1st ed. 2016, XX, 256 p. 48 illus., 8 illus. in color.
Softcover
ISBN 978-3-319-31461-7
Series: C.I.M.E. Foundation Subseries, Vol. 2158
* Equally interesting for mathematicians (pure and applied), physicists
and engineers due to the interdisciplinary nature of the subject
* Covers background material as well as aspects that represent the
state-of-the-art therefore recommended both for the novice and the
expert
* The discussions cover a wide range of open problems
This volume brings together four lecture courses on modern aspects of water waves.
The intention, through the lectures, is to present quite a range of mathematical ideas,
primarily to show what is possible and what, currently, is of particular interest.
Water waves of large amplitude can only be fully understood in terms of nonlinear effects,
linear theory being not adequate for their description. Taking advantage of insights from
physical observation, experimental evidence and numerical simulations, classical and
modern mathematical approaches can be used to gain insight into their dynamics. The
book presents several avenues and offers a wide range of material of current interest.
Due to the interdisciplinary nature of the subject, the book should be of interest to
mathematicians (pure and applied), physicists and engineers.
The lectures provide a useful source for those who want to begin to investigate how
mathematics can be used to improve our understanding of water wave phenomena. In
addition, some of the material can be used by those who are already familiar with one
branch of the study of water waves, to learn more about other areas. The lectures cover
background material as well as aspects that represent the state-of-the-art. We therefore
commend this collection of lectures to both the novice and the expert.
Series: Universitext
1st ed. 2016, Approx. 370 p. 46 illus., 13 illus. in color.
Softcover
ISBN 978-1-4471-6810-2
* Develops functional analysis in an original way, motivated by
natural examples of plane geometryProvides many examples and
counterexamples to help the reader understand the meaning,
usefulness and optimality of most notions and theoremsOffers a
large number of remarks and footnotes, which point readers to the
historical origins and development of most notions and results
This textbook, based on three series of lectures held by the author at the University
of Strasbourg, presents functional analysis in a non-traditional way by generalizing
elementary theorems of plane geometry to spaces of arbitrary dimension. This approach
leads naturally to the basic notions and theorems. Most results are illustrated by the small
*p spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes
Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut
versions of the classical theorems of Fubini-Tonelli and Radon-Nikodym.
Lectures on Functional Analysis and the Lebesgue Integral presents the most important
topics for students, with short, elegant proofs. The exposition style follows the Hungarian
mathematical tradition of Paul Erd?s and others. The order of the first two parts,
functional analysis and the Lebesgue integral, may be reversed. In the third and final part
they are combined to study various spaces of continuous and integrable functions. Several
beautiful, but almost forgotten, classical theorems are also included.
Both undergraduate and graduate students in pure and applied mathematics, physics and
engineering will find this textbook useful. Only basic topological notions and results are
used and various simple but pertinent examples and exercises illustrate the usefulness
and optimality of most theorems. Many of these examples are new or difficult to localize
in the literature, and the original sources of most notions and results are indicated to help
the reader understand the genesis and development of the field.
1st ed. 2016, Approx. 420 p. 10 illus.
Hardcover
ISBN 978-981-10-0529-9
* Presents a unified theory of reproducing kernels that is fundamental,
beautiful and widely applicable in mathematicsDeals with the
new discretizations and the Tikhonov regularization for practical
constructions of the solutions by computers.in analysis
* Introduces many global, up-to-date topics of general interest from
the general theory of N. Aronszajn
This book provides a large extension of the general theory of reproducing kernels
published by N. Aronszajn in 1950, with many concrete applications.
In Chapter 1, many concrete reproducing kernels are first introduced with detailed
information. Chapter 2 presents a general and global theory of reproducing kernels
with basic applications in a self-contained way. Many fundamental operations among
reproducing kernel Hilbert spaces are dealt with. Chapter 2 is the heart of this book.
Chapter 3 is devoted to the Tikhonov regularization using the theory of reproducing
kernels with applications to numerical and practical solutions of bounded linear operator
equations.
In Chapter 4, the numerical real inversion formulas of the Laplace transform are presented
by applying the Tikhonov regularization, where the reproducing kernels play a key role in
the results.
Chapter 5 deals with ordinary differential equations; Chapter 6 includes many concrete
results for various fundamental partial differential equations. In Chapter 7, typical integral
equations are presented with discretization methods. These chapters are applications
of the general theories of Chapter 3 with the purpose of practical and numerical
constructions of the solutions.
1st ed. 2016, X, 300 p. 30 illus., 10 illus. in color.
Hardcover
ISBN 978-3-319-31938-4
Series: Problem Books in Mathematics
* Describes the origin and history behind conjectures and problems in
graph theory
* Provides various methods to solving research problems in the field
* Provides strong pedagogical content for graduate students and a
reference to researchers in the field
This is the first in a series of volumes, which provide an extensive overview of conjectures
and open problems in graph theory. The readership of each volume is geared toward
graduate students who may be searching for research ideas. However, the wellestablished
mathematician will find the overall exposition engaging and enlightening.
Each chapter, presented in a story-telling style, includes more than a simple collection
of results on a particular topic. Each contribution conveys the history, evolution, and
techniques used to solve the authors’ favorite conjectures and open problems, enhancing
the reader’s overall comprehension and enthusiasm.
The editors were inspired to create these volumes by the popular and well attended
special sessions, entitled “My Favorite Graph Theory Conjectures," which were held at
the winter AMS/MAA Joint Meeting in Boston (January, 2012), the SIAM Conference on
Discrete Mathematics in Halifax (June,2012) and the winter AMS/MAA Joint meeting in
Baltimore(January, 2014). In an effort to aid in the creation and dissemination of open
problems, which is crucial to the growth and development of a field, the editors requested
the speakers, as well as notable experts in graph theory, to contribute to these volumes.
1ere ed. 2016, Env. 600 p.
Hardcover
ISBN 978-3-319-30057-3
Series: Progress in Mathematics, Vol. 317
* Donne une vue d'ensemble d'une methode puissante, la formule des
traces
* Reprend en un ouvrage unique toute une partie de la theorie
jusqu'alors eparse dans la litterature
* Le resultat demontre est le point de depart d'applications en
arithmetique et en geometrie
* Le livre complete les travaux de J. Arthur qui sont l'une des avancees
majeures du domaine
Ce travail en deux volumes donne la preuve de la stabilisation de la formule des trace
tordue.
Stabiliser la formule des traces tordue est la methode la plus puissante connue
actuellement pour comprendre l'action naturelle du groupe des points adeliques d'un
groupe reductif, tordue par un automorphisme, sur les formes automorphes de carre
integrable de ce groupe. Cette comprehension se fait en reduisant le probleme, suivant
les idees de Langlands, a des groupes plus petits munis d'un certain nombre de donnees
auxiliaires; c'est ce que l'on appelle les donnees endoscopiques. L'analogue non tordu a
ete resolu par J. Arthur et dans ce livre on suit la strategie de celui-ci.
Publier ce travail sous forme de livre permet de le rendre le plus complet possible.
Les auteurs ont repris la theorie de l'endoscopie tordue developpee par R. Kottwitz et
D. Shelstad et par J.-P. Labesse. Ils donnent tous les arguments des demonstrations
meme si nombre d'entre eux se trouvent deja dans les travaux d'Arthur concernant le
cas de la formule des traces non tordue. Ce travail permet de rendre inconditionnelle
la classification que J. Arthur a donnee des formes automorphes de carre integrable
pour les groupes classiques quasi-deployes, c’etait pour les auteurs une des principales
motivations pour l’ecrire.
Cette partie contient les preuves de la stabilisation geometrique et de la partie spectrale
en particulier de la partie discrete de ce terme, ce qui est le point d'aboutissement de ce
sujet.
408pp Apr 2016
ISBN: 978-981-4704-90-8 (hardcover)
This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.
In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.
Foundations:
Differentiable Manifolds
Finsler Metrics
Connections and Curvatures
S-Curvature
Riemann Curvature
Further Studies:
Projective Changes
Comparison Theorems
Fundamental Groups of Finsler Manifolds
Minimal Immersions and Harmonic Maps
Einstein Metrics
Miscellaneous Topics
Appendix:
Maple Program
Readership: Graduates and researchers interested in Finsler geometry.