Series: Probability Theory and Stochastic Modelling
1st ed. 2019, XVIII, 549 p.
Hardcover 9781493995776
Illustrates the use of these methods using a wide variety of discrete and
continuous time models
Timely and important topic with significant developments over the last 15 years
Includes both theory and links with applications
This book presents broadly applicable methods for the large deviation and moderate deviation
analysis of discrete and continuous time stochastic systems. A feature of the book is the
systematic use of variational representations for quantities of interest such as normalized
logarithms of probabilities and expected values. By characterizing a large deviation principle in
terms of Laplace asymptotics, one converts the proof of large deviation limits into the
convergence of variational representations. These features are illustrated though their
application to a broad range of discrete and continuous time models, including stochastic
partial differential equations, processes with discontinuous statistics, occupancy models, and
many others. The tools used in the large deviation analysis also turn out to be useful in
understanding Monte Carlo schemes for the numerical approximation of the same probabilities
and expected values. This connection is illustrated through the design and analysis of
importance sampling and splitting schemes for rare event estimation. The book assumes a
solid background in weak convergence of probability measures and stochastic analysis, and is
suitable for advanced graduate students, postdocs and researchers
Series: Universitext
1st ed. 2019, XVIII, 556 p.
Hardcover 9781493996421
Provides a comprehensive introduction to submanifold theory
Engages the reader throughout with many examples and exercises
Reaches the frontier of knowledge in the subject
This book provides a comprehensive introduction to Submanifold theory, focusing on general
properties of isometric and conformal immersions of Riemannian manifolds into space forms.
One main theme is the isometric and conformal deformation problem for submanifolds of
arbitrary dimension and codimension. Several relevant classes of submanifolds are also
discussed, including constant curvature submanifolds, submanifolds of nonpositive extrinsic
curvature, conformally flat submanifolds and real Kaehler submanifolds. This is the first
textbook to treat a substantial proportion of the material presented here. The first chapters are
suitable for an introductory course on Submanifold theory for students with a basic
background on Riemannian geometry.The remaining chapters could be used in a more
advanced course by students aiming at initiating research on the subject, and are also intended
to serve as a reference for specialists in the field
Series: Springer Undergraduate Mathematics Series
1st ed. 2019, VIII, 280 p. 65 illus., 3 illus. in color.
Softcover 9783030192969
Suitable for undergraduate courses in continuum mechanics or fluid dynamics
Provides an introduction to nonlinear acoustics and theory of nonlinear wave
propagation in gases
Includes almost 80 exercises with solutions
This book provides a concise introduction to continuum mechanics, with a particular emphasis
on fluid dynamics, suitable for upper undergraduate students in applied mathematics and
related subjects. Starting with a preliminary chapter on tensors, the main topic of the book
begins in earnest with the chapters on continuum kinematics and dynamics. Following chapters
cover linear elasticity and both incompressible and compressible fluids. Special topics of note
include nonlinear acoustics and the theory of motion of viscous thermal conducting
compressible fluids. Based on an undergraduate course taught for over a decade, this textbook
assumes only familiarity with multivariate calculus and linear algebra. It includes many
exercises with solutions and can serve as textbook for lecture courses at the undergraduate
and masters level.
Series: Springer Proceedings in Mathematics & Statistics
1st ed. 2019, Approx. 300 p.
Hardcover 9783030200152
The book presents the proceedings of the 23rd International Conference on Difference
Equations and Applications, ICDEA 2017, held at the West University of Timioara, Romania,
under the auspices of the International Society of Difference Equations (ISDE), July 24 - 28,
2017. It includes new and significant contributions in the field of difference equations, discrete
dynamical systems and their applications in various sciences. Disseminating recent studies and
related results and promoting advances, the book appeals to PhD students, researchers,
educators and practitioners in the field.
Series: Contributions to Statistics
Approx. 190 p. 11 illus.
Hardcover 9783030175184
Presents the latest advances in matrix theory and statistics
Includes methods for solving big data problems
Features contributions by leading experts in the area
This volume features selected, refereed papers on various aspects of statistics, matrix theory
and its applications to statistics, as well as related numerical linear algebra topics and
numerical solution methods, which are relevant for problems arising in statistics and in big
data. The contributions were originally presented at the 25th International Workshop on
Matrices and Statistics (IWMS 2016), held in Funchal (Madeira), Portugal on June 6-9, 2016.
The IWMS workshop series brings together statisticians, computer scientists, data scientists and
mathematicians, helping them better understand each otherfs tools, and fostering new
collaborations at the interface of matrix theory and statistics.
Series: Operator Theory: Advances and Applications
1st ed. 2019, Approx. 350 p.
Hardcover 9783030188764
Provides unique insights on the Gibbs semigroups theory
Extends the theory to general results
Includes three appendices
This book focuses on the theory of the Gibbs semigroups, which originated in the 1970s and
was motivated by the study of strongly continuous operator semigroups with values in the
trace-class ideal. The book offers an up-to-date, exhaustive overview of the advances achieved
in this theory after half a century of development. It begins with a tutorial introduction to the
necessary background material, before presenting the Gibbs semigroups and then providing
detailed and systematic information on the Trotter-Kato product formulae in the trace-norm
topology. In addition to reviewing the state-of-art concerning the Trotter-Kato product formulae,
the book extends the scope of exposition from the trace-class ideal to other ideals. Here,
special attention is paid to results on semigroups in symmetrically normed ideals and in the
Dixmier ideal. By examining the progress made in Gibbs semigroup theory and in extensions of
the Trotter-Kato product formulae to symmetrically normed and Dixmier ideals, the book shares
timely and valuable insights for readers interested in pursuing these subjects further. As such,
it will appeal to researchers, undergraduate and graduate students in mathematics and
mathematical physics.
Series: Progress in Mathematics
1st ed. 2019, Approx. 350 p.
Hardcover 9783030183141
Introduces innovative ergodic techniques to Diophantine approximation in
non-Archimedean local fields
Gives numerous first published error terms in geometric counting and
equidistribution problems
Bridges the gap between the equidistribution and counting results with
potentials on negatively curved manifolds and the ones without potential on trees
This book provides a complete exposition of equidistribution and counting problems weighted
by a potential function of common perpendicular geodesics in negatively curved manifolds and
simplicial trees. Avoiding any compactness assumptions, the authors extend the theory of
Patterson-Sullivan, Bowen-Margulis and Oh-Shah (skinning) measures to CAT(-1) spaces with
potentials. The work presents a proof for the equidistribution of equidistant hypersurfaces to
Gibbs measures, and the equidistribution of common perpendicular arcs between for instance
closed geodesics. Using tools from ergodic theory (including coding by topological Markov
shifts, and an appendix by Buzzi that relates weak Gibbs measures and equilibrium states for
them), the authors further prove the variational principle and rate of mixing for the geodesic
flow on metric and simplicial trees?again without the need for any compactness or torsionfree
assumptions. In a series of applications, using the Bruhat-Tits trees over non-Archimedean
local fields, the authors subsequently prove further important results: the Mertens formula and
the equidistribution of Farey fractions in function fields, the equidistribution of quadratic
irrationals over function fields in their completions, and asymptotic counting results of the
representations by quadratic norm forms.