Series: Universitext
1st ed. 2017, XII, 200 p. 18 illus., 17 illus. in color.
Printed book
Softcover
ISBN 978-3-319-56220-9
* Provides a clear and rapid introduction to many hot topics in the field
of hyperplane arrangements
* Introduces basic definitions and key notions and takes the reader
right up to open questions
* Contains a wealth of exercises of varying levels of difficulty
This textbook provides an accessible introduction to the rich and beautiful area
of hyperplane arrangement theory, where discrete mathematics, in the form of
combinatorics and arithmetic, meets continuous mathematics, in the form of the topology
and Hodge theory of complex algebraic varieties.
The topics discussed in this book range from elementary combinatorics and discrete
geometry to more advanced material on mixed Hodge structures, logarithmic connections
and Milnor fibrations. The author covers a lot of ground in a relatively short amount of
space, with a focus on defining concepts carefully and giving proofs of theorems in detail
where needed. Including a number of surprising results and tantalizing open problems,
this timely book also serves to acquaint the reader with the rapidly expanding literature
on the subject.
Hyperplane Arrangements will be particularly useful to graduate students and researchers
who are interested in algebraic geometry or algebraic topology. The book contains
numerous exercises at the end of each chapter, making it suitable for courses as well as
self-study.
**************************************************************************************************
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern
Surveys in Mathematics, Vol. 64
1st ed. 2017, Approx. 300 p.
Printed book
Hardcover
ISBN 978-3-319-56477-7
* Will become the standard reference of the field
* Introduces new mathematical treatment of parametrised measure
models
* Includes general results on sufficient statistics, Cramer-Rao
inequality, uniqueness of Fisher metric and Amari-Chentsov tensor
* Provides new applications of information geometry
The book provides a comprehensive introduction and a novel mathematical foundation of
the field of information geometry with complete proofs and detailed background material
on measure theory, Riemannian geometry and Banach space theory. Parametrised
measure models are defined as fundamental geometric objects, which can be both finite
or infinite dimensional. Based on these models, canonical tensor fields are introduced
and further studied, including the Fisher metric and the Amari-Chentsov tensor, and
embeddings of statistical manifolds are investigated.
This novel foundation then leads to application highlights, such as generalizations and
extensions of the classical uniqueness result of Chentsov or the Cramer-Rao inequality.
Additionally, several new application fields of information geometry are highlighted, for
instance hierarchical and graphical models, complexity theory, population genetics, or
Markov Chain Monte Carlo.
The book will be of interest to mathematicians who are interested in geometry,
information theory, or the foundations of statistics, to statisticians as well as to scientists
interested in the mathematical foundations of complex systems.
Series on Concrete and Applicable Mathematics: Volume 21
396pp May 2017
ISBN: 978-981-3147-60-7 (hardcover)
ISBN: 978-981-3149-97-7 (softcover)
This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations.
Functional Equations and Applications
Historical Development of Functional Equations
Methods of Solving Functional Equations
General Solution of Euler*Lagrange Quadratic Type Functional Equations
General Solution of Cubic Type Functional Equations
General Solution of Quartic Type Functional Equations
General Solution of Quintic and Sextic Functional Equations
Mixed Type Functional Equations
Mixed Type Functional Equations (continued)
Two-Variable and Three-Variable Functional Equations
The Ulam Stability Problem
Stability of Functional Equations in Various Spaces
Functional Inequalities
Ulam*Hyers Stabilities of Functional Equations in Felbin's Normed Spaces
Stabilities of Functional Equations on C*-algebras and Lie C*-algebras
Ulam Stability of Mixed Type Mappings on Restricted Domains
Related Topics on Distributions and Hyperfunctions and Jordan Lie Homomorphisms
Exercises and Open Problems
Advanced undergraduates, postgraduates and researchers who are interested in functional equations and functional inequalities.
ISBN: 978-2-85629-849-7
Series, Volume: Memoires de la Societe Mathematique de France, Number 150
Bibliographic Information: Published: 15 January 2017; Copyright Year: 2017; Pages: 119; Softcover
Subject Classification
Mathematical Physics
Differential Equations
Graduate students and research mathematicians interested in the theory of modified gravity.
This monograph solves the Cauchy problem for the f (R ) theory of modified gravity, which generalizes
Einstein’s theory. In the Einstein*Hilbert functional, the spacetime scalar curvature R is replaced by a
nonlinear function f (R ). The field equations are of order four in the derivatives of the metric.
In this pioneering work, the authors provide a rigorous validation of this theory by analyzing the singular
convergence of f (R ) toward R .
Information for our distributors: A publication of the Societe Mathematique de France, Marseilles (SMF),
distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the
SMF. AMS individual members receive a 10% discount and members of the SMF receive a 30% discount from
list. No other discounts apply.