Series: Universitext
1st Edition., 2011, X, 199 p., Softcover
ISBN: 978-0-85729-226-1
December 2010
Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Additionally, some of the simplest variational methods are evolving as classical tools in the field of nonlinear differential equations.
This book is an introduction to variational methods and their applications to semilinear elliptic problems. Providing a comprehensive overview on the subject, this book will support both student and teacher engaged in a first course in nonlinear elliptic equations. The material is introduced gradually, and in some cases redundancy is added to stress the fundamental steps in theory-building. Topics include differential calculus for functionals, linear theory, and existence theorems by minimization techniques and min-max procedures.
Requiring a basic knowledge of Analysis, Functional Analysis and the most common function spaces, such as Lebesgue and Sobolev spaces, this book will be of primary use to graduate students based in the field of nonlinear partial differential equations. It will also serve as valuable reading for final year undergraduates seeking to learn about basic working tools from variational methods and the management of certain types of nonlinear problems.
Series: Operator Theory: Advances and Applications, Vol. 214
1st Edition., 2011, X, 172 p., Hardcover
ISBN: 978-3-7643-9993-1
February 12, 2011
This volume contains the proceedings of the OTAMP 2008 (Operator Theory, Analysis and Mathematical Physics) conference held at the Mathematical Research and Conference Center in Bedlewo near Poznan. It is composed of original research articles describing important results presented at the conference, some with extended review sections, as well as presentations by young researchers. Special sessions were devoted to random and quasi-periodic differential operators, orthogonal polynomials, Jacobi and CMV matrices, and quantum graphs. The contributions also reflect new trends in spectral theory, where much emphasis is given to operators with magnetic fields and non-self-adjoint problems.
The book is geared towards scientists from advanced undergraduate students to researchers interested in the recent development on the borderline between operator theory and mathematical physics, especially spectral theory for Schrodinger operators and Jacobi matrices.
Series: Publications of the Scuola Normale Superiore, Vol. 12
Subseries: CRM Series
1st Edition., 2011, 450 p., Softcover
ISBN: 978-88-7642-374-1
Due: January 7, 2011
These are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with - mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, - local dynamics: parabolic systems, small denominator questions, - new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, - a new family of resurgent functions related to knot theory.
C. M. Bender, D. W. Hook, K. S. Kooner: Complex Elliptic Pendulum.- F. Bracci: Parabolic attitude.- J. Ecalle, S. Sharma: Power series with sum-product Taylor coefficients and their resurgence algebra.- J. Raissy: Brjuno conditions for linearization in presence of resonance.- J.-Y. Thibon: Noncommutative symmetric functions and combinatorial Hopf algebras.- C. Bogner, S. Weinzierl: Feynman graphs in perturbative quantum field theory.- A. J. Corcho, F. Linares, C. Matheus: Multilinear estimates for the 2D and 3D Zakharov-Rubenchik systems.- J. Ecalle: The flexion structure and dimorphy: flexion units, singulators, generators, and the enumeration of multizeta irreducible.- J. Ecalle: (title to follow).- S. Kamimoto, T. Kawai, T. Koike, Y. Takei: On a Schrodinger equation with a merging pair of a simple pole and a simple turning point ? Alien calculus of WKB solutions through microlocal analysis.- R. Schafke: (title to follow).
Series: Progress in Mathematical Physics, Vol. 61
1st Edition., 2011, Approx. 170 p., Hardcover
ISBN: 978-3-0348-0083-9
Due: April 2011
This tenth book in the Poincar´e Seminar Series describes recent developments in the statistical physics of two related but still poorly understood topics ? glasses, especially the glass transition, and the statics and dynamics of granular systems. This field has emerged as one of the most challenging frontiers of statistical physics in the last two decades, and is notable for its very active interchange between experiment, theory, and numerical studies. Both, the theoretical and experimental aspects are covered, and particular care is devoted to the pedagogical nature of the presentations. The book is directed towards a large audience of physicists and mathematicians.
Content Level ≫ Research
Keywords ≫ colloidal glasses - glass transition - granular flow - jamming transitions - random first order transition theory
Related subjects ≫ Complexity - Mathematics
1st Edition., 2011, 573 p. 380 illus., 250 in color., Hardcover
ISBN: 978-3-642-17285-4
Due: February 2011
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
1 Pappos's Theorem: Nine Proofs and Three Variations.- 2 Projective Planes.- 3 Homogeneous Coordinates.- 4 Lines and Cross-Ratios.- 5 Calculating with Points on Lines.- 6 Determinants.- 7 More on Bracket Algebra.- 8 Quadrilateral Sets and Liftings.- 9 Conics and Their Duals.- 10 Conics and Perspectivity.- 11 Calculating with Conics.- 12 Projective $d$-space.- 13 Diagram Techniques.- 14 Working with diagrams.- 15 Configurations, Theorems, and Bracket Expressions.- 16 Complex Numbers: A Primer.- 17 The Complex Projective Line.- 18 Euclidean Geometry.- 19 Euclidean Structures from a Projective Perspective.- 20 Cayley-Klein Geometries.- 21 Measurements and Transformations.- 22 Cayley-Klein Geometries at Work.- 23 Circles and Cycles.- 24 Non-Euclidean Geometry: A Historical Interlude.- 25 Hyperbolic Geometry.- 26 Selected Topics in Hyperbolic Geometry.- 27 What We Did Not Touch.- References.- Index.