Features state-of-the-art, mathematically and scientifically diverse
perspectives and descriptions
Addresses open fundamental questions in the quest for understanding the
natural and physical world
Enriches readersf mathematical grasp of naturefs beauty
This unique book gathers various scientific and mathematical approaches to and descriptions
of the natural and physical world stemming from a broad range of mathematical areas ? from
model systems, differential equations, statistics, and probability ? all of which scientifically and
mathematically reveal the inherent beauty of natural and physical phenomena. Topics include
Archimedean and Non-Archimedean approaches to mathematical modeling; thermography
model with application to tungiasis inflammation of the skin; modeling of a tick-Killing Robot;
various aspects of the mathematics for Covid-19, from simulation of social distancing scenarios
to the evolution dynamics of the coronavirus in some given tropical country to the
spatiotemporal modeling of the progression of the pandemic. Given its scope and approach,
the book will benefit researchers and students of mathematics, the sciences and engineering,
and everyone else with an appreciation for the beauty of nature. The outcome is a
mathematical enrichment of naturefs beauty in its various manifestations. This volume honors
Dr. John Adam, a Professor at Old Dominion University, USA, for his lifetime achievements in
the fields of mathematical modeling and applied mathematics. Dr. Adam has published over
110 papers and authored several books.
Due 2021-11-11
1st ed. 2021, VIII, 292 p. 18 illus., 8 illus. in color.
Hardcover : ISBN 978-3-030-84595-7
Product category : Contributed volume
Series : STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health
Mathematics : Systems Theory, Control
Features state-of-the-art developments, techniques, and applications of nonArchimedean analysis
Gathers contributions by leading international experts in the field
Introduces open problems and areas for future research
This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its
applications. Featuring new techniques developed by leading experts in the field, it highlights
the relevance and depth of this important area of mathematics, in particular its expanding
reach into the physical, biological, social, and computational sciences as well as engineering
and technology. In the last forty years the connections between non-Archimedean mathematics
and disciplines such as physics, biology, economics and engineering, have received
considerable attention. Ultrametric spaces appear naturally in models where hierarchy plays a
central role ? a phenomenon known as ultrametricity. In the 80s, the idea of using ultrametric
spaces to describe the states of complex systems, with a natural hierarchical structure,
emerged in the works of Fraunfelder, Parisi, Stein and others. A central paradigm in the physics
of certain complex systems ? for instance, proteins ? asserts that the dynamics of such a
system can be modeled as a random walk on the energy landscape of the system. To
construct mathematical models, the energy landscape is approximated by an ultrametric space
(a finite rooted tree), and then the dynamics of the system is modeled as a random walk on
the leaves of a finite tree. In the same decade, Volovich proposed using ultrametric spaces in
physical models dealing with very short distances. This conjecture has led to a large body of
research in quantum field theory and string theory. In economics, the non-Archimedean utility
theory uses probability measures with values in ordered non-Archimedean fields. Ultrametric
spaces are also vital in classification and clustering techniques.
Due 2021-11-01
1st ed. 2021, IV, 260 p. 46 illus., 23 illus. in color.
Hardcover : ISBN 978-3-030-81975-0
Product category : Contributed volume
Series : STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health
Mathematics : Number Theory
Presents complete proofs of deep results in probability
Provides essential tools and methods
Discusses a number of classical problems and fundamental open questions
This book provides an in-depth account of modern methods used to bound the supremum of
stochastic processes. Starting from first principles, it takes the reader to the frontier of current
research. This second edition has been completely rewritten, offering substantial improvements
to the exposition and simplified proofs, as well as new results. The book starts with a thorough
account of the generic chaining, a remarkably simple and powerful method to bound a
stochastic process that should belong to every probabilistfs toolkit. The effectiveness of the
scheme is demonstrated by the characterization of sample boundedness of Gaussian
processes. Much of the book is devoted to exploring the wealth of ideas and results generated
by thirty years of efforts to extend this result to more general classes of processes, culminating
in the recent solution of several key conjectures. A large part of this unique book is devoted to
the authorfs influential work. While many of the results presented are rather advanced, others
bear on the very foundations of probability theory. In addition to providing an invaluable
reference for researchers, the book should therefore also be of interest to a wide range of
readers.
Due 2021-11-11
2nd ed. 2021, X, 671 p. 13 illus.
Hardcover : ISBN 978-3-030-82594-2
Product category : Monograph
Series : Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
/ A Series of Modern Surveys in Mathematics
Mathematics : Probability Theory and Stochastic Processes
Gives a modern account of the Hardy?Littlewood circle method
Including its workings over number fields and function fields
Illustrates the use of the circle method in algebraic geometry
The Hardy?Littlewood circle method was invented over a century ago to study integer solutions
to special Diophantine equations, but it has since proven to be one of the most successful
allpurpose tools available to number theorists. Not only is it capable of handling remarkably
general systems of polynomial equations defined over arbitrary global fields, but it can also
shed light on the space of rational curves that lie on algebraic varieties. This book, in which the
arithmetic of cubic polynomials takes centre stage, is aimed at bringing beginning graduate
students into contact with some of the many facets of the circle method, both classical and
modern.This monograph is the winner of the 2021 Ferran Sunyer i Balaguer Prize, a
prestigious award for books of expository nature presenting the latest developments in an
active area of research in mathematics.
Due 2021-11-16
1st ed. 2021, X, 140 p. 2 illus. in color.
Hardcover : ISBN 978-3-030-86871-0
Product category : Monograph
Series : Progress in Mathematics
Mathematics : Number Theory
Presents a thorough study of geometric, analytic and probabilistic aspects of
infinite graphs, including recent results
Provides a very accessible introduction to general Dirichlet form theory by
focusing on discrete spaces
Relates spectral theory, the heat equation and intrinsic metrics on graphs
The spectral geometry of infinite graphs deals with three major themes and their interplay: the
spectral theory of the Laplacian, the geometry of the underlying graph, and the heat flow with
its probabilistic aspects. In this book, all three themes are brought together coherently under
the perspective of Dirichlet forms, providing a powerful and unified approach. The book gives a
complete account of key topics of infinite graphs, such as essential self-adjointness, Markov
uniqueness, spectral estimates, recurrence, and stochastic completeness. A major feature of the
book is the use of intrinsic metrics to capture the geometry of graphs. As for manifolds,
Dirichlet forms in the graph setting offer a structural understanding of the interaction between
spectral theory, geometry and probability. For graphs, however, the presentation is much more
accessible and inviting thanks to the discreteness of the underlying space, laying bare the main
concepts while preserving the deep insights of the manifold case. Graphs and Discrete Dirichlet
Spaces offers a comprehensive treatment of the spectral geometry of graphs, from the very
basics to deep and thorough explorations of advanced topics. With modest prerequisites, the
book can serve as a basis for a number of topics courses, starting at the undergraduate level.
Due 2021-11-02
XVI, 666 p. 4 illus.
Hardcover : ISBN 978-3-030-81458-8
Product category : Monograph
Series : Grundlehren der mathematischen Wissenschaften
Mathematics : Graph Theory
This book provides an overview of the latest progress on rationality questions in algebraic
geometry. It discusses new developments such as universal triviality of the Chow group of zero
cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli
spaces and birational invariants of group actions on varieties, contributed by the foremost
experts in their fields. The question of whether an algebraic variety can be parametrized by
rational functions of as many variables as its dimension has a long history and played an
important role in the history of algebraic geometry. Recent developments in algebraic geometry
have made this question again a focal point of research and formed the impetus to organize a
conference in the series of conferences on the island of Schiermonnikoog. The book follows in
the tradition of earlier volumes, which originated from conferences on the islands Texel and
Schiermonnikoog.
Due 2021-11-13
Approx. 380 p.
Hardcover : ISBN 978-3-030-75420-4
Product category : Proceedings
Series : Progress in Mathematics
Mathematics : Algebraic Geometry
Provides an thorough introduction to function spaces, ranging from
elementary to advanced material
Each chapter contains clearly stated learning objectives and numerous
exercises
Includes applications to partial differential equations
Simultaneously introduces Sobolev functions and functions of bounded
variation
This textbook provides a thorough-yet-accessible introduction to function spaces, through the
central concepts of integrability, weakly differentiability and fractionally differentiability. In an
essentially self-contained treatment the reader is introduced to Lebesgue, Sobolev and BVspaces,
before being guided through various generalisations such as Bessel-potential spaces,
fractional Sobolev spaces and Besov spaces. Written with the student in mind, the book
gradually proceeds from elementary properties to more advanced topics such as lower
dimensional trace embeddings, fine properties and approximate differentiability, incorporating
recent approaches. Throughout, the authors provide careful motivation for the underlying
concepts, which they illustrate with selected applications from partial differential equations,
demonstrating the relevance and practical use of function spaces. Assuming only multivariable
calculus and elementary functional analysis, as conveniently summarised in the opening
chapters, A Course in Function Spaces is designed for lecture courses at the graduate level and
will also be a valuable companion for young researchers in analysis.
Due 2022-05-16
1st ed. 2022, Approx. 400 p. 28 illus., 5 illus. in color.
Softcover : ISBN 978-3-030-80642-2
Product category : Graduate/advanced undergraduate textbook
Series : Universitext
Mathematics : Functional Analysis