1st ed. 2017, XIII, 124 p. 7 illus.
Softcover
ISBN 978-1-4939-6983-8
Series: SpringerBriefs in Mathematics
* Unified and self-contained presentation of fundamental tools in
continuum mechanics
* Provides a constructive and descriptive approach to the
mathematical framework with a growing level of complexity
* Numerous connections between different topics are included to
appeal to a wide audience
This Brief is mainly devoted to two classical and related results: the existence of a
right inverse of the divergence operator and the so-called Korn Inequalities. It is
well known that both results are fundamental tools in the analysis of some classic
differential equations, particularly in those arising in fluid dynamics and elasticity. Several
connections between these two topics and improved Poincare inequalities are extensively
treated. From simple key ideas the book is growing smoothly in complexity. Beginning
with the study of these problems on star-shaped domains the arguments are extended
first to John domains and then to Holder α domains where the need of weighted spaces
arises naturally. In this fashion, the authors succeed in presenting in an unified and
concise way several classic and recent developments in the field. These features certainly
makes this Brief useful for students, post-graduate students, and researchers as well.
2017, XXV, 842 p. 146 illus., 52 illus.
in color.
Softcover
ISBN 978-3-319-52248-7
Series: Springer Texts in Statistics
* Second edition includes new material on screening experiments and
analysis of mixed models, a new chapter on computer experiments,
added “Using R” sections, updated SAS output, and use of SAS Proc
Mixed
* Presents a step-by-step guide to design, including a planning
checklist that emphasizes practical considerations
* Explains all the basics of analysis: estimation of treatment contrasts
and analysis of variance, while also applying these in a wide variety
of settings
* Utilizes data drawn from real experiments
This textbook takes a strategic approach to the broad-reaching subject of experimental
design by identifying the objectives behind an experiment and teaching practical
considerations that govern design and implementation, concepts that serve as the
basis for the analytical techniques covered. Rather than a collection of miscellaneous
approaches, chapters build on the planning, running, and analyzing of simple
experiments in an approach that results from decades of teaching the subject. In
most experiments, the procedures can be reproduced by readers, thus giving them a
broad exposure to experiments that are simple enough to be followed through their
entire course. Outlines of student and published experiments appear throughout the
text and as exercises at the end of the chapters. The authors develop the theory of
estimable functions and analysis of variance with detail, but at a mathematical level that
is simultaneously approachable. Throughout the book, statistical aspects of analysis
complement practical aspects of design.
This new, second edition includes
* an additional chapter on computer experiments
* additional "Using R” sections at the end of each chapter to illustrate R code and output
* updated output for all SAS programs and use of SAS Proc Mixed
* new material on screening experiments and analysis of mixed models
Angela Dean, PhD, is Professor Emeritus of Statistics and a member of the Emeritus
Academy at The Ohio State University, Columbus, Ohio. She is a fellow of the American
Statistical Association and the Institute of Mathematical Statistics. Her research interests
include design of screening and computer experiments.
Daniel Voss, PhD, is Professor Emeritus of Mathematics and Statistics and former Interim
Dean of the College of Science and Mathematics at Wright State University, Dayton, Ohio.
1st ed. 2017, VIII, 156 p.
Hardcover
ISBN 978-3-319-53906-5
Series: Algebra and Applications, Vol. 23
* Provides the first systematic treatment of formal matrices in a single
volume
* Examines injective, flat, projective and hereditary modules over
formal matrix rings of order 2 in great detail
* Includes concrete examples that illustrate the structures of formal
matrix rings
This monograph is a comprehensive account of formal matrices, examining homological
properties of modules over formal matrix rings and summarising the interplay between
Morita contexts and K theory.
While various special types of formal matrix rings have been studied for a long time
from several points of view and appear in various textbooks, for instance to examine
equivalences of module categories and to illustrate rings with one-sided non-symmetric
properties, this particular class of rings has, so far, not been treated systematically.
Exploring formal matrix rings of order 2 and introducing the notion of the determinant of
a formal matrix over a commutative ring, this monograph further covers the Grothendieck
and Whitehead groups of rings.
Graduate students and researchers interested in ring theory, module theory and operator
algebras will find this book particularly valuable. Containing numerous examples, Formal
Matrices is a largely self-contained and accessible introduction to the topic, assuming a
solid understanding of basic algebra.
1st ed. 2017, XX, 197 p. 58 illus., 34 illus. in
color.
Hardcover
ISBN 978-3-319-53039-0
Series: Understanding Complex Systems
* Introduces novel approaches to nonlinear control systems
* Self-contained presentation suitable also for newcomers to the field
* Contains many worked examples
This book acquaints readers with recent developments in dynamical systems theory and
its applications, with a strong focus on the control and estimation of nonlinear systems.
Several algorithms are proposed and worked out for a set of model systems, in particular
so-called input-affine or bilinear systems, which can serve to approximate a wide class
of nonlinear control systems. These can either take the form of state space models or be
represented by an input-output equation.
The approach taken here further highlights the role of modern mathematical and
conceptual tools, including differential algebraic theory, observer design for nonlinear
systems and generalized canonical forms.
2017, XIII, 384 p. 40 illus., 9 illus. in
color.
Hardcover
ISBN 978-3-319-53690-3
Series: Applied Mathematical Sciences, Vol. 90
* Provides an introduction to an advanced area of research ideal for
beginners
* Problems included at the end of each chapter
* Included topics lead to current literature and research
This third edition text provides expanded material on the restricted three body problem
and celestial mechanics. With each chapter containing new content, readers are provided
with new material on reduction, orbifolds, and the regularization of the Kepler problem,
all of which are provided with applications.
The previous editions grew out of graduate level courses in mathematics, engineering,
and physics given at several different universities. The courses took students who had
some background in differential equations and lead them through a systematic grounding
in the theory of Hamiltonian mechanics from a dynamical systems point of view.
This text provides a mathematical structure of celestial mechanics ideal for beginners, and
will be useful to graduate students and researchers alike.
Reviews of the second edition:
"The primary subject here is the basic theory of Hamiltonian differential equations
studied from the perspective of differential dynamical systems. The N-body problem is
used as the primary example of a Hamiltonian system, a touchstone for the theory as
the authors develop it. This book is intended to support a first course at the graduate
level for mathematics and engineering students. … It is a well-organized and accessible
introduction to the subject … . This is an attractive book … ." (William J. Satzer, The
Mathematical Association of America, March, 2009)
“The second edition of this text infuses new mathematical substance and relevance
into an already modern classic … and is sure to excite future generations of readers. …
This outstanding book can be used not only as an introductory course at the graduate
level in mathematics, but also as course material for engineering graduate students.
… it is an elegant and invaluable reference for mathematicians and scientists with an
interest in classical and celestial mechanics, astrodynamics, physics, biology, and related
fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)
1st ed. 2017, X, 390 p. 60 illus., 32 illus. in
color.
Hardcover
ISBN 978-3-319-54710-7
Series: Applied and Numerical Harmonic Analysis
* Presents state-of-the-art results in theoretical harmonic analysis,
image and signal processing, quantization, algorithms and
representationsWritten and reviewed by the leading experts in the
fieldSelected from over ten years of annual talks at the Norbert
Wiener Center
This volume consists of contributions spanning a wide spectrum of harmonic analysis
and its applications written by speakers at the February Fourier Talks from 2002 * 2016.
Containing cutting-edge results by an impressive array of mathematicians, engineers,
and scientists in academia, industry and government, it will be an excellent reference
for graduate students, researchers, and professionals in pure and applied mathematics,
physics, and engineering.
* Theoretical harmonic analysis
* Image and signal processing
* Quantization
* Algorithms and representations
The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic
Analysis and Applications. Located at the University of Maryland, College Park, the Norbert
Wiener Center provides a state-of- the-art research venue for the broad emerging area of
mathematical engineering.