Due 2019-01-24
2018, X, 304 p. 49 illus., 46 illus. in color.
Hardcover
ISBN 978-3-030-03903-5
The book gives a complete description of the Canonical Grobner Cover
Detailed description of three selected problems for which GC gives a new
perspective
All the algorithms described have been included in the software “grobcov.lib”
library
Written by one of the leading experts in GC
This book is divided into two parts, one theoretical and one focusing on applications, and offers
a complete description of the Canonical Grobner Cover, the most accurate algebraic method for
discussing parametric polynomial systems. It also includes applications to the Automatic
Deduction of Geometric Theorems, Loci Computation and Envelopes. The theoretical part is a
self-contained exposition on the theory of Parametric Grobner Systems and Bases. It begins
with Weispfenning’s introduction of Comprehensive Grobner Systems (CGS) in 1992, and
provides a complete description of the Grobner Cover (GC), which includes a canonical
discussion of a set of parametric polynomial equations developed by Michael Wibmer and the
author. In turn, the application part selects three problems for which the Grobner Cover offers
valuable new perspectives. The automatic deduction of geometric theorems (ADGT) becomes
fully automatic and straightforward using GC, representing a major improvement on all
previous methods. In terms of loci and envelope computation, GC makes it possible to
introduce a taxonomy of the components and automatically compute it. The book also
generalizes the definition of the envelope of a family of hypersurfaces, and provides algorithms
for its computation, as well as for discussing how to determine the real envelope. All the
algorithms described here have also been included in the software library “grobcov.lib”
implemented in Singular by the author, and serve as a User Manual for it.
Due 2019-01-23
2018, Approx. 300 p.
Hardcover
ISBN 978-3-030-04087-1
Highlights the most advanced research topics in the field of structured matrix
analysis
Gathers contributions by the foremost international research groups
Will benefit researchers, PhD students and post-docs alike
This book gathers selected contributions presented at the INdAM Meeting Structured Matrices
in Numerical Linear Algebra: Analysis, Algorithms and Applications, held in Cortona, Italy on
September 4-8, 2017. Highlights cutting-edge research on Structured Matrix Analysis, it covers
theoretical issues, computational aspects, and applications alike. The contributions, written by
authors from the foremost international groups in the community, trace the main research
lines and treat the main problems of current interest in this field. The book offers a valuable
resource for all scholars who are interested in this topic, including researchers, PhD students
and post docs.
Due 2019-03-14
2019, Approx. 360 p.
Hardcover
ISBN 978-3-030-01525-1
Provides the theory and methods to solve stochastic quickest detection tasks
in disorder problems
Shows that most quickest detection problems can be reformulated as optimal
stopping problems
Examines both the discrete-time and continuous-time cases
This monograph focuses on those stochastic quickest detection tasks in disorder problems that
arise in the dynamical analysis of statistical data. These include quickest detection of randomly
appearing targets, of spontaneously arising effects, and of arbitrage (in financial mathematics).
There is also currently great interest in quickest detection methods for randomly occurring
intrusions in information systems and in the design of defense methods against cyber-attacks.
The author shows that the majority of quickest detection problems can be reformulated as
optimal stopping problems where the stopping time is the moment the occurrence of disorder
is signaled. Thus, considerable attention is devoted to the general theory of optimal stopping
rules, and to its concrete problem-solving methods. The exposition covers both the discrete
time case, which is in principle relatively simple and allows step-by-step considerations, and
the continuous-time case, which often requires more technical machinery such as martingales,
supermartingales, and stochastic integrals. There is a focus on the well-developed apparatus of
Brownian motion, which enables the exact solution of many problems. The last chapter
presents applications to financial markets. Researchers and graduate studentsinterested in
probability, decision theory and statistical sequential analysis will find this book useful.
Due 2019-01-19
2018, X, 120 p. 22 illus., 2 illus. in color.
Softcover
ISBN 978-3-030-02854-1
In this partly expository work, a framework is developed for building exotic circle actions of
certain classical groups. The authors give general combination theorems for indiscrete isometry
groups of hyperbolic space which apply to Fuchsian and limit groups. An abundance of integervalued
subadditive defect-one quasimorphisms on these groups follow as a corollary. The main
classes of groups considered are limit and Fuchsian groups. Limit groups are shown to admit
large collections of faithful actions on the circle with disjoint rotation spectra. For Fuchsian
groups, further flexibility results are proved and the existence of non-geometric actions of free
and surface groups is established. An account is given of the extant notions of semi-conjugacy,
showing they are equivalent. This book is suitable for experts interested in flexibility of
representations, and for non-experts wanting an introduction to group representations into
circle homeomorphism groups.
Due 2019-04-10
2019, X, 290 p.
Softcover
ISBN 978-3-030-03717-8
Gives benchmark examples for differential-algebraic equations from various
sciences
Shows how state of the art techniques involving DAEs can be applied to
various, challenging problems
Can be used as a companion book in applied courses in several disciplines
This volume encompasses prototypical, innovative and emerging examples and benchmarks of
Differential-Algebraic Equations (DAEs) and their applications, such as electrical networks,
chemical reactors, multibody systems, and multiphysics models, to name but a few. Each article
begins with an exposition of modelling, explaining whether the model is prototypical and for
which applications it is used. This is followed by a mathematical analysis, and if appropriate, a
discussion of the numerical aspects including simulation. Additionally, benchmark examples are
included throughout the text. Mathematicians, engineers, and other scientists, working in both
academia and industry either on differential-algebraic equations and systems or on problems
where the tools and insight provided by differential-algebraic equations could be useful, would
find this book resourceful.