Series: Association for Women in Mathematics Series, Vol. 5
1st ed. 2017, XV, 356 p. 54 illus., 43 illus. in color.
Hardcover
ISBN 978-3-319-51591-5
* Contains survey and research articles by leading experts
* Features fully-refereed high quality papers exploring new results and
trends in spectral theory, mathematical physics, geometric function
theory, partial differential equations, and the novel field of chromatic
derivatives
* Examines the remarkable connections between harmonic analysis
and operator theory
This book is the second of a two volume series. Covering a range of subjects from operator
theory and classical harmonic analysis to Banach space theory, this book features fullyrefereed,
high-quality papers exploring new results and trends in weighted norm
inequalities, Schur-Agler class functions, complex analysis, dynamical systems, and dyadic
harmonic analysis. Graduate students and researchers in analysis will find inspiration
in the articles collected in this volume, which emphasize the remarkable connections
between harmonic analysis and operator theory. A survey of the two weight problem
for the Hilbert transform and an expository article on the Clark model to the case of nonsingular
measures and applications to the study of rank-one perturbations are included.
The material for this volume is based on the 13th New Mexico Analysis Seminar held at the
University of New Mexico, April 3-4, 2014 and on several special sections of the Western
Spring Sectional Meeting at the University of New Mexico, April 4-6,2014. During the
event, participants honored the memory of Cora Sadosky*a great mathematician who
recently passed away and who made significant contributions to the field of harmonic
analysis. Cora was an exceptional scientist and human being. She was a world expert in
harmonic analysis and operator theory, publishing over fifty-five research papers and
authoring a major textbook in the field. Participants of the conference include new and
senior researchers, recent doctorates as well as leading experts in the area.
1st ed. 2017, VI, 139 p. 5 illus., 3 illus. in color.
Softcover
ISBN 978-3-319-51752-0
Series: Research Perspectives CRM Barcelona, Vol. 6
This book is divided into two parts, the first of which seeks to connect the phase
transitions of various disciplines, including game theory, and to explore the synergies
between statistical physics and combinatorics. Phase Transitions has been an active
multidisciplinary field of research, bringing together physicists, computer scientists
and mathematicians. The main research theme explores how atomic agents that act
locally and microscopically lead to discontinuous macroscopic changes. Adopting this
perspective has proven to be especially useful in studying the evolution of random and
usually complex or large combinatorial objects (like networks or logic formulas) with
respect to discontinuous changes in global parameters like connectivity, satisfiability
etc. There is, of course, an obvious strategic element in the formation of a transition: the
atomic agents “selfishly” seek to optimize a local parameter. However, up to now this
game-theoretic aspect of abrupt, locally triggered changes had not been extensively
studied.
In turn, the book’s second part is devoted to mathematical and computational methods
applied to the pricing of financial contracts and the measurement of financial risks. The
tools and techniques used to tackle these problems cover a wide spectrum of fields,
like stochastic calculus, numerical analysis, partial differential equations, statistics and
econometrics. Quantitative Finance is a highly active field of research and is increasingly
attracting the interest of academics and practitioners alike. The material presented
addresses a wide variety of new challenges for this audience.
2017, XVII, 248 p. 17 illus.
Hardcover
ISBN 978-3-319-50928-0
Series: Probability Theory and Stochastic Modelling, Vol. 40
* Promotes original analytic methods to determine the invariant
measure of two-dimensional random walks in domains with
boundaries. These processes appear in several mathematical areas
(Stochastic Networks, Analytic Combinatorics, Quantum Physics).
* The second edition includes additional recent results on the group of
the random walk. It presents also case-studies from queueing theory
and enumerative combinatorics.
This monograph aims to promote original mathematical methods to determine the
invariant measure of two-dimensional random walks in domains with boundaries.
Such processes arise in numerous applications and are of interest in several areas of
mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum
Physics. This second edition consists of two parts.
Part I is a revised upgrade of the first edition (1999), with additional recent results on the
group of a random walk. The theoretical approach given therein has been developed
by the authors since the early 1970s. By using Complex Function Theory, Boundary Value
Problems, Riemann Surfaces, and Galois Theory, completely new methods are proposed
for solving functional equations of two complex variables, which can also be applied to
characterize the Transient Behavior of the walks, as well as to find explicit solutions to
the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable
Systems.
Part II borrows special case-studies from queueing theory (in particular, the famous
problem of Joining the Shorter of Two Queues) and enumerative combinatorics
(Counting, Asymptotics).
Researchers and graduate students should find this book very useful.
2017, XV, 406 p. 4 illus.
Hardcover
ISBN 978-3-319-51657-8
Series: Applied Mathematical Sciences, Vol. 127
* Covers most important recent developments in inverse problems
* Presented in a readable and informative manner
* Introduces both scientific and engineering researchers as well as
graduate students to the significant work done in this area in recent
years, relating it to broader themes in mathematical analysis
* Includes current open research problems
This third edition expands upon the earlier edition by adding nearly 40 pages of new
material reflecting the analytical and numerical progress in inverse problems in last 10
years. As in the second edition, the emphasis is on new ideas and methods rather than
technical improvements. These new ideas include use of the stationary phase method in
the two-dimensional elliptic problems and of multi frequencies\temporal data to
improve stability and numerical resolution. There are also numerous corrections
and improvements of the exposition throughout.
This book is intended for mathematicians working with partial differential equations
and their applications, physicists, geophysicists, and financial, electrical, and mechanical
engineers involved with nondestructive evaluation, seismic exploration, remote sensing,
and various kinds of tomography.
Review of the second edition:
"The first edition of this excellent book appeared in 1998 and became a standard
reference for everyone interested in analysis and numerics of inverse problems in partial
differential equations. … The second edition is considerably expanded and reflects
important recent developments in the field … . Some of the research problems from the
first edition have been solved … ." (Johannes Elschner, Zentralblatt MATH, Vol. 1092 (18),
2006)
Series: Problem Books in Mathematics
1st ed. 2017, X, 622 p. 65 illus.
Hardcover
ISBN 978-3-319-53870-9
* Combines an in-depth overview of the theory with problems
presented at several Mathematical Olympiads around the
world Offers a comprehensive course on problem-solving
techniquesPresents a coherent development of mathematical
ideas and methods behind problem solvingBrings several classical,
relevant results of various fields in mathematics
This book provides a comprehensive, in-depth overview of elementary mathematics
as explored in Mathematical Olympiads around the world. It expands on topics usually
encountered in high school and could even be used as preparation for a first-semester
undergraduate course. This first volume covers Real Numbers, Functions, Real Analysis,
Systems of Equations, Limits and Derivatives, and much more.
As part of a collection, the book differs from other publications in this field by not being a
mere selection of questions or a set of tips and tricks that applies to specific problems. It
starts from the most basic theoretical principles, without being either too general or too
axiomatic. Examples and problems are discussed only if they are helpful as applications
of the theory. Propositions are proved in detail and subsequently applied to Olympic
problems or to other problems at the Olympic level.
The book also explores some of the hardest problems presented at National and
International Mathematics Olympiads, as well as many essential theorems related to the
content. An extensive Appendix offering hints on or full solutions for all difficult problems
rounds out the book.