International Book Series of Mathematical Texts
2013; 244 pp; hardcover
The volume contains the proceedings of the conference held in Bordeaux in 2011 to honor the 70th birthday of Nikolai Nikolski. It gathers some of the most relevant contributions presented, written by first-rate analysts. Below is a list of the main subjects covered:
*function spaces and reproducing kernels
*Toeplitz and Hankel operators
*spectral synthesis
*spectral theory
*semigroups of operators
*singular integral operators
*functional models
*rational and meromorphic approximations
*Fourier analysis
A publication of the Theta Foundation. Distributed worldwide, except in Romania, by the AMS.
Graduate students and research mathmaticians interested in analysis.
*V. Adamyan and B. Pavlov -- Modified analytic perturbation procedure and chain rule for scattering matrices
*A. Baranov, Y. Belov, A. Borichev, and D. Yakubovich -- Recent developments in spectral synthesis for exponential systems and for non-self-adjoint operators
*A. Baranov and D. Sarason -- Quotient representations of inner functions
*L. Baratchart -- Rational approximation, meromorphic approximation, extremal domains, weak asymptotics, non-Hermitian orthogonality
*A. Bottcher -- Best constants for Markov type inequalities in Hilbert space norms
*A. Brudnyi -- Stein-like theory for Banach-valued holomorphic functions on the maximal ideal space of H∞ and the operator corona problem of Sz.-Nagy
*S. A. Denisov -- Multidimensional L2 conjecture: A survey
*L. Golinskii and S. Kupin -- On discrete spectrum of complex perturbations of finite band Schrodinger operators
*M. Haase -- The functional calculus approach to operator cosine functions
*Y. I. Lyubarskii and E. Malinnikova -- Composition operators on model spaces
*H. Queffelec -- Approximation numbers of classes of symbolic operators
*F. Shamoyan -- On the Fourier coefficients of functions of bounded type on the unit torus
*S. Treil -- Sharp A2 estimates of Haar shifts via Bellman function
*M. Veraar -- Embedding results for γ-spaces
*A. Volberg and B. D. Wick -- Bergman-type singular integral operators on metric spaces
Courant Lecture Notes, Volume: 24
2013; approx. 133 pp; softcover
ISBN-13: 978-0-8218-4359-8
Expected publication date is January 16, 2014.
Applications in modern biotechnology and molecular medicine often require simulation of biomolecular systems in atomic representation with immense length and timescales that are far beyond the capacity of computer power currently available. As a consequence, there is an increasing need for reduced models that describe the relevant dynamical properties while at the same time being less complex. In this book the authors exploit the existence of metastable sets for constructing such a reduced molecular dynamics model, the so-called Markov State Model (MSM), with good approximation properties on the long timescales.
With its many examples and illustrations, this book is addressed to graduate students, mathematicians, and practical computational scientists wanting an overview of the mathematical background for the ever increasing research activity on how to construct MSMs for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecular sensors to molecular aggregation. This book bridges the gap between mathematical research on molecular dynamics and its practical use for realistic molecular systems by providing readers with tools for performing in-depth analysis of simulation and data-analysis methods.
Graduate students and research mathematicians interested in molecular dynamics.
*Transfer operator approach to conformation dynamics
*Dynamics
*Metastability
*Transfer operators and generators
*Projected transfer operators
*Transition path theory
*Concluding remarks
*Some mathematical aspects of transfer operators
*Definition of exit rates
*Bibliography
CRM Monograph Series, Volume: 32
2014; 224 pp; hardcover
ISBN-13: 978-1-4704-0961-6
Expected publication date is January 6, 2014.
This book provides a detailed description of the Riemann-Hilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random matrix models as well as to the six-vertex model. The RH approach was an important ingredient in the proofs of universality in unitary matrix models. This book gives an introduction to the unitary matrix models and discusses bulk and edge universality. The six-vertex model is an exactly solvable two-dimensional model in statistical physics, and thanks to the Izergin-Korepin formula for the model with domain wall boundary conditions, its partition function matches that of a unitary matrix model with nonpolynomial interaction. The authors introduce in this book the six-vertex model and include a proof of the Izergin-Korepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the six-vertex model with domain wall boundary conditions in all the three phases: disordered, ferroelectric, and antiferroelectric.
Graduate students and research mathematicians interested in random matrices and statistical mechanics
Student Mathematical Library, Volume: 69
2013; approx. 316 pp; softcover
ISBN-13: 978-0-8218-9138-4
Expected publication date is January 13, 2014.
This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark.
Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more.
In the last couple of chapters, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.
Undergraduate and graduate students interested in classical mechanics and ordinary differential equations.
*One degree of freedom
*More degrees of freedom
*Rigid body motion
*Variational principles of mechanics
*Classical problems of calculus of variations
*The conditions of Legendre and Jacobi for a minimum
*Optimal control
*Heuristic foundations of Hamiltonian mechanics
*Bibliography
*Index
CBMS Regional Conference Series in Mathematics, Number: 118
2013; 308 pp; softcover
ISBN-13: 978-1-4704-1012-4
Expected publication date is January 6, 2014.
This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory.
The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature.
Graduate students and research mathematicians interested in complex geometry, Hodge theory, and representation theory.
*The classical theory: Part I
*The classical theory: Part II
*Polarized Hodge structures and Mumford-Tate groups and domains
*Hodge representations and Hodge domains
*Discrete series and n-cohomology
*Geometry of flag domains: Part 1
*Geometry of flag domains: Part II
*Penrose transforms in the two main examples
*Automorphic cohomology
*Miscellaneous topics and some questions
*Bibliography
*Index
*Notations used in the talks