Format: Hardback, 155 pages, height x width: 235x155 mm, 2 Illustrations, black and white; XIII, 155 p. 2 illus
Series: The Frontiers Collection
Pub. Date: 27-Mar-2023
ISBN-13: 9783031212536
This book deals with the rise of mathematics in physical sciences, beginning with Galileo and Newton and extending to the present day. The book is divided into two parts. The first part gives a brief history of how mathematics was introduced into physics-despite its "unreasonable effectiveness" as famously pointed out by a distinguished physicist-and the criticisms it received from earlier thinkers. The second part takes a more philosophical approach and is intended to shed some light on that mysterious effectiveness. For this purpose, the author reviews the debate between classical philosophers on the existence of innate ideas that allow us to understand the world and also the philosophically based arguments for and against the use of mathematics in physical sciences. In this context, Schopenhauer's conceptions of causality and matter are very pertinent, and their validity is revisited in light of modern physics. The final question addressed is whether the effectiveness of mathematics can be explained by its "existence" in an independent platonic realm, as Goedel believed. The book aims at readers interested in the history and philosophy of physics. It is accessible to those with only a very basic (not professional) knowledge of physics.
Shahen Hacyan studied Physics (1965-1968) at the National Autonomous University of Mexico (UNAM) and obtained a Ph.D. in Theoretical Physics in 1972 at the University of Sussex, UK. After returning to Mexico, he took up a position at the Institute of Astronomy, at UNAM. His fields of interest at that time were Relativistic Astrophysics, General Relativity and Cosmology. In 1990, he moved to the Institute of Physics, also at UNAM, and worked on Quantum Field Theory and Quantum Optics, as well as delving into philosophical aspects of Physics. Prof. Hacyan is currently Investigador Titular C (equivalent to Full Professor) at UNAM. Shahen Hacyan has published more than 90 scientific papers in respected international journals such as Physical Reviews, Astrophysical Journal, Journal of Mathematical Physics. He has also been very active as Popularizer of science in Mexico, having published 11 popular science books, 9 of them with Fondo de Cultura Economica (FCE), the main editorial house in Mexico. From 1994 to 2009, Prof. Hacyan was in charge of a weekly newspaper column on popular science, Aleph Cero, in one of the main Mexican newspapers, Reforma. There he published more than 600 articles on popular science. His 11 books on popular science span all of theoretical physics and beyond, addressing Cosmology, Black Holes, Relativity, the Quantum World and the Universe, Interstellar Travels, Quantum Mechanics and Gravitational Waves. In 2004, again with FCE, he also published a book about the philosophy of Physics, Fisica y Metafisica del Espacio y el Tiempo (Physics and metaphysics of space and time).
Format: Paperback / softback, 186 pages, height x width: 235x155 mm, XV, 186 p., 1 Paperback / softback
Pub. Date: 19-Apr-2023
ISBN-13: 9783031139161
Written by an author who was at the forefront of developments in multivariable spectral theory during the seventies and the eighties, this book describes the spectral mapping theorem in various settings. In this second edition, the Bluffer's Guide has been revised and expanded, whilst preserving the engaging style of the first.
Starting with a summary of the basic algebraic systems ? semigroups, rings and linear algebras ? the book quickly turns to topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Key aspects of spectral theory are covered, in one and several variables. Finally the case of an arbitrary set of variables is discussed.
Spectral Mapping Theorems is an accessible and easy-to-read guide, providing a convenient overview of the topic to both students and researchers.
"I certainly plan to add it to my own mathematical library" ? Anthony Wickstead in the Irish Mathematical Society Bulletin
"An excellent read" ? Milena Stanislavova in the Mathematical Reviews
"[ Offers] a fresh perspective even for experts [ ...] Recommended" ? David Feldman in Choice
1 Algebra.- 2 Topology.- 3 Topological algebra.- 4 Spectral theory.- 5 Several variables.- 6 Many Variables.
Format: Paperback / softback, 330 pages, height x width: 235x155 mm, 21 Illustrations, color; 3 Illustrations, black and white; XII, 330 p. 24 illus., 21 illus. in color
Series: Abel Symposia 16
Pub. Date: 22-Feb-2023
ISBN-13: 9783030812980
This book consists of contributions from the participants of the Abel Symposium 2019 held in Alesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity. The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.
Four-dimensional homogeneous generalizations of Einstein Metrics.- Conformal and isometric embeddings of gravitational instantons.- Recent results on closed G2-structures, by Anna Fino and Alberto Raffero.- Almost Zoll affine surfaces.- Distinguished curves and fist integrals on Poincare-Einstein and other conformally singular geometries.- A car as parabolic geometry.- Legendrian cone structures and contact prolongations.- The search for solitons on homogeneous spaces.- On Ricci negative Lie groups.- Semi-Riemannian cones.- Building new Einstein spaces by deforming symmetric Einstein spaces.- Remarks on highly supersymmetric backgrounds of 11-dimensional supergravity.- Krichever-Novikov type algebras.
Format: Paperback / softback, 580 pages, height x width: 235x155 mm,
68 Illustrations, color; 19 Illustrations, black and white; XX, 580 p. 87 illus., 68 illus. in color.
Series: Applied Mathematical Sciences 209
Pub. Date: 10-Mar-2023
ISBN-13: 9783030914295
Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose-Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin-Ono, Davey-Stewartson, and Kadomtsev-Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena.By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.
Acronyms.- Glossary.- 1 General Introduction.- 2 Generalities and Basic Facts.- 3 Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE.- 4 Davey-Stewartson and Related Systems.- 5 Kadomtsev-Petviashvili and Related Equations.- 6 Novikov-Veselov and Derivative Nonlinear Schroedinger Equations.- Index.
Format: Paperback / softback, 353 pages, height x width: 235x155 mm, 112 Tables,
color; 84 Illustrations, color; 11 Illustrations, black and white; X, 353 p. 95 illus., 84 illus. in color.
Series: Fields Institute Communications 85
Pub. Date: 23-Feb-2023
ISBN-13: 9783030850555
Curated by the Fields Institute for Research in Mathematical Sciences from their COVID-19 Math Modelling Seminars, this first in a series of volumes on the mathematics of public health allows readers to access the dominant ideas and techniques being used in this area, while indicating problems for further research. This work brings together experts in mathematical modelling from across Canada and the world, presenting the latest modelling methods as they relate to the COVID-19 pandemic. A primary aim of this book is to make the content accessible so that researchers share the core methods that may be applied elsewhere. The mathematical theories and technologies in this book can be used to support decision makers on critical issues such as projecting outbreak trajectories, evaluating public health interventions for infection prevention and control, developing optimal strategies to return to a new normal, and designing vaccine candidates and informing mass immunization program. Topical coverage includes: basic susceptible-exposed-infectious-recovered (SEIR) modelling framework modified and applied to COVID-19 disease transmission dynamics; nearcasting and forecasting for needs of critical medical resources including personal protective equipment (PPE); predicting COVID-19 mortality; evaluating effectiveness of convalescent plasma treatment and the logistic implementation challenges; estimating impact of delays in contact tracing; quantifying heterogeneity in contact mixing and its evaluation with social distancing; modelling point of care diagnostics of COVID-19; and understanding non-reporting and underestimation. Further, readers will have the opportunity to learn about current modelling methodologies and technologies for emerging infectious disease outbreaks, pandemic mitigation rapid response, and the mathematics behind them. The volume will help the general audience and experts to better understand the important role that mathematics has been playing during this on-going crisis in supporting critical decision-making by governments and public health agencies.
Diverse local epidemics reveal the distinct effects of population density, demographics, climate, depletion of susceptibles, and intervention in the first wave of COVID-19 in the United States (N. Ashfordi, B. Holder, M. Bahrami, D. Lichtblau).- Describing, modelling and forecasting the spatial and temporal spread of COVID-19 (J. Arino).- A logistic growth model with logistically varying carrying capacity for Covid-19 deaths using data from Ontario, Canada (G. Bucyibaruta, C.B. Dean, E.M. Renouf).- COVID-19 in Ontario (R. Fields, L Humphrey, E.W. Thommes, M.G. Cojocaru).- Sub-epidemic model forecasts during the first wave of the COVID-19 pandemic in the USA and European hotspots (G. Chowell, R. Rothenberg, K. Roosa, A. Tariq, J.M. Hyman, R. Luo).- A Model on the Large Scale Use of Convalescent Plasma to Treat Patients with Severe Symptoms (X. Huo).- Don't wait, re-escalate: delayed action results in longer duration of COVID-19 restrictions (A. Hurford, J. Watmough).- Generalized Additive Models to Capture the Death Rates in Canada COVID-19 (F. Izadi).- Real-time prediction of the end of an epidemic wave (Q. Griette, Z. Liu, P. Magal, R.N. Thompson).- The Effect that Heterogeneity in Social Distancing Has on the Infection Peak (C. McCluskey).- Forecasting PPE Demand for Ontario Acute Care Hospitals During COVID-19 (B. Sander).- Learning COVID-19 Mitigation Strategies using Reinforcement Learning (N. Denis, A. El-Hajj, B Drummond, Y. Abiza, K.C. Gopaluni).- Joint Modeling of Hospitalization and Mortality of Ontario Covid-19 cases (D.Z. Xi).- Evaluating the risk of reopening the border: a case study of Ontario (Canada) to New York (USA) using mathematical modeling (P. Yuan, E. Aruffo, Q. Li, J. Li, Y. Tan, T. Zheng, J. David, N. Ogden, E. Gatov, E. Gournis, S. Collier, B. Sander, G. Fan, J. Heffernan, J. Li, J.D. Kong, J. Arino, J. Belair, J. Watmough, H. Zhu).- Optimal staged reopening schedule based on ICU capacity (K. Nah, M. Chen, A. Asgary, Z. McCarthy, F. Scarabel, Y. Xiao, N.L. Bragazzi, J.M. Heffernan, N.H. Ogden, J.Wu).- Mathematics of the Pandemic (M.R. Murty, V.K. Murty).- A mathematical model for evaluating the impact of non-pharmaceutical interventions on the COVID-19 epidemic in the United Kingdom (H. Zhu).- COVID-19 in Japan (H. Nishiura).