Series: Lecture Notes in Mathematics, Vol. 1938
Subseries: Fondazione C.I.M.E., Firenze ,
2008, Approx. 370 p., Softcover
ISBN: 978-3-540-78278-0
Due: April 23, 2008
About this book
Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics.
The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.
Series: Lecture Notes in Mathematics, Vol. 1939
Subseries: Fondazione C.I.M.E., Firenze ,
2008, Approx. 265 p., Softcover
ISBN: 978-3-540-78314-5
Due: April 16, 2008
About this book
Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems.
This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.
Table of contents
Preface by the volume editors Daniele Boffi, and Lucia Gastaldi.- Mixed Finite Element Methods (Ricardo G. Duran).- Finite Elements for the Stokes Problem (Daniele Boffi, Franco Brezzi, Michel Fortin).- Polynomial Exact Sequences and Projection-Based Interpolation with Application toMaxwell Equations (Leszek Demkowicz).- Finite Element Methods for Linear Elasticity (Richard S. Falk).- Finite Elements for the Reissner-Mindlin Plate (Richard S. Falk).
Series: Springer Monographs in Mathematics
2008, Approx. 550 p., Hardcover
ISBN: 978-3-540-77532-4
Due: April 9, 2008
About this book
Ulrich Kohlenbach presents an applied form of proof theory that has led in recent years to new results in number theory, approximation theory, nonlinear analysis, geodesic geometry and ergodic theory (among others). This applied approach is based on logical transformations (so-called proof interpretations) and concerns the extraction of effective data (such as bounds) from prima facie ineffective proofs as well as new qualitative results such as independence of solutions from certain parameters, generalizations of proofs by elimination of premises.
The book first develops the necessary logical machinery emphasizing novel forms of Godel's famous functional ('Dialectica') interpretation. It then establishes general logical metatheorems that connect these techniques with concrete mathematics. Finally, two extended case studies (one in approximation theory and one in fixed point theory) show in detail how this machinery can be applied to concrete proofs in different areas of mathematics.
Table of contents
Preface.- Introduction.- Unwinding of proofs (`Proof Mining').- Intuitionistic and classical arithmetic in all finite types.- Representation of Polish metric spaces.- Modified realizability.- Majorizability and the fan rule.- Semi-intuitionistic systems and monotone modified realizability.- Godel's functional (`Dialectica') interpretation.- Semi-intuitionistic systems and monotone functional interpretation.- Systems based on classical logic and functional interpretation.- Functional interpretation of full classical analysis.- A non-standard principle of uniform boundedness.- Elimination of monotone Skolem functions.- The Friedman-Dragalin A-translation.- Applications to analysis: general metatheorems I.- Case study I: Uniqueness proofs in approximation theory.- Applications to analysis: general metatheorems II.- Case study II: Applications to the fixed point theory of nonexpansive mappings.- Final comments.- References.- Index.
2008, XVI, 256 p. 125 illus., Hardcover
ISBN: 978-1-84628-996-5
Due: April 2008
About this textbook
Filled with lots of clear examples
Very well illustrated
Provides an excellent introduction to geometric algebra for computer graphics
Since its invention, geometric algebra has been applied to various branches of physics such as cosmology and electrodynamics, and is now being embraced by the computer graphics community where it is providing new ways of solving geometric problems. It took over two thousand years to discover this algebra, which uses a simple and consistent notation to describe vectors and their products.
John Vince (best-selling author of a number of books including eGeometry for Computer Graphicsf and eVector Analysis for Computer Graphicsf) tackles this new subject in his usual inimitable style, and provides an accessible and very readable introduction.
The first five chapters review the algebras of real numbers, complex numbers, vectors, and quaternions and their associated axioms, together with the geometric conventions employed in analytical geometry. As well as putting geometric algebra into its historical context, John Vince provides chapters on Grassmannfs outer product and Cliffordfs geometric product, followed by the application of geometric algebra to reflections, rotations, lines, planes and their intersection. The conformal model is also covered, where a 5D Minkowski space provides an unusual platform for unifying the transforms associated with 3D Euclidean space.
Filled with lots of clear examples and useful illustrations, this compact book provides an excellent introduction to geometric algebra for computer graphics.
Table of contents
Introduction.- Elementary Algebra.- Complex Algebra.- Vector Algebra.- Quaternion Algebra.- Geometric Conventions.- History of Geometric Algebra.- The Geometric Product.- Reflections and Rotations.- Geometric Algebra and Geometry.- Conformal Geometry.- Applications of Geometric Algebra in Computer Graphics.- Programming Tools for Geometric Algebra.- Conclusion.- References.
Series: Lecture Notes in Mathematics, Vol. 1934
Subseries: Seminaire de Probabilites
2008, Approx. 470 p., Softcover
ISBN: 978-3-540-77912-4
Due: April 2, 2008
About this book
Stochastic processes are as usual the main subject of the Seminaire, with contributions on Brownian motion (fractional or other), Levy processes, martingales and probabilistic finance. Other probabilistic themes are also present: large random matrices, statistical mechanics. The contributions in this volume provide a sampling of recent results on these topics. All contributions with the exception of two are written in English language.
Table of contents
A. Dermoune, Ph. Heinrich : Spectral gap for a colored disordered lattice gas.-D. Feral : On large deviations for the spectral measure of discrete Coulomb gas.- O. Khorunzhiy : Estimates for moments of random matrices with Gaussian elements.- M. Capitaine, M. Casalis : Geometric interpretation of the cumulants for random matrices previously defined as convolutions on the symmetric group.- A. Kyprianou, Z. Palmowski : Fluctuations of spectrally negative Markov additive processes.- J. Bertoin, A. Lindner, R. Maller : On continuity properties of the law of integrals of Levy processes.- D. Baraka, T. S. Mountford : A law of the iterated logarithm for fractional Brownian motions.- I. Nourdin : A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimensio local time in R1.- I. Bailleul : Une preuve simple dfun resultat de Dufresne.- L. Serlet : Creation or deletion of a drift on a Brownian trajectory.- A. M. G. Cox : Extending Chacon-Walsh: minimality and generalised starting distributions.- J. Brossard, C. Leuridan : Transformations browniennes et complements independants : resultats et problemes ouverts.- J.-C. Gruet : Hyperbolic random walks.- D. Bakry, N. Huet : The hypergroup property and representation of Markov kernels.- D. Williams : A new look at eMarkovianf Wiener-Hopf theory.- F. Bolley : Separability and completeness for the Wasserstein distance.- N. Privault : A probabilistic interpretation to the symmetries of a discrete heat equation.- S. Kaji : On tail distributions of supremum and quadratic variation of cadlag local martingales.- P. Friz, N. Victoir : The Burkholder-Davis-Gundy inequality for enhanced martingales.- Yu. Kabanov, C. Stricker : On martingale selectors of conevalued processes.- I. Klein : No asymptotic free lunch reviewed in the light of Orlicz spaces.- M. Rasonyi : New methods in the arbitrage theory of financial markets with transaction costs.
Series: Lecture Notes in Mathematics , Vol. 1935
2008, Approx. 135 p., Softcover
ISBN: 978-3-540-77910-0
Due: April 15, 2008
About this book
This volume introduces an entirely new pseudodifferential analysis on the line, the opposition of which to the usual (Weyl-type) analysis can be said to reflect that, in representation theory, between the representations from the discrete and from the (full, non-unitary) series, or that between modular forms of the holomorphic and substitute for the usual Moyal-type brackets. This pseudodifferential analysis relies on the one-dimensional case of the recently introduced anaplectic representation and analysis, a competitor of the metaplectic representation and usual analysis.
Besides researchers and graduate students interested in pseudodifferential analysis and in modular forms, the book may also appeal to analysts and physicists, for its concepts making possible the transformation of creation-annihilation operators into automorphisms, simultaneously changing the usual scalar product into an indefinite but still non-degenerate one.
Table of contents
Preface.- Introduction.- The Metaplectic and Anaplectic Representations.- The One-dimensional Alternative Pseudodifferential Analysis.- From Anaplectic Analysis to Usual Analysis.- Pseudodifferential Analysis and Modular Forms.- Index.- Bibliography.