1st ed. 2016, XV, 261 p. 23 illus.
Hardcover
ISBN 978-3-319-31801-1
* Covers a relatively new area of logic, introduced by Vaananen, that
has seen rapid development
* Dependence logic has applications in numerous, seemingly
unrelated subjects, including causality, random variables in statistics,
database theory, Mendelian genetics, and quantum physics
* Will be of interest to a broad group of logicians, mathematicians,
statisticians, philosophers, and scientists
In this volume, different aspects of logics for dependence and independence are
discussed, including both the logical and computational aspects of dependence logic,
and also applications in a number of areas, such as statistics, social choice theory,
databases, and computer security. The contributing authors represent leading experts
in this relatively new field, each of whom was invited to write a chapter based on talks
given at seminars held at the Schloss Dagstuhl Leibniz Center for Informatics in Wadern,
Germany (in February 2013 and June 2015) and an Academy Colloquium at the Royal
Netherlands Academy of Arts and Sciences (March 2014). Altogether, these chapters
provide the most up-to-date look at this developing and highly interdisciplinary field
and will be of interest to a broad group of logicians, mathematicians, statisticians
philosophers, and scientists.
1st ed. 2016, VIII, 280 p. 1 illus.
Hardcover
ISBN 978-3-319-32347-3
Series: CMS Books in Mathematics
* Includes a balance of well-known theorems and applications as well
as new research and results
* Provides a clear account of background information in Stonean
spaces, Banach spaces, Banach lattices, Banach algebras, and
measure theory
* Discusses new approaches and syntheses of classical theorem with
new examples
This book gives a coherent account of the theory of Banach spaces and Banach lattices,
using the spaces C_0(K) of continuous functions on a locally compact space K as the main
example. The study of C_0(K) has been an important area of functional analysis for many
years. It gives several new constructions, some involving Boolean rings, of this space as
well as many results on the Stonean space of Boolean rings. The book also discusses when
Banach spaces of continuous functions are dual spaces and when they are bidual spaces.
1st ed. 2016, XIX, 410 p.
Hardcover
ISBN 978-981-10-0915-0
* Presents a collection of reports on the most recent results on CR
submanifolds in various ambient spaces
* Explores the applications of CR geometry, and in particular the
theory of CR submanifolds, to other scientific areas
* Attempts to fill in the gap between the geometry of the second
fundamental form of a CR submanifold and the more mathematical
analysis oriented aspects of CR geometry
* Pays a tribute to Professor Aurel Bejancu, the 1978 discoverer of the
notion of a CR submanifold of a Hermitian manifold
This book gathers contributions by respected experts on the theory of isometric
immersions between Riemannian manifolds, and focuses on the geometry of CR
structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic
recast of the tangential Cauchy?Riemann equations in complex analysis involving several
complex variables. The book covers a wide range of topics such as Sasakian geometry,
Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian
geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds.
Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR
submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview
of several topics in the geometry of CR submanifolds. Presenting detailed information on
the most recent advances in the area, it represents a useful resource for mathematicians
and physicists alike.
1st ed. 2016, X, 525 p. 83 illus., 17 illus. in color.
Hardcover
ISBN 978-3-319-32160-8
* Self-contained presentation of methods, theory, and results related
to some of the most important open problems in mathematics
* Useful for advanced graduate courses and seminars as well as
for researchers (pure and applied) working toward the proof of
longstanding open problems in mathematical sciences
* First book to treat a wide range of fields of open problems in
mathematics and the status of problems' solutions to date
The goal in putting together this unique compilation was to present the current status
of the solutions to some of the most essential open problems in pure and applied
mathematics. Emphasis is also given to problems in interdisciplinary research for which
mathematics plays a key role. This volume comprises highly selected contributions by
some of the most eminent mathematicians in the international mathematical community
on longstanding problems in very active domains of mathematical research. A joint
preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr.
written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of
Nash’s legendary mathematical achievements.
The treatment in this book includes open problems in the following fields: algebraic
geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry,
topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory,
cryptography, theoretical computer science, and more. Extensive discussions surrounding
the progress made for each problem are designed to reach a wide community of readers,
from graduate students and established research mathematicians to physicists, computer
scientists, economists, and research scientists who are looking to develop essential and
modern new methods and theories to solve a variety of open problems.
1st ed. 2016, X, 617 p. 44 illus., 22 illus. in color.
Hardcover
ISBN 978-3-319-31336-8
* Contains contributions from leading experts in nonlinear
mathematics Features a wide variety of topics that will attract a
diverse readership
* Unifies several theories and methods
This volume, dedicated to the eminent mathematician Vladimir Arnold, presents a
collection of research and survey papers written on a large spectrum of theories and
problems that have been studied or introduced by Arnold himself. Emphasis is given
to topics relating to dynamical systems, stability of integrable systems, algebraic and
differential topology, global analysis, singularity theory and classical mechanics. A number
of applications of Arnold’s groundbreaking work are presented. This publication will assist
graduate students and research mathematicians in acquiring an in-depth understanding
and insight into a wide domain of research of an interdisciplinary nature.
1st ed. 2016, VI, 204 p. 7 illus.
Hardcover
ISBN 978-3-319-32900-0
Series: Springer Proceedings in Mathematics & Statistics, Vol. 160
Presenting the collaborations of over thirty international experts in the latest
developments in pure and applied mathematics, this volume serves as an anthology
of research with a common basis in algebra, functional analysis and their applications.
Special attention is devoted to non-commutative algebras, non-associative algebras,
operator theory and ring and module theory. These themes are relevant in research and
development in coding theory, cryptography and quantum mechanics.
The topics in this volume were presented at the Workshop on Non-Associative & Non-
Commutative Algebra and Operator Theory, held May 23?25, 2014 at Cheikh Anta
Diop University in Dakar, Senegal in honor of Professor Amin Kaidi. The workshop was
hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry
and Applications, in cooperation with the University of Almeria and the University of
Malaga. Dr. Kaidi's work focuses on non-associative rings and algebras, operator theory
and functional analysis, and he has served as a mentor to a generation of mathematicians
in Senegal and around the world