Presents the set function \mathcal{T}, of great importance to the study of
continuum theory, in a clear and structured way
Starts with a gentle introductory chapter, gradually advancing towards
modern applications
Brings open problems that can potentially encourage topologists to advance
in the field
This book presents, in a clear and structured way, the set function \mathcal{T} and how it
evolved since its inception by Professor F. Burton Jones in the 1940s. It starts with a very solid
introductory chapter, with all the prerequisite material for navigating through the rest of the
book. It then gradually advances towards the main properties, Decomposition theorems,
\mathcal{T}-closed sets, continuity and images, to modern applications. The set function
\mathcal{T} has been used by many mathematicians as a tool to prove results about the
semigroup structure of the continua, and about the existence of a metric continuum that
cannot be mapped onto its cone or to characterize spheres. Nowadays, it has been used by
topologists worldwide to investigate open problems in continuum theory. This book can be of
interest to both advanced undergraduate and graduate students, and to experienced
researchers as well. Its well-defined structure make this book suitable not only for self-study
but also as support material to seminars on the subject. Its many open problems can
potentially encourage mathematicians to contribute with further advancements in the field.
Due 2021-04-11
1st ed. 2021, VIII, 322 p. 32 illus.
Hardcover
ISBN 978-3-030-65080-3
Product category : Monograph
Series : Developments in Mathematics
Mathematics : Topology
Overviews the tactical points involved in disaster relief
Outlines hurdles from mitigation and preparedness to response and recovery
Uses mathematical models to describe natural and man-made disasters
Based on the ?gFourth International Conference on Dynamics of Disasters?h (Kalamata, Greece,
July 2019), this volume includes contributions from experts who share their latest discoveries
on natural and unnatural disasters. Authors provide overviews of the tactical points involved in
disaster relief, outlines of hurdles from mitigation and preparedness to response and recovery,
and uses for mathematical models to describe natural and man-made disasters. Topics covered
include economics, optimization, machine learning, government, management, business,
humanities, engineering, medicine, mathematics, computer science, behavioral studies,
emergency services, and environmental studies will engage readers from a wide variety of
fields and backgrounds.
Due 2021-04-15
1st ed. 2021, VIII, 292 p. 74 illus.
Hardcover
ISBN 978-3-030-64972-2
Product category : Contributed volume
Series : Springer Optimization and Its Applications
Mathematics : Operations Research, Mathematical Programming
Designed to enable young mathematicians to tackle concrete research
problems
Gives an overview of recent developments in arithmetic and geometry over
local fields
Provides a self-contained course on Drinfeld modules and non-Archimedean
analytic geometry
This volume introduces some recent developments in Arithmetic Geometry over local fields. Its
seven chapters are centered around two common themes: the study of Drinfeld modules and
non-Archimedean analytic geometry. The notes grew out of lectures held during the research
program "Arithmetic and geometry of local and global fields" which took place at the Vietnam
Institute of Advanced Study in Mathematics (VIASM) from June to August 2018. The authors,
leading experts in the field, have put great effort into making the text as self-contained as
possible, introducing the basic tools of the subject. The numerous concrete examples and
suggested research problems will enable graduate students and young researchers to quickly
reach the frontiers of this fascinating branch of mathematics
Due 2021-04-15
1st ed. 2021, X, 210 p. 13 illus.
Softcover
ISBN 978-3-030-66248-6
Product category : Contributed volume
Series : Lecture Notes in Mathematics
Mathematics : Number Theory
Describes a new theory, with potential applications to related branches of
functional analysis and quantum mechanics
Covers operator algebraic aspects of the theory as well as its physical
applications
Proves all results in detail, with the operator algebraic basics included in an
appendix
This book is devoted to the study of Tomita's observable algebras, their structure and
applications. It begins by building the foundations of the theory of T*-algebras and CT*-
algebras, presenting the major results and investigating the relationship between the operator
and vector representations of a CT*-algebra. It is then shown via the representation theory of
locally convex *-algebras that this theory includes Tomita?Takesaki theory as a special case;
every observable algebra can be regarded as an operator algebra on a Pontryagin space with
codimension 1. All of the results are proved in detail and the basic theory of operator algebras
on Hilbert space is summarized in an appendix. The theory of CT*-algebras has connections
with many other branches of functional analysis and with quantum mechanics. The aim of this
book is to make Tomita?fs theory available to a wider audience, with the hope that it will be
used by operator algebraists and researchers in these related fields.
Due 2021-04-23
1st ed. 2021, X, 172 p.
Softcover
ISBN 978-3-030-68892-9
Product category : Monograph
Series : Lecture Notes in Mathematics
Mathematics : Functional Analysis
Explores unsolved problems and new directions related to domain evolutions
on Riemann surfaces
Presents potentially fruitful ideas around the ill-posed suction problem
Gives elementary, but intriguing, examples involving only polynomials and
rational functions
This book studies solutions of the Polubarinova?Galin and Lowner?Kufarev equations, which
describe the evolution of a viscous fluid (Hele-Shaw) blob, after the time when these solutions
have lost their physical meaning due to loss of univalence of the mapping function involved.
When the mapping function is no longer locally univalent interesting phase transitions take
place, leading to structural changes in the data of the solution, for example new zeros and
poles in the case of rational maps. This topic intersects with several areas, including
mathematical physics, potential theory and complex analysis. The text will be valuable to
researchers and doctoral students interested in fluid dynamics, integrable systems, and
conformal field theory.
Due 2021-04-29
1st ed. 2021, X, 150 p. 12 illus. in color.
Softcover
ISBN 978-3-030-69862-1
Product category : Monograph
Series : Lecture Notes in Mathematics
Mathematics : Functions of a Complex Variable
Presents a detailed treatment of fixed point theory and its applications
Includes rigorous mathematical proofs, recent developments, and approaches
associated with fixed point theory
Appeals to graduate students, teachers, and researchers alike
This book collects papers on major topics in fixed point theory and its applications. Each
chapter is accompanied by basic notions, mathematical preliminaries and proofs of the main
results. The book discusses common fixed point theory, convergence theorems, split variational
inclusion problems and fixed point problems for asymptotically nonexpansive semigroups; fixed
point property and almost fixed point property in digital spaces, nonexpansive semigroups over
CAT() spaces, measures of noncompactness, integral equations, the study of fixed points that
are zeros of a given function, best proximity point theory, monotone mappings in modular
function spaces, fuzzy contractive mappings, ordered hyperbolic metric spaces, generalized
contractions in b-metric spaces, multi-tupled fixed points, functional equations in dynamic
programming and Picard operators. This book addresses the mathematical community working
with methods and tools of nonlinear analysis. It also serves as a reference, source for
examples and new approaches associated with fixed point theory and its applications for a
wide audience including graduate students and researchers.
Due 2021-05-06
1st ed. 2021, XXI, 478 p. 5 illus., 1 illus. in color.
Hardcover
ISBN 978-981-33-6646-6
Product category : Contributed volume
Mathematics : Functional Analysis
Problems of prescribing the extrinsic geometry and curvature of foliations are
central to the book
Presents the state of the art in geometric and analytical theory of foliations
Designed for newcomers to the field as well as experienced geometers
working in Riemannian geometry, foliation theory, differential topology, and a
wide range of researchers in differential equations and their applications
This book is devoted to geometric problems of foliation theory, in particular those related to
extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is
central to the discussion, and a version of the deep problem of the Ricci curvature for the case
of mixed curvature of foliations is examined. The book is divided into five chapters that deal
with integral and variation formulas and curvature and dynamics of foliations. Different
approaches and methods (local and global, regular and singular) in solving the problems are
described using integral and variation formulas, extrinsic geometric flows, generalizations of the
Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable'
Finsler metrics. The book presents the state of the art in geometric and analytical theory of
foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed
for newcomers to the field as well as experienced geometers working in Riemannian geometry,
foliation theory, differential topology, and a wide range of researchers in differential equations
and their applications. It may also be a useful supplement to postgraduate level work and can
inspire new interesting topics to explore.
Due 2021-05-12
1st ed. 2021, XV, 297 p. 22 illus., 4 illus. in color.
Hardcover
ISBN 978-3-030-70066-9
Product category : Monograph
Series : Progress in Mathematics
Mathematics : Differential Geometry
Equivariant Gysin Morphism and Equivariant Euler Classes
Gives a deep insight into the subject through an efficient and entirely original
approach
Provides a clear, highly informative historical presentation of group actions,
from the starting point of the theory
Offers an ideal complement to a course on de Rham cohomology
Contains numerous concrete examples of the derived duality functor
This book carefully presents a unified treatment of equivariant Poincare duality in a wide
variety of contexts, illuminating an area of mathematics that is often glossed over elsewhere.
The approach used here allows the parallel treatment of both equivariant and nonequivariant
cases. It also makes it possible to replace the usual field of coefficients for cohomology, the
field of real numbers, with any field of arbitrary characteristic, and hence change (equivariant)
de Rham cohomology to the usual singular (equivariant) cohomology . The book will be of
interest to graduate students and researchers wanting to learn about the equivariant extension
of tools familiar from non-equivariant differential geometry
Due 2021-05-08
XVI, 334 p. 8 illus., 1 illus. in color.
Softcover
ISBN 978-3-030-70439-1
Product category : Monograph
Series : Lecture Notes in Mathematics
Mathematics : Algebraic Topology