Contemporary Mathematics, Volume: 635
2015; 210 pp; softcover
ISBN-13: 978-1-4704-1050-6
Expected publication date is April 30, 2015.
This volume contains the proceedings of the AMS Special Session on Nonlinear Waves and Integrable Systems, held on April 13-14, 2013, at the University of Colorado, Boulder, Colorado.
The field of nonlinear waves is an exciting area of modern mathematical research that also plays a major role in many application areas from physics and fluids. The articles in this volume present a diverse cross section of topics from this field including work on the Inverse Scattering Transform, scattering theory, inverse problems, numerical methods for dispersive wave equations, and analytic and computational methods for free boundary problems. Significant attention to applications is also given throughout the articles with an extensive presentation on new results in the free surface problem in fluids.
This volume will be useful to students and researchers interested in learning current techniques in studying nonlinear dispersive systems from both the integrable systems and computational points of view.
Graduate students and research mathematicians interested in nonlinear wave equations and applications.
B. Herbst, G. Nieddu, and A. D. Trubatch -- Recurrence in the Korteweg-de Vries equation?
F. Demontis, C. van der Mee, and F. Vitale -- On the location of the discrete eigenvalues for defocusing Zakharov-Shabat systems having potentials with nonvanishing boundary conditions
R. Croke, J. L. Mueller, M. Music, P. Perry, S. Siltanen, and A. Stahel -- The Novikov-Veselov equation: Theory and computation
R. Croke, J. L. Mueller, and A. Stahel -- Transverse instability of plane wave soliton solutions of the Novikov-Veselov equation
G. D. Lyng -- Semiclassical soliton ensembles for the focusing nonlinear Schrodinger equation: Recent developments
J. Wilkening -- Relative-periodic elastic collisions of water waves
K. Oliveras and B. Deconinck -- The instabilities of periodic traveling water waves with respect to transverse perturbations
K. Oliveras and V. Vasan -- Relationships between the pressure and the free surface independent of the wave speed
J. Wilkening and V. Vasan -- Comparison of five methods of computing the Dirichlet-Neumann operator for the water wave problem
Contemporary Mathematics, Volume: 636
2015; 266 pp; softcover
ISBN-13: 978-1-4704-1480-1
Expected publication date is April 30, 2015.
This volume contains the proceedings of the workshop on Infinite Products of Operators and Their Applications, held from May 21-24, 2012, at the Technion-Israel Institute of Technology, Haifa, Israel.
The papers cover many different topics regarding infinite products of operators and their applications: projection methods for solving feasibility and best approximation problems, arbitrarily slow convergence of sequences of linear operators, monotone operators, proximal point algorithms for finding zeros of maximal monotone operators in the presence of computational errors, the Pascoletti-Serafini problem, remetrization for infinite families of mappings, Poisson's equation for mean ergodic operators, vector-valued metrics in fixed point theory, contractivity of infinite products and mean convergence theorems for generalized nonspreading mappings.
Graduate students and research mathematicians interested in applied functional analysis, operator theory, and optimization.
H. H. Bauschke and V. R. Koch -- Projection methods: Swiss army knives for solving feasibility and best approximation problems with halfspaces
A. Ben-Israel -- Projectors on intersections of subspaces
J. M. Borwein and L. Yao -- Recent progress on monotone operator theory
R. Davidi, Y. Censor, R. W. Schulte, S. Geneser, and L. Xing -- Feasibility-seeking and superiorization algorithms applied to inverse treatment planning in radiation therapy
F. Deutsch and H. Hundal -- Arbitrarily slow convergence of sequences of linear operators
A. Gibali, K.-H. Kufer, and P. Suss -- Reformulating the Pascoletti-Serafini problem as a bi-level optimization problem
J. Jachymski -- Remetrization theorems for finite families of mappings and hyperbolic iterated function systems
M. Lin and L. Suciu -- Poisson's equation for mean ergodic operators
A. Petru?el, C. Urs, and O. Mle?ni?e -- Vector-valued metrics in fixed point theory
R. A. Polyak -- Projected gradient method for non-negative least square
R. A. Polyak -- Nonlinear equilibrium for resource allocation problems
E. Pustylnik and S. Reich -- Infinite products of discontinuous operators
S. Reich and A. J. Zaslavski -- Contractivity, porosity and infinite products
B. Schultze, M. Witt, Y. Censor, R. Schulte, and K. E. Schubert -- Performance of hull-detection algorithms for proton computed tomography reconstruction
W. Takahashi, N.-C. Wong, and J.-C. Yao -- Attractive point and mean convergence theorems for new generalized nonspreading mappings in Banach spaces
A. J. Zaslavski -- Proximal point algorithms for finding zeros of maximal monotone operators in the presence of computational errors
Pure and Applied Undergraduate Texts, Volume: 24
2015; approx. 318 pp; hardcover
ISBN-13: 978-1-4704-1852-6
Expected publication date is May 25, 2015.
Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first course and are interested in learning more advanced results.
Undergraduate and graduate students and research mathematicians interested in linear algebra, linear systems, graph theory, block designs, matrices, and error correcting codes.
Preliminaries
Inner product spaces and orthogonality
Eigenvalues, eigenvectors, diagonalization, and triangularization
The Jordan and Weyr canonical forms
Unitary similarity and normal matrices
Hermitian matrices
Vector and matrix norms
Some matrix factorizations
Field of values
Simultaneous triangularization
Circulant and block cycle matrices
Matrices of zeros and ones
Block designs
Hadamard matrices
Graphs
Directed graphs
Nonnegative matrices
Error correcting codes
Linear dynamical systems
Bibliography
Index
CBMS Regional Conference Series in Mathematics, Number: 122
2015; 161 pp; softcover
ISBN-13: 978-1-4704-2014-7
Expected publication date is June 15, 2015.
This monograph deals with recent advances in the study of the long-time asymptotics of large solutions to critical nonlinear dispersive equations. The first part of the monograph describes, in the context of the energy critical wave equation, the "concentration-compactness/rigidity theorem method" introduced by C. Kenig and F. Merle. This approach has become the canonical method for the study of the "global regularity and well-posedness" conjecture (defocusing case) and the "ground-state" conjecture (focusing case) in critical dispersive problems.
The second part of the monograph describes the "channel of energy" method, introduced by T. Duyckaerts, C. Kenig, and F. Merle, to study soliton resolution for nonlinear wave equations. This culminates in a presentation of the proof of the soliton resolution conjecture, for the three-dimensional radial focusing energy critical wave equation.
It is the intent that the results described in this book will be a model for what to strive for in the study of other nonlinear dispersive equations.
Graduate students and research mathematicians interested in nonlinear wave equations.
Asterisque, Number: 366
2014; 136 pp; softcover
ISBN-13: 978-2-85629-796-4
The authors obtain new oscillation inequalities in metric spaces in terms of the Peetre K-functional and the isoperimetric profile. Applications provided include a detailed study of fractional Sobolev inequalities and the Morrey-Sobolev embedding theorems in different contexts. In particular, the authors include a detailed study of Gaussian measures as well as probability measures between Gaussian and exponential. They show a kind of reverse Polya-Szego principle that allows them to obtain continuity as a self-improvement from boundedness, using symmetrization inequalities.
The authors' methods also allow for precise estimates of growth envelopes of generalized Sobolev and Besov spaces on metric spaces. The authors also consider embeddings into BMO and their connection to Sobolev embeddings.
A publication of the Societe Mathematique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians interested in Sobolev inequalities.
Introduction
Preliminaries
Oscillation, K-functionals and isoperimetry
Embedding into continuous functions
Examples and applications
Fractional Sobolev inequalities in Gaussian measures
On limiting Sobolev embeddings and BMO
Estimation of growth "envelopes"
Lorentz spaces with negative indices
Connection with the work of Garsia and his collaborators
Appendix A. Some remarks on the calculation of K-functionals
Bibliography
*
Asterisque, Number: 365
2014; 177 pp; softcover
ISBN-13: 978-2-85629-795-7
This volume has two papers which can be read separately. The first paper concerns local collapsing in Riemannian geometry. The authors prove that a three-dimensional compact Riemannian manifold which is locally collapsed, with respect to a lower curvature bound, is a graph manifold. This theorem was stated by Perelman without proof and was used in his proof of the geometrization conjecture.
The second paper is about the geometrization of orbifolds. A three-dimensional closed orientable orbifold, which has no bad suborbifolds, is known to have a geometric decomposition. This is known from the work of Perelman in the manifold case, along with earlier work of Boileau-Leeb-Porti, Boileau-Maillot-Porti, Boileau-Porti, Cooper-Hodgson-Kerckhoff and Thurston. The authors give a new, logically independent, unified proof of the geometrization of orbifolds, using Ricci flow.
A publication of the Societe Mathematique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians interested in collapsing, orbifolds, and geometrization.
Locally collapsed 3-manifolds
Geometrization of three-dimensional orbifolds via Ricci flow
References