Contemporary Mathematics, Volume: 513
2010; approx. 276 pp; softcover
ISBN-13: 978-0-8218-4834-0
Expected publication date is June 20, 2010.
This volume is the first of two volumes representing leading themes of current research in nonlinear analysis and optimization. The articles are written by prominent researchers in these two areas and bring the readers, advanced graduate students and researchers alike, to the frontline of the vigorous research in these important fields of mathematics.
This volume contains articles on nonlinear analysis. Topics covered include the convex feasibility problem, fixed point theory, mathematical biology, Mosco stability, nonexpansive mapping theory, nonlinear partial differential equations, optimal control, the proximal point algorithm and semigroup theory. The companion volume (Contemporary Mathematics, Volume 514) is devoted to optimization.
Graduate students and research mathematicians interested in nonlinear analysis and its applications.
A. S. Ackleh, K. Deng, and Q. Huang -- Existence-uniqueness results and difference approximations for an amphibian juvenile-adult model
S. Aizicovici, N. S. Papageorgiou, and V. Staicu -- Three nontrivial solutions for p-Laplacian Neumann problems with a concave nonlinearity near the origin
V. Barbu -- Optimal stabilizable feedback controller for Navier-Stokes equations
H. H. Bauschke and X. Wang -- Firmly nonexpansive and Kirszbraun-Valentine extensions: A constructive approach via monotone operator theory
R. E. Bruck -- On the random product of orthogonal projections in Hilbert space II
D. Butnariu, E. Resmerita, and S. Sabach -- A Mosco stability theorem for the generalized proximal mapping
A. Cegielski -- Generalized relaxations of nonexpansive operators and convex feasibility problems
Y. Censor and A. Segal -- Sparse string-averaging and split common fixed points
T. Dominguez Benavides and S. Phothi -- Genericity of the fixed point property for reflexive spaces under renormings
K. Goebel and B. Sims -- Mean Lipschitzian mappings
T. Ibaraki and W. Takahashi -- Generalized nonexpansive mappings and a proximal-type algorithm in Banach spaces
W. Kaczor, T. Kuczumow, and N. Michalska -- The common fixed point set of commuting nonexpansive mapping in Cartesian products of weakly compact convex sets
L. Leu?tean -- Nonexpansive iterations in uniformly convex W-hyperbolic spaces
G. Lopez, V. Martin-Marquez, and H.-K. Xu -- Halpern's iteration for nonexpansive mappings
J. W. Neuberger -- Lie generators for local semigroups
H.-K. Xu -- An alternative regularization method for nonexpansive mappings with applications
Contemporary Mathematics, Volume: 514
2010; approx. 298 pp; softcover
ISBN-13: 978-0-8218-4835-7
Expected publication date is June 27, 2010.
This volume is the second of two volumes representing leading themes of current research in nonlinear analysis and optimization. The articles are written by prominent researchers in these two areas and bring the readers, advanced graduate students and researchers alike, to the frontline of the vigorous research in important fields of mathematics.
This volume contains articles on optimization. Topics covered include the calculus of variations, constrained optimization problems, mathematical economics, metric regularity, nonsmooth analysis, optimal control, subdifferential calculus, time scales and transportation traffic. The companion volume (Contemporary Mathematics, Volume 513) is devoted to nonlinear analysis.
Graduate students and research mathematicians interested in nonlinear analysis, optimization, and applications.
J.-P. Aubin and S. Martin -- Travel time tubes regulating transportation traffic
R. Baier and E. Farkhi -- The directed subdifferential of DC functions
Z. Balanov, W. Krawcewicz, and H. Ruan -- Periodic solutions to O(2)-symmetric variational problems: O(2) times S^1- equivariant gradient degree approach
J. F. Bonnans and N. P. Osmolovskii -- Quadratic growth conditions in optimal control problems
J. M. Borwein and S. Sciffer -- An explicit non-expansive function whose subdifferential is the entire dual ball
G. Buttazzo and G. Carlier -- Optimal spatial pricing strategies with transportation costs
R. A. C. Ferreira and D. F. M. Torres -- Isoperimetric problems of the calculus of variations on time scales
M. Foss and N. Randriampiry -- Some two-dimensional mathcal A-quasiaffine functions
F. Giannessi, A. Moldovan, and L. Pellegrini -- Metric regular maps and regularity for constrained extremum problems
V. Y. Glizer -- Linear-quadratic optimal control problem for singularly perturbed systems with small delays
T. Maruyama -- Existence of periodic solutions for Kaldorian business fluctuations
D. Mozyrska and E. Paw?uszewicz -- Delta and nabla monomials and generalized polynomial series on time scales
D. Pallaschke and R. Urba?ski -- Morse indexes for piecewise linear functions
J.-P. Penot -- Error bounds, calmness and their applications in nonsmooth analysis
F. Rampazzo -- Commutativity of control vector fields and "inf-commutativity"
A. J. Zaslavski -- Stability of exact penalty for classes of constrained minimization problems in finite-dimensional spaces
CRM Proceedings & Lecture Notes, Volume: 50
2010; 403 pp; softcover
ISBN-13: 978-0-8218-4777-0
Expected publication date is May 12, 2010.
A five-day conference celebrating the legacy of Raoul Bott was held at the CRM on June 9-13, 2008. The conference focused on the extraordinary impact Bott had on both topology and interactions between mathematics, physics and technology. The conference was co-organized by the Clay Mathematics Institute and had support from the National Science Foundation (Award 0805925). Montreal was a natural venue for such an event since Raoul Bott obtained two degrees in Electrical Engineering at McGill University in the 1940s and an Honorary Doctorate from McGill in 1987. The fact that Bott's presence is still fresh in the minds of all those involved made for a tremendous amount of enthusiasm and every attempt has been made to channel this energy into this book.
The contributions to this book come from three generations of Bott's students, coauthors, and fellow kindred spirits in order to cover six decades of Bott's research, identify his enduring mathematical legacy, and the consequences for emerging fields. The contributions can be read independently. In order to help a whole to emerge from the parts, the book is broken into four sections and to make the book accessible to a wide audience, each section starts with easier-to-read reminiscences and works its way into more involved papers.
Undergraduates, graduate students and research mathematicians interested in the life and work of Raoul Bott.
P. R. Kotiuga -- Introduction
Montreal, the 1940s, and mathematical prehistory
C. Bott -- My parents' Montreal years and growing up with Raoul as my father
J. Lambek -- Raoul Bott, McGill, the 1940s
P. R. Kotiuga -- Iron rings, Doctor Honoris Causa Raoul Bott, Carl Herz, and a hidden hand
J. H. Hubbard -- The Bott-Duffin synthesis of electrical circuits
Early students and colleagues
P. D. Lax, F. Hirzebruch, B. Mazur, L. Conlon, E. B. Curtis, H. M. Edwards, J. Huebschmann, and H. Shulman -- Raoul Bott as we knew him
M. Atiyah -- Working with Raoul Bott: From geometry to physics
H. M. Edwards -- The algorithmic side of Riemann's mathematics
M. W. Hirsch -- Actions of Lie groups and Lie algebras on manifolds
J. J. Kohn -- PDE from the point of view of multiplier ideals
P. Baum -- Dirac operator and K-theory for discrete groups
J. L. Heitsch -- The Lefschetz principle, fixed point theory, and index theory
J. Cantwell and L. Conlon -- A new look at the theory of levels
A. Haefliger -- On the space of morphisms between Etale groupoids
Localization, equivariance and outgrowths of Morse theory and periodicity
J. A. Bernhard, N. Hingston, J. Stasheff, and V. Guillemin -- Raoul Bott as we knew him
N. Hingston -- Loop products on connected sums of projective spaces
J. A. Bernhard -- Equivariant cohomology and reflections
L. Jeffrey -- Connectedness of level sets of the moment map for torus actions on the based loop group
L. W. Tu -- Computing characteristic numbers using fixed points
H. Hohnhold, S. Stolz, and P. Teichner -- From minimal geodesics to supersymmetric field theories
Dualities and interactions with quantum field theory
C. Vafa -- Raoul Bott as my math teacher
S. Lu -- A physics colloquium at McGill that changed my life
E. Witten -- Geometric Langlands from six dimensions
J. Block -- Duality and equivalence of module categories in noncommutative geometry
G. R. Cavalcanti and M. Gualtieri -- Generalized complex geometry and T-duality
D. S. Freed, M. J. Hopkins, J. Lurie, and C. Teleman -- Topological quantum field theories from compact Lie groups
CRM Proceedings & Lecture Notes, Volume: 51
2010; 214 pp; softcover
ISBN-13: 978-0-8218-4879-1
Expected publication date is May 8, 2010.
Hilbert spaces of analytic functions are currently a very active field of complex analysis. The Hardy space is the most senior member of this family. However, other classes of analytic functions such as the classical Bergman space, the Dirichlet space, the de Branges-Rovnyak spaces, and various spaces of entire functions, have been extensively studied. These spaces have been exploited in different fields of mathematics and also in physics and engineering. For example, de Branges used them to solve the Bieberbach conjecture. Modern control theory is another place that heavily exploits the techniques of analytic function theory. This book grew out of a workshop held in December 2008 at the CRM in Montreal and provides an account of the latest developments in the field of analytic function theory.
Graduate students and research mathematicians interested in analytic function theory.
J. A. Ball and V. Bolotnikov -- Canonical de Branges-Rovnyak model transfer-function realization for multivariable Schur-class functions
N. Arcozzi, R. Rochberg, and E. Sawyer -- Two variations on the Drury-Averson space
S. R. Garcia and W. T. Ross -- The norm of a truncated Toeplitz operator
A. Boivin and C. Zhu -- Approximation in weighted Hardy spaces for the unit disc
R. G. Douglas and J. Sarkar -- Some remarks on the Toeplitz corona problem
E. Fricain and A. Hartmann -- Regularity on the boundary in spaces of holomorphic functions on the unit disk
D. Khavinson and E. Lundberg -- The search for singularities of solutions to the Dirichlet problem: Recent developments
O. El-Fallah, K. Kellay, and T. Ransford -- Invariant subspaces of the Dirichlet space
J. Mashreghi, T. Ransford, and M. Shabankhah -- Arguments of zero sets in the Dirichlet space
J. Zemanek -- Questions on Volterra operators
D.-C. Chang, G. Dafni, and H. Yue -- Nonhomogeneous div-curl decompositions for local Hardy spaces on a domain
R. Fournier and S. Ruscheweyh -- On the Bohr radius for simply connected plane domains
A. Boivin and C. Zhu -- Completeness of the system {f(lambda_{n}z)} in {L_a^2}[Omega]
J. Mashreghi -- A formula for the logarithmic derivative and its applications
H. Wulan and C. Xiong -- Composition operators on the minimal Mobius invariant space
P. M. Gauthier -- Whether regularity is local for the generalized Dirichlet problem