1st ed. 2017, XVIII, 432 p. 25 illus., 16 illus.
in color.
Softcover
ISBN 978-3-319-51318-8
Series: Lecture Notes in Mathematics, Vol. 2176
* Provides an up-to-date survey of three important topics at the
intersection of combinatorics and commutative algebra
* Numerous examples and algorithms illustrate relevant
computational aspects of the subject
* Gives a broad introduction to important topics aimed at researchers
of all levels
Featuring up-to-date coverage of three topics lying at the intersection of combinatorics
and commutative algebra, namely Koszul algebras, primary decompositions and
subdivision operations in simplicial complexes, this book has its focus on computations.
"Computations and combinatorics in commutative algebra" has been written by experts
in both theoretical and computational aspects of these three subjects and is aimed at a
broad audience, from experienced researchers who want to have an easy but deep review
of the topics covered to postgraduate students who need a quick introduction to the
techniques. The computational treatment of the material, including plenty of examples
and code, will be useful for a wide range of professionals interested in the connections
between commutative algebra and combinatorics.
Approx. 350 p. 2 illus.
Softcover
ISBN 978-3-319-51294-5
Series: Lecture Notes in Mathematics, Vol. 2139
* The only book on the market which describes the evaluation of
Selberg zeta functions for character deformations via the transfer
operator method
* Gives a detailed description of numerical methods and analytic
theories in one book
* Provides animations and over 50 color illustrations, helping the
reader to get a better understanding
* Gives numerical and analytical results on new phenomena related to
singular perturbations of hyperbolic Laplacians
This book presents a method for evaluating Selberg zeta functions via transfer operators
for the full modular group and its congruence subgroups with characters. Studying zeros
of Selberg zeta functions for character deformations allows us to access the discrete
spectra and resonances of hyperbolic Laplacians under both singular and non-singular
perturbations. Areas in which the theory has not yet been sufficiently developed, such as
the spectral theory of transfer operators or the singular perturbation theory of hyperbolic
Laplacians, will profit from the numerical experiments discussed in this book. Detailed
descriptions of numerical approaches to the spectra and eigenfunctions of transfer
operators and to computations of Selberg zeta functions will be of value to researchers
active in analysis, while those researchers focusing more on numerical aspects will
benefit from discussions of the analytic theory, in particular those concerning the transfer
operator method and the spectral theory of hyperbolic spaces.
1st ed. 2017, X, 440 p. 24 illus., 16 illus. in
color.
Softcover
ISBN 978-3-319-51950-0
Series: Lecture Notes in Mathematics, Vol. 2177
* 15 chapters written by experts in their fields give a comprehensive
overview of the modern theory of tensor valuationsIncludes new
yet unpublished results that make this volume an up-to-date survey
of valuation theoryChapters on applications of tensor valuations
deepen understanding and emphasize the usefulness of theoretical
concepts
The purpose of this volume is to give an up-to-date introduction to tensor valuations and
their applications. Starting with classical results concerning scalar-valued valuations on
the families of convex bodies and convex polytopes, it proceeds to the modern theory
of tensor valuations. Product and Fourier-type transforms are introduced and various
integral formulae are derived. New and well-known results are presented, together
with generalizations in several directions, including extensions to the non-Euclidean
setting and to non-convex sets. A variety of applications of tensor valuations to models in
stochastic geometry, to local stereology and to imaging are also discussed.
1st ed. 2017, X, 150 p. 20 illus., 1 illus. in
color.
Softcover
ISBN 978-3-319-52095-7
Series: Ecole d'Ete de Probabilites de Saint-Flour, Vol. 2181
* Provides a self-contained presentation in a clear and pedagogical
style
* Includes a special chapter on Bessel processes with detailed
discussions of results scattered across the literature
* Offers an original point of view on a booming subject (SPDEs)
Studying the fine properties of solutions to Stochastic (Partial) Differential Equations with
reflection at a boundary, this book begins with a discussion of classical one-dimensional
diffusions as the reflecting Brownian motion, devoting a chapter to Bessel processes,
and moves on to function-valued solutions to SPDEs. Inspired by the classical stochastic
calculus for diffusions, which is unfortunately still unavailable in infinite dimensions,
it uses integration by parts formulae on convex sets of paths in order to describe the
behaviour of the solutions at the boundary and the contact set between the solution and
the obstacle. The text may serve as an introduction to space-time white noise, SPDEs and
monotone gradient systems. Numerous open research problems in both classical and new
topics are proposed.