Due 2018-07-24
1st ed. 2018, X, 170 p.
Printed book
Softcover
ISBN 978-3-319-92706-0
Series
Pseudo-Differential Operators
Explores a new approach to the Riemann hypothesis
Explains the link between the theory of modular distributions and the
classical one of modular forms
Includes previously unpublished material
Classically developed as a tool for partial differential equations, theanalysis of operators known
as pseudodifferential analysis is here regardedas a possible help in questions of arithmetic.
The operators which make upthe main subject of the book can be characterized in terms of
congruencearithmetic.They enjoy a Eulerian structure, and are applied to the searchfor new
conditions equivalent to the Riemann hypothesis. These consist inthe validity of certain
parameter-dependent estimates for a class of Hermitianforms of finite rank. The Littlewood
criterion, involving sums ofMobius coefficients, and the Weil so-called explicit formula, which
leads tohis positivity criterion, fit within this scheme, using in the first case
Weyl'spseudodifferential calculus, in the second case Fuchs'. The book should beof interest to
people looking for new possible approaches to the Riemannhypothesis, also to new
perspectives on pseudodifferential analysis and onthe way it combines with modular form
theory. Analysts will have no difficulty with the arithmetic aspects, with which, save for very few
Due 2018-07-27
1st ed. 2018, Approx. 400 p.
11 illus.
Printed book
Hardcover
ISBN 978-3-662-57412-6
17 survey articles in an active research field
Modern algebraic and topological methods
Includes open problems in various connected areas
This volume contains 17 surveys that cover many recent developments in Discrete Geometry
and related fields. Besides presenting the state-of-the-art of classical research subjects like
packing and covering, it also offers an introduction to new topological, algebraic and
computational methods in this very active research field. The readers will find a variety of
modern topics and many fascinating open problems that may serve as starting points for
research.
Due 2018-08-22
1st ed. 2018, X, 320 p. 41
illus., 15 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-91781-8
Presents a Lagrangian approach model to formulate various fields of
continuum physics
Extends the classical theories based on Riemann geometry to Riemann-Cartan
geometry
Describes non-homogeneous continuum and spacetime with torsion in
Einstein-Cartan relativistic gravitation
This book presents a Lagrangian approach model to formulate various fields of continuum
physics, ranging from gradient continuum elasticity to relativistic gravito-electromagnetism. It
extends the classical theories based on Riemann geometry to Riemann-Cartan geometry, and
then describesnon-homogeneouscontinuum and spacetime with torsion in Einstein-Cartan
relativistic gravitation. It investigates two aspects of invariance of the Lagrangian: covariance of
formulation following the method of Lovelock and Rund, and gauge invariance where the active
diffeomorphism invariance is considered by using local Poincare gauge theory according to the
Utiyama method. Further, it develops various extensions of strain gradient continuum elasticity,
relativistic gravitation and electromagnetism when the torsion field of the Riemann-Cartan
continuum is not equal to zero.Lastly, it derives heterogeneous wave propagation equations
within twisted and curved manifolds and proposes a relation between electromagnetic potential
and torsion tensor.
1st ed. 2018, XVI, 304 p. 88 illus., 43
illus. in color.
Printed book
Hardcover
ISBN 978-3-319-90025-4
Series: Springer Proceedings in Mathematics & Statistics
This volume contains 13 selected keynote papers presented at the Fourth International
Conference on Numerical Analysis and Optimization. Held every three years at Sultan Qaboos
University in Muscat, Oman, this conference highlights novel and advanced applications of
recent research in numerical analysis and optimization. Each peer-reviewed chapter featured in
this book reports on developments in key fields, such as numerical analysis, numerical
optimization, numerical linear algebra, numerical differential equations, optimal control,
approximation theory, applied mathematics, derivative-free optimization methods, programming
models, and challenging applications that frequently arise in statistics, econometrics, finance,
physics, medicine, biology, engineering and industry. Any graduate student or researched
wishing to know the latest research in the field will be interested in this volume. This book is
dedicated to the late Professors Mike JD Powell and Roger Fletcher, who were the pioneers
and leading figures in the mathematics of nonlinear optimization.
Due 2018-08-20
1st ed. 2018, XIII, 282 p.
70 illus., 44 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-91142-7
Presents cutting-edge research from a wide variety of science and
engineering fields that use inductive statistics
Examines and discusses the foundations of inductive statistics, addressing
the growing difficulty in choosing the optimal method to apply to problems
due to the increasing availability of Bayesian methodological alternatives
Expands the available research on Bayesian methods and promotes their
application in the scientific community
These proceedings from the 37th International Workshop on Bayesian Inference and Maximum
Entropy Methods in Science and Engineering (MaxEnt 2017), held in Sao Carlos, Brazil, aim to
expand the available research on Bayesian methods and promote their application in the
scientific community. They gather research from scholars in many different fields who use
inductive statistics methods and focus on the foundations of the Bayesian paradigm, their
comparison to objectivistic or frequentist statistics counterparts, and their appropriate
applications. Interest in the foundations of inductive statistics has been growing with the
increasing availability of Bayesian methodological alternatives, and scientists now face much
more difficult choices in finding the optimal methods to apply to their problems. By carefully
examining and discussing the relevant foundations, the scientific community can avoid applying
Bayesian methods on a merely ad hoc basis. For over 35 years, the MaxEnt workshops have
explored the use of Bayesian and Maximum Entropy methods in scientific and engineering
application contexts.
1st ed. 2018, X, 160 p.
Printed book
Softcover
ISBN 978-3-319-92416-8
Provides a systematic and accessible treatment of results on measurable
partitions
Presents a new point of view: From the spectral theory of transfer operators
and universal Hilbert space, to new interconnections between dynamical
systems, and their use in multiresolution analysis
Numerous explicit examples make direct links between the theory and a
multitude of diverse applications
The subject of this book stands at the crossroads of ergodic theory and measurable dynamics.
With an emphasis on irreversible systems, the text presents a framework of multi-resolutions
tailored for the study of endomorphisms, beginning with a systematic look at the latter. This
entails a whole new set of tools, often quite different from those used for the “easier” and welldocumented
case of automorphisms. Among them is the construction of a family of positive
operators (transfer operators), arising naturally as a dual picture to that of endomorphisms.
The setting (close to one initiated by S. Karlin in the context of stochastic processes) is
motivated by a number of recent applications, including wavelets, multi-resolution analyses,
dissipative dynamical systems, and quantum theory. The automorphism-endomorphism
relationship has parallels in operator theory, where the distinction is between unitary operators
in Hilbert space and more general classes of operators such as contractions. There is also a
non-commutative version: While the study of automorphisms of von Neumann algebras dates
back to von Neumann, the systematic study of their endomorphisms is more recent; together
with the results in the main text, the book includes a review of recent related research papers,
some by the co-authors and their collaborators.
Due 2018-08-08
6th ed. 2018, IX, 326 p.
284 illus., 6 illus. in color.
Printed book
Hardcover
ISBN 978-3-662-57264-1
New chapter on Van der Waerden’s permanent conjecture
New sections on the asymptotics for the number of Latin squares
New proof for the Basel problem
Geometric explanation for the involution proof for Fermat's two squares
theorem
This revised and enlarged sixth edition ofProofs from THE BOOKfeatures an entirely new
chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and
delightful proofs in other chapters. From the citation on the occasion of the 2018 "Steele Prize
for Mathematical Exposition" “… It is almost impossible to write a mathematics book that can
be read and enjoyed by peopleof all levels and backgrounds, yet Aigner and Ziegler accomplish
this feat of exposition with virtuoso style. […] This book does an invaluable service to
mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when
they speak about beauty.” From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a
glimpse of mathematical heaven, where clever insights and beautiful ideas combine in
astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ...
Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that
our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful
observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and
to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a
pleasure to read as well: the style is clear and entertaining, the level is close to elementary,
the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter,
January 1999 "Martin Aigner and Gunter Ziegler succeeded admirably in putting together a
broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdos.
The theorems are so fundamental, their proofs so elegant and the remaining open questions
so intriguing that every mathematician, regardless of speciality, can benefit from reading this
book. ... " SIGACT News, December 2011
Due 2018-08-16
1st ed. 2018, X, 132 p. 37
illus., 23 illus. in color.
Printed book
Softcover
ISBN 978-3-319-93826-4
Gathers together results that were previously only available in papers
Explores the graph approach as a way to better understand probability
measurement in a quantum framework
Presents the fundamental concepts and tools for those interested in pursuing
research in this field
This book explores two of the most striking features of quantum theory ? contextuality and
nonlocality ? using a formulation based on graph theory. Quantum theory provides a set of
rules to predict probabilities of different outcomes in different experimental settings, and both
contextuality and nonlocality play a fundamental role in interpreting the outcomes. In this
work, the authors highlight how the graph approach can lead to a better understanding of this
theory and its applications. After presenting basic definitions and explaining the noncontextuality
hypothesis, the book describes contextuality scenarios using compatibility
hypergraphs. It then introduces the exclusivity graph approach, which relates a number of
important graph-theoretical concepts to contextuality. It also presents open problems such as
the so-called Exclusivity Principle, as well as a selection of important topics, like sheaftheoretical
approach, hypergraph approach, and alternative proofs of contextuality.