Series: Theses (Scuola Normale Superiore), Vol. 21
1st ed. 2016, Approx. 250 p.
Printed book
Softcover
ISBN 978-88-7642-556-1
* Strong inter-disciplinary approach merging Mathematics, Geology
and Physics
* Comprehensive study of volcanic hazard in a caldera system,
including vent location, size of the eruption and time forecasts for
the event
* Uncertainty quantification with a detailed assessment of epistemic
uncertainty
This study provides innovative mathematical models for assessing the eruption
probability and associated volcanic hazards, and applies them to the Campi Flegrei
caldera in Italy. Throughout the book, significant attention is devoted to quantifying the
sources of uncertainty affecting the forecast estimates.
The Campi Flegrei caldera is certainly one of the world’s highest-risk volcanoes, with
more than 70 eruptions over the last 15,000 years, prevalently explosive ones of varying
magnitude, intensity and vent location. In the second half of the twentieth century the
volcano apparently once again entered a phase of unrest that continues to the present.
Hundreds of thousands of people live inside the caldera and over a million more in the
nearby city of Naples, making a future eruption of Campi Flegrei an event with potentially
catastrophic consequences at the national and European levels.
Series: Springer Undergraduate Mathematics Series
1st ed. 2016, IX, 169 p.
Printed book
Softcover
ISBN 978-3-319-42185-8
* Presents non-standard exercises at undergraduate level from various
mathematical subjects
* Provides hints to solve the problems, suggesting paths to follow
* Inspires readers to putting their knowledge to use and to learning
new techniques and tricks
This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly
from the fields of real analysis, calculus, matrices, convexity, and optimization.
Most of the problems presented here are non-standard and some require broad
knowledge of different mathematical subjects in order to be solved. The author provides
some hints and (partial) answers and also puts these carefully chosen exercises into
context, presents information on their origins, and comments on possible extensions.
With stars marking the levels of difficulty, these tapas show or prove something
interesting, challenge the reader to solve and learn, and may have surprising results.
This first volume of Mathematical Tapas will appeal to mathematicians, motivated
undergraduate students from science-based areas, and those generally interested in
mathematics.
Series: Universitext
1st ed. 2016, XVII, 321 p. 10 illus.
Printed book
Softcover
ISBN 978-3-319-43930-3
* An entire part of the text is devoted to applications to Markov chains,
combinatorics, and automata theory
* Accessible to a wide readership of graduate students and
researchers, including non-experts in semigroups
* Contains exercises, chapter notes, and thoroughly worked examples
This first text on the subject provides a comprehensive introduction to the representation
theory of finite monoids. Carefully worked examples and exercises provide the bells and
whistles for graduate accessibility, bringing a broad range of advanced readers to the
forefront of research in the area. Highlights of the text include applications to probability
theory, symbolic dynamics, and automata theory. Comfort with module theory, a
familiarity with ordinary group representation theory, and the basics of Wedderburn
theory, are prerequisites for advanced graduate level study. Researchers in algebra,
algebraic combinatorics, automata theory, and probability theory, will find this text
enriching with its thorough presentation of applications of the theory to these fields.
Prior knowledge of semigroup theory is not expected for the diverse readership that may
benefit from this exposition. The approach taken in this book is highly module-theoretic
and follows the modern flavor of the theory of finite dimensional algebras.
The content is divided into 7 parts. Part I consists of 3 preliminary chapters with no prior knowledge
beyond group theory assumed. Part II forms the core of the material giving a modern
module-theoretic treatment of the Clifford *Munn*Ponizovskii theory of irreducible
representations. Part III concerns character theory and the character table of a monoid.
Part IV is devoted to the representation theory of inverse monoids and categories and Part
V presents the theory of the Rhodes radical with applications to triangularizability. Part VI
features 3 chapters devoted to applications to diverse areas of mathematics and forms a
high point of the text. The last part, VII, is concerned with advanced topics. There are also
3 appendices reviewing finite dimensional algebras, group representation theory, and
Mobius inversion.
Series: Springer Series in Statistics
1st ed. 2016, Approx. 620 p. 96 illus. in
color.
Printed book
Hardcover
ISBN 978-3-319-43251-9
* Presents a detailed, almost encyclopedic account of nonlinear time
series analysis
* Shows concrete applications of modern nonlinear time series analysis
on a variety of empirical time series, with a liberal use of color
graphics
* Provides a toolbox of discrete-time nonlinear models, methods, tests
and concepts
This book provides an overview of the current state-of-the-art of nonlinear time series
analysis, richly illustrated with examples, pseudocode algorithms and real-world
applications. Avoiding a “theorem-proof” format, it shows concrete applications on a
variety of empirical time series. The book can be used in graduate courses in nonlinear
time series and at the same time also includes interesting material for more advanced
readers. Though it is largely self-contained, readers require an understanding of basic
linear time series concepts, Markov chains and Monte Carlo simulation methods.
The book covers time-domain and frequency-domain methods for the analysis of both
univariate and multivariate (vector) time series. It makes a clear distinction between
parametric models on the one hand, and semi- and nonparametric models/methods on
the other. This offers the reader the option of concentrating exclusively on one of these
nonlinear time series analysis methods.
To make the book as user friendly as possible, major supporting concepts and specialized
tables are appended at the end of every chapter. In addition, each chapter concludes with
a set of key terms and concepts, as well as a summary of the main findings. Lastly, the
book offers numerous theoretical and empirical exercises, with answers provided by the
author in an extensive solutions manual.
Series: Lecture Notes in Mathematics, Vol. 2163
1st ed. 2016, Approx. 230 p.
Printed book
Softcover
ISBN 978-3-319-41068-5
* This is the first book on stochastic porous media equations
* Concentrates on essential points, including existence, uniqueness,
ergodicity and finite time extinction results
* Presents the state of the art of the subject in a concise, but
reasonably self-contained way
* Includes both the slow and fast diffusion case, but also the critical
case, modeling self-organized criticality
Focusing on stochastic porous media equations, this book places an emphasis
on existence theorems, asymptotic behavior and ergodic properties of the
associated transition semigroup. Stochastic perturbations of the porous media equation
have reviously been considered by physicists, but rigorous mathematical existence results
have only recently been found.
The porous media equation models a number of different physical phenomena, including
the flow of an ideal gas and the diffusion of a compressible fluid through porous media,
and also thermal propagation in plasma and plasma radiation. Another important
application is to a model of the standard self-organized criticality process, called the
"sand-pile model" or the "Bak-Tang-Wiesenfeld model".
The book will be of interest to PhD students and researchers in mathematics, physics and
biology.
Series: Lecture Notes in Mathematics, Vol. 2164
1st ed. 2016, Approx. 250 p. 22 illus., 2 illus.
in color.
Printed book
Softcover
ISBN 978-3-319-43058-4
* Accessible to graduate studentsProvides introductions leading to the
forefront of several current research areas
* A broad sampling of ergodic geometry
These lectures center on ergodicity of the (Weil-Petersson) geodesic flow on a
nonpositively curved space whose points are negatively curved metrics on surfaces.
The subject matter is anchored by a self-contained introduction to hyperbolic dynamics
and ergodic theory and complemented by lectures that show the deep connections of
geodesic flows in negative curvature with on one hand Diophantine approximation and
on the other hand with the ergodic theory of horocycle flows.