Engineering Use of Group-Theoretic Bifurcation Theory
Exercises at the ends of chapters or sections
Solutions to selected exercises in the book
Detailed Illustrations
This book provides a modern static imperfect bifurcation theory applicable to bifurcation
phenomena of physical and engineering problems and fills the gap between the mathematical
theory and engineering practice. Systematic methods based on asymptotic, probabilistic, and
group theoretic standpoints are used to examine experimental and computational data from
numerous examples, such as soil, sand, kaolin, honeycomb, and domes. For mathematicians,
static bifurcation theory for finite-dimensional systems, as well as its applications for practical
problems, is illuminated by numerous examples. Engineers may find this book, with its
minimized mathematical formalism, to be a useful introduction to modern bifurcation theory.
This third edition strengthens group representation and group-theoretic bifurcation theory.
Several large scale applications have been included in association with the progress of
computational powers. Problems and answers have been provided. Review of First Edition: "The
book is unique in considering the experimental identification of material-dependent bifurcations
in structures such as sand, Kaolin (clay), soil and concrete shells. … These are studied
statistically. … The book is an excellent source of practical applications for mathematicians
working in this field. … A short set of exercises at the end of each chapter makes the book
more useful as a text. The book is well organized and quite readable for non-specialists." Henry
W. Haslach, Jr., Mathematical Reviews, 2003
3rd ed. 2019, XXV, 590 p.
239 illus., 33 illus. in color.
Hardcover
ISBN 978-3-030-21472-2
Softcover
ISBN 978-3-030-21475-3
Product category : Graduate/advanced undergraduate textbook
Series : Applied Mathematical Sciences
Mathematics : Systems Theory, Control
Is the first comprehensive introduction of Mordell?Weil lattices that does not
assume extensive prerequisites
Shows that the theory of Mordell?Weil lattices itself is very powerful yet
relatively easy to master and apply
Demonstrates with many examples and applications how Mordell?Weil lattices
connect with several areas of mathematics
This book lays out the theory of Mordell?Weil lattices, a very powerful and influential tool at
the crossroads of algebraic geometry and number theory, which offers many fruitful
connections to other areas of mathematics. The book presents all the ingredients entering into
the theory of Mordell?Weil lattices in detail, notably, relevant portions of lattice theory, elliptic
curves, and algebraic surfaces. After defining Mordell?Weil lattices, the authors provide several
applications in depth. They start with the classification of rational elliptic surfaces. Then a
useful connection with Galois representations is discussed. By developing the notion of
excellent families, the authors are able to design many Galois representations with given Galois
groups such as the Weyl groups of E6, E7 and E8. They also explain a connection to the
classical topic of the 27 lines on a cubic surface. Two chapters deal with elliptic K3 surfaces, a
pulsating area of recent research activity which highlights many central properties of Mordell?
Weil lattices. Finally, the book turns to the rank problem?one of the key motivations for the
introduction of Mordell?Weil lattices. The authors present the state of the art of the rank
problem for elliptic curves both over Q and over C(t) and work out applications to the sphere
packing problem. Throughout, the book includes many instructive examples illustrating the
theory
1st ed. 2019, XVI, 431 p. 32
illus., 9 illus. in color.
Hardcover
ISBN 978-981-32-9300-7
Softcover
ISBN 978-981-32-9303-8
Product category : Monograph
Series : Ergebnisse der Mathematik und ihrer
Grenzgebiete. 3. Folge / A Series of
Modern Surveys in Mathematics
Mathematics : Algebraic Geometry
Features comprehensively direct and inverse problems for graphs of strings
Appeals to both researchers in mathematics and practitioners in engineering
Presents the relation between classes of rational functions and their poles
and zeros
Considering that the motion of strings with finitely many masses on them is described by
difference equations, this book presents the spectral theory of such problems on finite graphs
of strings. The direct problem of finding the eigenvalues as well as the inverse problem of
finding strings with a prescribed spectrum are considered. This monograph gives a
comprehensive and self-contained account on the subject, thereby also generalizing known
results. The interplay between the representation of rational functions and their zeros and
poles is at the center of the methods used. The book also unravels connections between finite
dimensional and infinite dimensional spectral problems on graphs, and between self-adjoint
and non-self-adjoint finite-dimensional problems. This book is addressed to researchers in
spectral theory of differential and difference equations as well as physicists and engineers who
may apply the presented results and methods to their research.
1st ed. 2020, XVI, 349 p.
Hardcover
ISBN 978-3-030-60483-7
Product category : Monograph
Series : Operator Theory: Advances and Applications
Mathematics : Operator Theory
Example-driven introduction to the broad field of geometry
Hundreds of real-world applications
Accessible to both lay and specialized readers
This book returns geometry to its natural habitats: the arts, nature and technology. Throughout
the book, geometry comes alive as a tool to unlock the understanding of our world. Assuming
only familiarity with high school mathematics, the book invites the reader to discover geometry
through examples from biology, astronomy, architecture, design, photography, drawing,
engineering and more. Lavishly illustrated with over 1200 figures, all of the geometric results
are carefully derived from scratch, with topics from differential, projective and non-Euclidean
geometry, as well as kinematics, introduced as the need arises. The mathematical results
contained in the book range from very basic facts to recent results, and mathematical proofs
are included although not necessary for comprehension. With its wide range of geometric
applications, this self-contained volume demonstrates the ubiquity of geometry in our world,
and may serve as a source of inspiration for architects, artists, designers, engineers, and
natural scientists. This new edition has been completely revised and updated, with new topics
and many new illustrations.
Due 2021-01-03
2nd ed. 2020, X, 697 p.
1153 illus., 1117 illus. in color.
Softcover
ISBN 978-3-030-61397-6
Product category : Undergraduate textbook
Mathematics : Geometry
Presents the methodology of Singular Spectrum Analysis (SSA)
Describes Multivariate Singular Spectrum Analysis (MSSA) and SSA for image
processing (2D-SSA)
Illustrated with examples and case studies
This book gives an overview of singular spectrum analysis (SSA). SSA is a technique of time
series analysis and forecasting combining elements of classical time series analysis,
multivariate statistics, multivariate geometry, dynamical systems and signal processing. SSA is
multi-purpose and naturally combines both model-free and parametric techniques, which
makes it a very special and attractive methodology for solving a wide range of problems
arising in diverse areas. Rapidly increasing number of novel applications of SSA is a
consequence of the new fundamental research on SSA and the recent progress in computing
and software engineering which made it possible to use SSA for very complicated tasks that
were unthinkable twenty years ago. In this book, the methodology of SSA is concisely but at
the same time comprehensively explained by two prominent statisticians with huge experience
in SSA. The book offers a valuable resource for a very wide readership, including professional
statisticians, specialists in signal and image processing, as well as specialists in numerous
applied disciplines interested in using statistical methods for time series analysis, forecasting,
signal and image processing. The second edition of the book contains many updates and some
new material including a thorough discussion on the place of SSA among other methods and
new sections on multivariate and multidimensional extensions of SSA
Due 2021-01-01
2nd ed. 2020, IX, 146 p. 43
illus., 38 illus. in color.
Softcover
ISBN 978-3-662-62435-7
Product category : Brief
Series : SpringerBriefs in Statistics
Statistics : Statistical Theory and Methods
Fills a gap found in existing monographs regarding feasible operatortheoretic foundations for wider applications
Provides a background of time-fractional derivatives from the viewpoint of the
operator theory in Sobolev spaces
Justifies well-posedness for fractional differential equations in a selfcontained manner
This book aims to establish a foundation for fractional derivatives and fractional differential
equations. The theory of fractional derivatives enables considering any positive order of
differentiation. The history of research in this field is very long, with its origins dating back to
Leibniz. Since then, many great mathematicians, such as Abel, have made contributions that
cover not only theoretical aspects but also physical applications of fractional calculus. The
fractional partial differential equations govern phenomena depending both on spatial and time
variables and require more subtle treatments. Moreover, fractional partial differential equations
are highly demanded model equations for solving real-world problems such as the anomalous
diffusion in heterogeneous media. The studies of fractional partial differential equations have
continued to expand explosively. However we observe that available mathematical theory for
fractional partial differential equations is not still complete. In particular, operator-theoretical
approaches are indispensable for some generalized categories of solutions such as weak
solutions, but feasible operator-theoretic foundations for wide applications are not available in
monographs. To make this monograph more readable, we are restricting it to a few
fundamental types of time-fractional partial differential equations, forgoing many other
important and exciting topics such as stability for nonlinear problems. However, we believe that
this book works well as an introduction to mathematical research in such vast fields.
Due 2020-12-19
1st ed. 2020, X, 134 p. 1 illus.
Softcover
ISBN 978-981-15-9065-8
Product category : Brief
Series : SpringerBriefs in Mathematics
Mathematics : Partial Differential Equations
Includes well-explained examples
Gives a comprehensive overview on the theory of C*-algebras
Evolves from a course given at the CRM in Barcelona
This book is directed towards graduate students that wish to start from the basic theory of C*-
algebras and advance to an overview of some of the most spectacular results concerning the
structure of nuclear C*-algebras. The text is divided into three parts. First, elementary notions,
classical theorems and constructions are developed. Then, essential examples in the theory,
such as crossed products and the class of quasidiagonal C*-algebras, are examined, and
finally, the Elliott invariant, the Cuntz semigroup, and the Jiang-Su algebra are defined. It is
shown how these objects have played a fundamental role in understanding the fine structure
of nuclear C*-algebras. To help understanding the theory, plenty of examples, treated in detail,
are included. This volume will also be valuable to researchers in the area as a reference guide.
It contains an extensive reference list to guide readers that wish to travel further.
Due 2020-12-30
1st ed. 2020, X, 324 p. 6 illus.
Softcover
ISBN 978-3-030-47464-5
Product category : Graduate/advanced undergraduate textbook
Series : Advanced Courses in Mathematics - CRM Barcelona
Mathematics : Functional Analysis
A modern compact introduction to factorization homology suited for graduate
students
Assumes no familiarity with advanced homotopy theory
Provides exercises that build intuition and help the reader to learn quickly
This book provides an informal and geodesic introduction to factorization homology, focusing
on providing intuition through simple examples. Along the way, the reader is also introduced to
modern ideas in homotopy theory and category theory, particularly as it relates to the use of
infinity-categories. As with the original lectures, the text is meant to be a leisurely read suitable
for advanced graduate students and interested researchers in topology and adjacent fields.
Due 2021-01-01
1st ed. 2020, XI, 85 p. 33 illus., 3 illus. in color.
Softcover
ISBN 978-3-030-61162-0
Product category : Brief
Series : SpringerBriefs in Mathematical Physics
Physics : Theoretical, Mathematical and Computational Physics