Courant Lecture Notes, Volume: 20
2010; 318 pp; softcover
ISBN-13: 978-0-8218-4957-6
Expected publication date is March 24, 2010.
Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing "electrostatically actuated" MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems--where the stationary MEMS models fit--are a well-developed field of PDEs, the type of inverse square nonlinearity that appears here helps shed a new light on the class of singular supercritical problems and their specific challenges.
Besides the practical considerations, the model is a rich source of interesting mathematical phenomena. Numerics, formal asymptotic analysis, and ODE methods give lots of information and point to many conjectures. However, even in the simplest idealized versions of electrostatic MEMS, one essentially needs the full available arsenal of modern PDE techniques to do the required rigorous mathematical analysis, which is the main objective of this volume. This monograph could therefore be used as an advanced graduate text for a motivational introduction to many recent methods of nonlinear analysis and PDEs through the analysis of a set of equations that have enormous practical significance.
Graduate students and research mathematicians interested in PDEs and applications.
Introduction
Part 1. Second-order equations modeling stationary MEMS
Estimates for the pull-in voltage
The branch of stable solutions
Estimates for the pull-in distance
The first branch of unstable solutions
Description of the global set of solutions
Power-law profiles on symmetric domains
Part 2. Parabolic equations modeling MEMS dynamic deflections
Different modes of dynamic deflection
Estimates on quenching times
Refined profile of solutions at quenching time
Part 3. Fourth-order equations modeling nonelastic MEMS
A fourth-order model with a clamped boundary on a ball
A fourth-order model with a pinned boundary on convex domains
Appendix A. Hardy-Rellich inequalities
Bibliography
Index
Contemporary Mathematics, Volume: 508
2010; 269 pp; softcover
ISBN-13: 978-0-8218-4740-4
Expected publication date is March 14, 2010.
This volume contains the proceedings of the Tenth International Conference on p-adic and Non-Archimedean Analysis, held at Michigan State University in East Lansing, Michigan, on June 30-July 3, 2008.
This volume contains a kaleidoscope of papers based on several of the more important talks presented at the meeting. It provides a cutting-edge connection to some of the most important recent developments in the field. Through a combination of survey papers, research articles, and extensive references to earlier work, this volume allows the reader to quickly gain an overview of current activity in the field and become acquainted with many of the recent sub-branches of its development.
Graduate students and research mathematicians interested in non-archimedian analysis.
J. Aguayo, S. Navarro, and M. Nova -- Strict topologies on spaces of vector-valued continuous functions over non-Archimedean field
B. Diarra -- Some subalgebras of the algebra of bounded linear operators of the one variable Tate algebra
A. Escassut and N. Mainetti -- The ultrametric corona problem
A. K. Katsaras -- Vector-valued p-adic measures
H. A. Keller and H. Ochsenius -- On the Clifford algebra of orthomodular spaces over Krull valued fields
K.-O. Lindahl -- Divergence and convergence of conjugacies in non-Archimedean dynamics
H. M. Moreno -- A criterion for the invertibility of Lipschitz operators on type separating spaces
M. Nilsson and R. Nyqvist -- On monomial dynamical systems on the p-adic n-torus
H. Ochsenius and E. Olivos -- On the value group and norms of a form Hilbert space
H. Ochsenius and W. H. Schikhof -- Compact perturbations of Fredholm operators on Norm Hilbert spaces over Krull valued fields
J. Ojeda -- Applications of the p-adic Nevanlinna theory to problems of uniqueness
C. Perez-Garcia and W. M. Schikhof -- Tensor products of p-adic locally convex spaces having the strongest locally convex topology
C. G. Petalas and A. K. Katsaras -- Tensor products of p-adic measures
A. Rodionov and S. Volkov -- p-adic arithmetic coding
K. Shamseddine and M. Berz -- Analysis on the Levi-Civita field, a brief overview
P.-A. Svensson -- Criteria for non-repelling fixed points
F. Tangara -- A p-adic q-deformation of the Weyl algebra, for q a p^N-th root of
Graduate Studies in Mathematics, Volume: 113
2010; approx. 278 pp; hardcover
ISBN-13: 978-0-8218-4949-1
Expected publication date is April 1, 2010.
Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes, and applies this theory to various special examples. The initial chapter is devoted to the most important classical example--one dimensional Brownian motion. This, together with a chapter on continuous time Markov chains, provides the motivation for the general setup based on semigroups and generators. Chapters on stochastic calculus and probabilistic potential theory give an introduction to some of the key areas of application of Brownian motion and its relatives. A chapter on interacting particle systems treats a more recently developed class of Markov processes that have as their origin problems in physics and biology.
This is a textbook for a graduate course that can follow one that covers basic probabilistic limit theorems and discrete time processes.
Graduate students and research mathematicians interested in probability.
One dimensional Brownian motion
Continuous time Markov chains
Feller processes
Interacting particle systems
Stochastic integration
Multidimensional Brownian motion and the Dirichlet problem
Appendix
Bibliography
Index
Contemporary Mathematics, Volume: 509
2010; 231 pp; softcover
ISBN-13: 978-0-8218-4886-9
Expected publication date is April 10, 2010.
This volume represents the 2007-2008 Jairo Charris Seminar in Algebra and Analysis on Differential Algebra, Complex Analysis and Orthogonal Polynomials, which was held at the Universidad Sergio Arboleda in Bogota, Colombia.
It provides the state of the art in the theory of Integrable Dynamical Systems based on such approaches as Differential Galois Theory and Lie Groups as well as some recent developments in the theory of multivariable and q-orthogonal polynomials, weak Hilbert's 16th Problem, Singularity Theory, Tournaments in flag manifolds, and spaces of bounded analytic functions on the unit circle.
The reader will also find survey presentations, an account of recent developments, and the exposition of new trends in the areas of Differential Galois Theory, Integrable Dynamical Systems, Orthogonal Polynomials and Special Functions, and Bloch-Bergman classes of analytic functions from a theoretical and an applied perspective.
The contributions present new results and methods, as well as applications and open problems, to foster interest in research in these areas.
Graduate students and research mathematicians interested in orthogonal polynomials, differential algebra, and integrability of dynamical systems.
D. Blazquez-Sanz and J. J. Morales-Ruiz -- Differential Galois theory of algebraic Lie-Vessiot systems
L. Fernandez, F. Marcellan, T. E. Perez, and M. A. Pinar -- Recent trends on two variable orthogonal polynomials
C. A. Gomez S. -- On the integrability of the Riccati equation
M. E. H. Ismail -- Two discrete systems of q-orthogonal polynomials
J. ?awrynowicz, L. F. Resendis O., and L. M. Tovar S. -- Like-hyperbolic Bloch-Bergman classes
J. T. Lazaro -- Some words about the application of Tchebycheff systems to weak Hilbert's 16th problem
D. Mond -- From the index of a differential operator to the Milnor number of a singularity
J. J. Morales-Ruiz and J.-P. Ramis -- Integrability of dynamical systems through differential Galois theory: a practical guide
M. Paredes and S. Pinzon -- Tournaments and parabolic almost complex structures on flag manifolds
Contemporary Mathematics, Volume: 509
2010; 231 pp; softcover
ISBN-13: 978-0-8218-4886-9
Expected publication date is April 10, 2010.
This volume represents the 2007-2008 Jairo Charris Seminar in Algebra and Analysis on Differential Algebra, Complex Analysis and Orthogonal Polynomials, which was held at the Universidad Sergio Arboleda in Bogota, Colombia.
It provides the state of the art in the theory of Integrable Dynamical Systems based on such approaches as Differential Galois Theory and Lie Groups as well as some recent developments in the theory of multivariable and q-orthogonal polynomials, weak Hilbert's 16th Problem, Singularity Theory, Tournaments in flag manifolds, and spaces of bounded analytic functions on the unit circle.
The reader will also find survey presentations, an account of recent developments, and the exposition of new trends in the areas of Differential Galois Theory, Integrable Dynamical Systems, Orthogonal Polynomials and Special Functions, and Bloch-Bergman classes of analytic functions from a theoretical and an applied perspective.
The contributions present new results and methods, as well as applications and open problems, to foster interest in research in these areas.
Graduate students and research mathematicians interested in orthogonal polynomials, differential algebra, and integrability of dynamical systems.
D. Blazquez-Sanz and J. J. Morales-Ruiz -- Differential Galois theory of algebraic Lie-Vessiot systems
L. Fernandez, F. Marcellan, T. E. Perez, and M. A. Pinar -- Recent trends on two variable orthogonal polynomials
C. A. Gomez S. -- On the integrability of the Riccati equation
M. E. H. Ismail -- Two discrete systems of q-orthogonal polynomials
J. ?awrynowicz, L. F. Resendis O., and L. M. Tovar S. -- Like-hyperbolic Bloch-Bergman classes
J. T. Lazaro -- Some words about the application of Tchebycheff systems to weak Hilbert's 16th problem
D. Mond -- From the index of a differential operator to the Milnor number of a singularity
J. J. Morales-Ruiz and J.-P. Ramis -- Integrability of dynamical systems through differential Galois theory: a practical guide
M. Paredes and S. Pinzon -- Tournaments and parabolic almost complex structures on flag manifolds
AMS Chelsea Publishing, Volume: 369
2010; 210 pp; hardcover
ISBN-13: 978-0-8218-4910-1
Expected publication date is March 7, 2010.
This book, which is a new edition of a book originally published in 1965, presents an introduction to the theory of higher-order elliptic boundary value problems. The book contains a detailed study of basic problems of the theory, such as the problem of existence and regularity of solutions of higher-order elliptic boundary value problems. It also contains a study of spectral properties of operators associated with elliptic boundary value problems. Weyl's law on the asymptotic distribution of eigenvalues is studied in great generality.
Graduate students and research mathematicians interested in partial differential equations.
Notations and conventions
Calculus of L^2 derivatives--Local properties
Calculus of L^2 derivatives--Global properties
Some inequalities
Elliptic operators
Local existence theory
Local regularity of solutions of elliptic systems
Garding's inequality
Global existence
Global regularity of solutions of strongly elliptic equations
Coerciveness
Coerciveness results of Aronszajn and Smith
Some results on linear transformations on a Hilbert space
Spectral theory of abstract operators
Eigenvalue problems for elliptic equations; The self-adjoint case
Non-self-adjoint eigenvalue problems
Completeness of the eigenfunctions
Bibliography
Notation index
Index