Describes an open and difficult mathematical problem, offering a new
research field for young investigators
Gives a brief but unified contrasting description of examination of dynamics
from a trajectory or an ensemble point of view
Highlights all of the problems attendant to the development of an
appropriate measure to examine ergodic behavior in infinite-dimensional
dynamical systems
Presents possible applications of functional calculus to infinite dimensional
dynamical systems
Offers a motivated area of research combining different fields of mathematics
This monograph has arisen out of a number of attempts spanning almost five decades to
understand how one might examine the evolution of densities in systems whose dynamics are
described by differential delay equations. Though the authors have no definitive solution to the
problem, they offer this contribution in an attempt to define the problem as they see it, and to
sketch out several obvious attempts that have been suggested to solve the problem and which
seem to have failed. They hope that by being available to the general mathematical
community, they will inspire others to consider?and hopefully solve?the problem. Serious
attempts have been made by all of the authors over the years and they have made reference
to these where appropriate
Mathematics : Analysis
Due 2020-12-05
1st ed. 2020, IX, 140 p. 33 illus., 11 illus. in color.
Hardcover
ISBN 978-1-0716-1071-8
Product category : Monograph
Series : Fields Institute Monographs
Surveys include known results with sample proof techniques for each
parameter
Generally focuses on primary dominating sets
Provides a reference for established researchers and graduate students
This volume comprises 16 contributions that present advanced topics in graph domination,
featuring open problems, modern techniques, and recent results. The focus is on primary
dominating sets such as paired domination, connected domination, restrained domination,
dominating functions, Roman domination, and power domination. Additionally, surveys include
known results with a sample of proof techniques for each parameter. Of extra benefit to the
reader, the first chapter includes a glossary of commonly used terms; the second chapter
provides an overview of models of domination from which the parameters are defined. The
book is intended to provide a reference for established researchers in the fields of domination
and graph theory and graduate students who wish to gain knowledge of the topics covered as
well as an overview of the major accomplishments in the field and proof techniques used.
Mathematics : Graph Theory
Due 2020-12-16
1st ed. 2020, VIII, 545 p. 50 illus., 49 illus. in color.
Hardcover
ISBN 978-3-030-51116-6
Product category : Contributed volume
Series : Developments in Mathematics
Interesting and enjoyable reading, even to a non expert readers
Each proposition presents clear and complete logical passages
Topics are introduced starting from simple concepts and then gradually go
through more complex steps
The text contains detailed and
complete proofs and includes instructive historical introductions
to key chapters. These serve to illustrate the hurdles faced by the scholars that developed the
theory, and allow the novice to approach the subject from a wider angle, thus appreciating the
human side of major figures in Mathematics.The style in which topics are addressed, albeit
informal, always maintains a rigorous character. The attention placed in the careful layout of
the logical steps of proofs, the abundant examples and the supplementary remarks
disseminated throughout all contribute to render the reading pleasant and facilitate the
learning process. The exposition is particularly suitable for students of Mathematics, Physics,
Engineering and Statistics, besides providing the foundation essential for the study of
Probability Theory and many branches of Applied Mathematics, including the Analysis of
Financial Markets and other areas of Financial Engineering.
Mathematics : Measure and Integration
Due 2020-12-12
1st ed. 2020, IX, 519 p. 19 illus., 16 illus. in color.
Softcover
ISBN 978-3-030-54939-8
Product category : Undergraduate textbook
Series : La Matematica per il 3+2
Presents a comprehensive treatment of the theory of quaternions
Engages the student reader with an accessible, approachable writing style
Offers numerous options for constructing introductory and advanced courses
Encompasses a vast wealth of knowledge to form an essential reference
This textbook presents a comprehensive treatment of the arithmetic theory of quaternion
algebras and orders, a subject with applications in diverse areas of mathematics. Written to be
accessible and approachable to the graduate student reader, this text collects and synthesizes
results from across the literature. Numerous pathways offer explorations in many different
directions, while the unified treatment makes this book an essential reference for students and
researchers alike. Divided into five parts, the book begins with a basic introduction to the
noncommutative algebra underlying the theory of quaternion algebras over fields, including the
relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion
algebras and orders follows. The third part considers analytic aspects, starting with zeta
functions and then passing to an idelic approach, offering a pathway from local to global that
includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic
geometry and low-dimensional topology follow, relating geometric and topological properties to
arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects
of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces.
Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many
fields. Graduate students interested in algebra, geometry, and number theory will appreciate
the many avenues and connections to be explored. Instructors will find numerous options for
constructing introductory and advanced courses, while researchers will value the all-embracing
treatment. Readers are assumed to have some familiarity with algebraic number theory and
commutative algebra, as well as the fundamentals of linear algebra, topology, and complex
analysis. More advanced topics call upon additional background, as noted, though essential
concepts and motivation are recapped throughout.
Mathematics : Associative Rings and Algebras
Due 2020-10-29
1st ed. 2020, XX, 833 p. 83 illus.
Hardcover
ISBN 978-3-030-56692-0
Product category : Graduate/advanced undergraduate textbook
Series : Graduate Texts in Mathematics
Presents selected works from algebra, geometry and discrete mathematics,
exploring the interaction among these fields
Focuses on combinatorial aspects of commutative algebra and algebraic
geometry, based on the transdisciplinary approach of the conference
Showcases papers from some of the most prominent figures in the field
This proceedings volume presents selected, peer-reviewed contributions from the 26th National
School on Algebra, which was held in Constana, Romania, on August 26-September 1, 2018.
The works cover three fields of mathematics: algebra, geometry and discrete mathematics,
discussing the latest developments in the theory of monomial ideals, algebras of graphs and
local positivity of line bundles. Whereas interactions between algebra and geometry go back at
least to Hilbert, the ties to combinatorics are much more recent and are subject of immense
interest at the forefront of contemporary mathematics research. Transplanting methods
between different branches of mathematics has proved very fruitful in the past ? for example,
the application of fixed point theorems in topology to solving nonlinear differential equations in
analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to
significant advances in our understanding of the asymptotic properties of line bundles in
geometry and multiplier ideals in algebra. This book is intended for advanced graduate
students, young scientists and established researchers with an interest in the overlaps between
different fields of mathematics. A volume for the 24th edition of this conference was previously
published with Springer under the title "Multigraded Algebra and Applications" (ISBN 978-3-
319-90493-1).
Mathematics : Commutative Rings and Algebras
1st ed. 2020, VIII, 182 p. 40 illus., 6 illus. in color.
Hardcover
ISBN 978-3-030-52110-3
Product category : Proceedings
Series : Springer Proceedings in Mathematics & Statistics
Features beautifully illustrated lectures on self-inducing structures with
cutting-edge results related to substitutions and tilings
Provides an easy introduction to S-adic systems and self-affine tilings
Includes chapters on games and undecidability questions and on the
spectrum of substitution tilings
This book presents a panorama of recent developments in the theory of tilings and related
dynamical systems. It contains an expanded version of courses given in 2017 at the research
school associated with the Jean -Morlet chair program. Tilings have been designed, used and
studied for centuries in various contexts. This field grew significantly after the discovery of
aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino
problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling
problems establish a bridge between the mutually influential fields of geometry, dynamical
systems, aperiodic order, computer science, number theory, algebra and logic. The main
properties of tiling dynamical systems are covered, with expositions on recent results in selfsimilarity
(and its generalizations, fusions rules and S-adic systems), algebraic developments
connected to physics, games and undecidability questions, and the spectrum of substitution
tilings.
Mathematics : Dynamical Systems and Ergodic Theory
Due 2020-11-26
1st ed. 2020, X, 460 p. 136 illus., 43 illus. in color.
Softcover
ISBN 978-3-030-57665-3
Product category : Contributed volume
Series : Lecture Notes in Mathematics
Young's Construction, Seminormal Representations, SL(2)
Representations, Heaps, Basics on Finite Fields
Offers an ideal supplement to a graduate level course on algebraic
combinatorics
Gives a unique take on a number of combinatorial constructs that are quite
timeless
Provides expositions which are detailed, but at the same time easily
accessible, very readable, and seemingly effortless
Capturing Adriano Garsia's unique perspective on essential topics in algebraic combinatorics,
this book consists of selected, classic notes on a number of topics based on lectures held at
the University of California, San Diego over the past few decades. The topics presented share a
common theme of describing interesting interplays between algebraic topics such as
representation theory and elegant structures which are sometimes thought of as being outside
the purview of classical combinatorics. The lectures reflect Garsiafs inimitable narrative style
and his exceptional expository ability. The preface presents the historical viewpoint as well as
Garsia's personal insights into the subject matter. The lectures then start with a clear treatment
of Alfred Young's construction of the irreducible representations of the symmetric group,
seminormal representations and Morphy elements. This is followed by an elegant application of
SL(2) representations to algebraic combinatorics. The last two lectures are on heaps, continued
fractions and orthogonal polynomials with applications, and finally there is an exposition on the
theory of finite fields. The book is aimed at graduate students and researchers in the field.
Mathematics : Field Theory and Polynomials
Due 2020-11-25
1st ed. 2020, XIV, 232 p. 36 illus.
Softcover
ISBN 978-3-030-58372-9
Product category : Monograph
Series : Lecture Notes in Mathematics