Author : Sidney A. Morris
Publisher : MDPI
Page : 229 pages
File Size : 18,13 MB
Release : 2018-09-27
Category : Mathematics
ISBN : 3038422681
This book is a printed edition of the Special Issue "Topological Groups: Yesterday, Today, Tomorrow" that was published in Axioms
Author : Sidney A. Morris
Publisher : MDPI
Page : 160 pages
File Size : 36,40 MB
Release : 2019-03-05
Category : Mathematics
ISBN : 303897644X
Following the tremendous reception of our first volume on topological groups called "Topological Groups: Yesterday, Today, and Tomorrow", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Well-known researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.
Author : Karl H. Hofmann
Publisher : Walter de Gruyter GmbH & Co KG
Page : 1076 pages
File Size : 36,7 MB
Release : 2023-10-23
Category : Mathematics
ISBN : 3111172600
Author : Fanzhang Li
Publisher : Walter de Gruyter GmbH & Co KG
Page : 534 pages
File Size : 17,52 MB
Release : 2018-11-05
Category : Computers
ISBN : 3110499509
This book explains deep learning concepts and derives semi-supervised learning and nuclear learning frameworks based on cognition mechanism and Lie group theory. Lie group machine learning is a theoretical basis for brain intelligence, Neuromorphic learning (NL), advanced machine learning, and advanced artifi cial intelligence. The book further discusses algorithms and applications in tensor learning, spectrum estimation learning, Finsler geometry learning, Homology boundary learning, and prototype theory. With abundant case studies, this book can be used as a reference book for senior college students and graduate students as well as college teachers and scientific and technical personnel involved in computer science, artifi cial intelligence, machine learning, automation, mathematics, management science, cognitive science, financial management, and data analysis. In addition, this text can be used as the basis for teaching the principles of machine learning. Li Fanzhang is professor at the Soochow University, China. He is director of network security engineering laboratory in Jiangsu Province and is also the director of the Soochow Institute of industrial large data. He published more than 200 papers, 7 academic monographs, and 4 textbooks. Zhang Li is professor at the School of Computer Science and Technology of the Soochow University. She published more than 100 papers in journals and conferences, and holds 23 patents. Zhang Zhao is currently an associate professor at the School of Computer Science and Technology of the Soochow University. He has authored and co-authored more than 60 technical papers.
Author : Carles Casacuberta
Publisher : Springer
Page : 118 pages
File Size : 36,38 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540473416
The Symposium on the Current State and Prospects of Mathematics was held in Barcelona from June 13 to June 18, 1991. Seven invited Fields medalists gavetalks on the development of their respective research fields. The contents of all lectures were collected in the volume, together witha transcription of a round table discussion held during the Symposium. All papers are expository. Some parts include precise technical statements of recent results, but the greater part consists of narrative text addressed to a very broad mathematical public. CONTENTS: R. Thom: Leaving Mathematics for Philosophy.- S. Novikov: Role of Integrable Models in the Development of Mathematics.- S.-T. Yau: The Current State and Prospects of Geometry and Nonlinear Differential Equations.- A. Connes: Noncommutative Geometry.- S. Smale: Theory of Computation.- V. Jones: Knots in Mathematics and Physics.- G. Faltings: Recent Progress in Diophantine Geometry.
Author : Jürgen Berndt
Publisher : Springer
Page : 135 pages
File Size : 39,98 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540491716
Generalized Heisenberg groups, or H-type groups, introduced by A. Kaplan, and Damek-Ricci harmonic spaces are particularly nice Lie groups with a vast spectrum of properties and applications. These harmonic spaces are homogeneous Hadamard manifolds containing the H-type groups as horospheres. These notes contain a thorough study of their Riemannian geometry by means of a detailed treatment of their Jacobi vector fields and Jacobi operators. Some problems are included and will hopefully stimulate further research on these spaces. The book is written for students and researchers, assuming only basic knowledge of Riemannian geometry, and it contains a brief survey of the background material needed to follow the entire treatment.
Author : Claudio Chamon
Publisher : Oxford University Press
Page : 705 pages
File Size : 50,68 MB
Release : 2017-02-16
Category : Science
ISBN : 019108879X
This book contains lecture notes by world experts on one of the most rapidly growing fields of research in physics. Topological quantum phenomena are being uncovered at unprecedented rates in novel material systems. The consequences are far reaching, from the possibility of carrying currents and performing computations without dissipation of energy, to the possibility of realizing platforms for topological quantum computation.The pedagogical lectures contained in this book are an excellent introduction to this blooming field. The lecture notes are intended for graduate students or advanced undergraduate students in physics and mathematics who want to immerse in this exciting XXI century physics topic. This Les Houches Summer School presents an overview of this field, along with a sense of its origins and its placement on the map of fundamental physics advancements. The School comprised a set of basic lectures (part 1) aimed at a pedagogical introduction of the fundamental concepts, which was accompanied by more advanced lectures (part 2) covering individual topics at the forefront of today's research in condensed-matter physics.
Author : Luigi Fortuna
Publisher : World Scientific
Page : 222 pages
File Size : 14,81 MB
Release : 2009-04-15
Category : Technology & Engineering
ISBN : 9814468592
Since the birth of the Chua circuit in 1983, a considerable number of fruitful, fascinating and relevant research topics have arisen. In honor of the 25th anniversary of the invention of Chua's circuit, this book presents the 25 years of research on the implementation of Chua's circuit, and also discusses future directions and emerging applications of recent results.The purpose of the book is to provide researchers, PhD students, and undergraduate students a research monograph containing both fundamentals on the topics and advanced results that have been recently obtained. With about 60 illustrations included in the book, it also shows the detailed schematics of several different implementations that can be easily reproduced with a low-cost experimental setup and PC-based measurement instrumentation.
Author : Thomas Bartsch
Publisher : Springer
Page : 162 pages
File Size : 11,67 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540480994
Symmetry has a strong impact on the number and shape of solutions to variational problems. This has been observed, for instance, in the search for periodic solutions of Hamiltonian systems or of the nonlinear wave equation; when one is interested in elliptic equations on symmetric domains or in the corresponding semiflows; and when one is looking for "special" solutions of these problems. This book is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functionals. These topological methods are developed in detail with new calculations of the equivariant Lusternik-Schnirelmann category and versions of the Borsuk-Ulam theorem for very general classes of symmetry groups. The Morse-Conley theory is applied to bifurcation problems, in particular to the bifurcation of steady states and hetero-clinic orbits of O(3)-symmetric flows; and to the existence of periodic solutions nearequilibria of symmetric Hamiltonian systems. Some familiarity with the usualminimax theory and basic algebraic topology is assumed.
Author : Tai-Danae Bradley
Publisher : MIT Press
Page : 167 pages
File Size : 30,19 MB
Release : 2020-08-18
Category : Mathematics
ISBN : 0262359626
A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.
