyperplane arrangements, and the other one by Volkmar Welker on free resolutions. Both topics are essential parts of current research in a variety of mathematical fields, and the present book makes these sophisticated tools available for graduate students.

Àâòîð: Berger, Mitchell A. Kauffman, Louis H. Khesin, Bor Íàçâàíèå: Lectures on topological fluid mechanics ISBN: 3642008364 ISBN-13(EAN): 9783642008368 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 7418 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: Contains research papers that cover topics such as fundamental aspects of mathematical fluid mechanics, topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, DNA tangles and knotted DNAs in sedimentation.

Àâòîð: Cardona Alexander Íàçâàíèå: Geometric, Algebraic and Topological Methods for Quantum Fie ISBN: 9814460044 ISBN-13(EAN): 9789814460040 Èçäàòåëüñòâî: World Scientific Publishing Ðåéòèíã: Öåíà: 24224 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory.This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.

Îïèñàíèå: This book presents the development and application of some topological methods in the analysis of data coming from 3D dynamical systems (or related
objects). The aim is to emphasize the scope and limitations of the methods, what they provide and what they do not provide. Braid theory, the topology of surface homeomorphisms,
data analysis and the reconstruction of phase-space dynamics are thoroughly addressed.

Îïèñàíèå: This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.

Àâòîð: Arnold Íàçâàíèå: Topological Methods in Hydrodynamics ISBN: 038794947X ISBN-13(EAN): 9780387949475 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 19304 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: Topological hydrodynamics is a young branch of mathematics studying topological features of flows with complicated trajectories, as well as their applications
to fluid motions. It is situated at the crossroad of hyrdodynamical stability theory, Riemannian and symplectic geometry, magnetohydrodynamics, theory of Lie algebras and Lie groups,
knot theory, and dynamical systems. Applications of this approach include topological classification of steady fluid flows, descriptions of the Korteweg-de Vries equation as a geodesic
flow, and results on Riemannian geometry of diffeomorphism groups, explaining, in particular, why longterm dynamical weather forecasts are not reliable.

Topological Methods
in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics for a unified point of view. T
e necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures. The book is accessible to graduate students as well as
to both pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems and differential geometry.

Îïèñàíèå: Since the 1980s, the theory of groups - in particular simple groups, finite and algebraic - has influenced a number of diverse areas of mathematics. Such areas
include topics where groups have been traditionally applied, such as algebraic combinatorics, finite geometries, Galois theory and permutation groups, as well as several more recent
developments. Among the latter are probabilistic and computational group theory, the theory of algebraic groups over number fields, and model theory, in each of which th
re has been a major recent impetus provided by simple group theory.

In addition, there is still great interest in local analysis in finite groups, with substantial new input from
methods of geometry and amalgams, and particular emphasis on the revision project for the classification of finite simple groups. This book contains 20 survey articles covering many of
the above developments. It should prove valuable for those working in the theory of groups and its applications.

Àâòîð: Ahlswede, Rudolf Blinovsky, Vladimir Íàçâàíèå: Lectures on advances in combinatorics ISBN: 3540786015 ISBN-13(EAN): 9783540786016 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 7424 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: Includes a solution to the 4m-conjecture of Erdos/Ko/Rado 1938, an answer to a question of Erdos (1962) in combinatorial number theory, and the discovery that the AD-inequality implies more general and sharper number theoretical inequalities than for instance Behrend`s inequality.

Àâòîð: Jin Akiyama; William Y.C. Chen; Mikio Kano; Xuelia Íàçâàíèå: Discrete Geometry, Combinatorics and Graph Theory ISBN: 3540706658 ISBN-13(EAN): 9783540706656 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 10394 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: This book constitutes the thoroughly refereed post-proceedings of the 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005, held in Tianjin, China, as well as in Xi`an, China, in November 2005. The 30 revised full papers address all current issues in discrete algorithmic geometry, combinatorics and graph theory.

Îïèñàíèå: This book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage
includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and
applications to best approximation theory, partial equations and boundary value problems. Self-contained and unified in presentation, the book considers the existence of equilibrium
points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities.

It also provides the latest developments in KKM theory and
degree theory for nonlinear set-valued mappings.

Îïèñàíèå: ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 14 18, 2002 at Taiyuan, Shanxi Province, China. This conference was
organized by Mathematical School of Peking University, Academy of Ma
hematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored
by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University. Attending the conference were 166 mathematicians from 21 countries and areas
in the world with 53 invited speakers and 30 contributors presenting their lectures.

This conference aims at an overview of the recent development in nonlinear analysis. It
covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrodinger equations, semilinear elliptic
equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.