Series: SpringerBriefs in Mathematics
1st ed. 2019, XII, 101 p. 75 illus.
Printed book
Softcover
Covers fundamentals of different interpretations of labeling graphs
Provides examples and illustrations for wide variety of graph labeling
Introduces new graph labeling with connection to Four Color Theorem
This book depicts graph labelings that have led to thought-provoking problems and
conjectures. Problems and conjectures in graceful labelings, harmonious labelings, prime
labelings, additive labelings, and zonal labelings are introduced with fundamentals, examples,
and illustrations. A new labeling with a connection to the four color theorem is described to aid
mathematicians to initiate new methods and techniques to study classical coloring problems
from a new perspective. Researchers and graduate students interested in graph labelings will
find the concepts and problems featured in this book valuable for finding new areas of research.
Softcover
ISBN 978-3-030-17458-3
Presents recent research on Kato's inequality for the benefit of a large class
of researchers working on operator inequalities
Provides complete proofs of the main results that will allow researchers to try
and extend Kato's inequality for semi-inner products in Banach spaces
Shows clear applications for numerical radius and norm inequalities to give
the readers the possibility to compare them with other similar results
Gives extensions of Kato's inequality for functions of operators that will allow
scientists to look for extensions to more general functional calculus than the
continuous functional calculus
The aim of this book is to present results related to Kato's famous inequality for bounded
linear operators on complex Hilbert spaces obtained by the author in a sequence of recent
research papers. As Linear Operator Theory in Hilbert spaces plays a central role in
contemporary mathematics, with numerous applications in fields including Partial Differential
Equations, Approximation Theory, Optimization Theory, and Numerical Analysis,the volume
isintended for use by both researchers in various fields and postgraduate students and
scientists applying inequalities in their specific areas.For the sake of completeness, all the
results presented are completely proved and the original references where they have been
firstly obtained are mentioned
Hardcover
ISBN 978-3-030-18220-5
Examines the qualitative study of solutions of superlinear elliptic and
parabolic partial differential equations and systems
Self-contained and up-to-date, taking special care on the didactical
preparation of the material
Devoted to problems that are intensively studied but have not been treated in
depth in the book literature so far
This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic
partial differential equations and systems. This class of problems contains, in particular, a
number of reaction-diffusion systems which arise in various mathematical models, especially in
chemistry, physics and biology. The first two chapters introduce to the field and enable the
reader to get acquainted with the main ideas by studying simple model problems, respectively
of elliptic and parabolic type. The subsequent three chapters are devoted to problems with
more complex structure; namely, elliptic and parabolic systems, equations with gradient
depending nonlinearities, and nonlocal equations. They include many developments which
reflect several aspects of current research. Although the techniques introduced in the first two
chapters provide efficient tools to attack some aspects of these problems, they often display
new phenomena and specifically different behaviors, whose study requires new ideas. Many
open problems are mentioned and commented. The book is self-contained and up-to-date, it
has a high didactic quality. It is devoted to problems that are intensively studied but have not
been treated so far in depth in the book literature. The intended audience includes graduate
and postgraduate students and researchers working in the field of partial differential equations
and applied mathematics. The first edition of this book has become one of the standard
references in the field. This second edition provides a revised text and contains a number of
updates reflecting significant recent advances that have appeared in this growing field since
the first edtion.
Due 2019-06-15
1st ed. 2019, X, 314 p. 527
illus., 1 illus. in color.
Hardcover
ISBN 978-3-030-17992-2
Their History and Construction from Ancient Times to AD 1600
Provides an English translation of the author's study on the science of magic squares
Contains an updated overview of the subject
Includes a full chapter on other magic figures
The science of magic squares witnessed an important development in the Islamicworld during
the Middle Ages, with a great variety of construction methods beingcreated and ameliorated.
The initial step was the translation, in the ninth century,of an anonymous Greek text containing
the description of certain highly developedarrangements, no doubt the culmination of ancient
research on magic squares.
Due 2019-06-19
1st ed. 2019, XIV, 593 p.
Softcover
ISBN 978-3-030-16488-1
Full treatment of basic properties of Lipschitz functions with numerous examples
A thorough presentation of various extension results for (scalar and vector) Lipschitz functions
Full treatment of Banach spaces of Lipschitz functions and of operators acting on them
A presentation of Lipschitz free Banach spaces with applications to
Kantorovich duality in the mass transportation problem
The aim of this book is to present various facets of the theory and applications of Lipschitz
functions, starting with classical and culminating with some recent results. Among the included
topics we mention: characterizations of Lipschitz functions and relations with other classes of
functions, extension results for Lipschitz functions and Lipschitz partitions of unity, Lipschitz
free Banach spaces and their applications, compactness properties of Lipschitz operators,
Bishop-Phelps type results for Lipschitz functionals, applications to best approximation in
metric and in metric linear spaces, Kantorovich-Rubinstein norm and applications to duality in
the optimal transport problem, Lipschitz mappings on geodesic spaces. The prerequisites are
basic results in real analysis, functional analysis, measure theory (including vector measures)
and topology, which, for reader's convenience, are surveyed in the first chapter of the book.
Due 2019-07-13
1st ed. 2019, XX, 220 p. 13
illus., 7 illus. in color.
Hardcover
ISBN 978-3-030-18182-6
Presents results of the last few decades on singular curvature theory and
integral geometry in a nearly comprehensive way
Includes the necessary facts from geometric measure theory in a separate chapter
Presents approaches that will help researchers achieve further progress in the field
The book describes how curvature measures can be introduced for certain classes of sets
withsingularities in Euclidean spaces. Its focus lies on sets with positive reach and some
extensions,which include the classical polyconvex sets and piecewise smooth submanifolds as
specialcases. The measures under consideration form a complete system of certain
Euclideaninvariants. Techniques of geometric measure theory, in particular, rectifiable currents
areapplied, and some important integral-geometric formulas are derived. Moreover, an
approach tocurvatures for a class of fractals is presented, which uses approximation by the
rescaledcurvature measures of small neighborhoods. The book collects results published
during the lastfew decades in a nearly comprehensive way
Due 2019-07-06
1st ed. 2019, Approx. 300 p.
12 illus., 11 illus. in color.
Hardcover
ISBN 978-3-030-17948-9
Presents cutting-edge results in the areas of control theory and PDEs, giving
a broad picture of recent advances
Contains contributions from leading experts
Includes theoretical studies and models for applications
This book presents cutting-edge contributions in the areas of control theory and partial
differential equations. Over the decades, control theory has had deep and fruitful interactions
with the theory of partial differential equations (PDEs). Well-known examples are the study of
the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and
stochastic optimal control and the development of modern analytical tools to study the
controllability of infinite dimensional systems governed by PDEs. In the present volume, leading
experts provide an up-to-date overview of the connections between these two vast fields of
mathematics. Topics addressed include regularity of the value function associated to finite
dimensional control systems, controllability and observability for PDEs, and asymptotic analysis
of multiagent systems. The book will be of interest for both researchers and graduate students
working in these areas.
Due 2019-07-13
1st ed. 2019, XV, 234 p.
Hardcover
ISBN 978-3-030-18151-2
First book on homogeneous pseudo-Riemannian structures
Covers the developments of the past 35 years up to the current state of the art
Important to the study of homogenous spaces
This book provides an up-to-date presentation of homogeneous pseudo-Riemannian structures,
an essential tool in the study of pseudo-Riemannian homogeneous spaces. Benefiting from
large symmetry groups, these spaces are of high interest in Geometry and Theoretical Physics.
Since the seminal book by Tricerri and Vanhecke, the theory of homogeneous structures has
been considerably developed and many applications have been found. The present work covers
a gap in the literature of more than 35 years, presenting the latest contributions to the field in
a modern geometric approach, with special focus on manifolds equipped with pseudoRiemannian
metrics. This unique reference on the topic will be of interest to researchers
working in areas of mathematics where homogeneous spaces play an important role, such as
Differential Geometry,Global Analysis, General Relativity, and Particle Physics.