Series: Springer Monographs in Mathematics
Originally published in the series: Perpectives Mathematical Logic
2nd ed. 2003. Corr. 2nd printing 2005, 2009, XXII, 536 p., Softcover
ISBN: 978-3-540-88866-6
The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contempory research. A "genetic" approach is taken, presenting the subject in the context of its historical development. With hindsight the consequential avenues are pursued and the most elegant or accessible expositions given. With open questions and speculations provided throughout the reader should not only come to appreciate the scope and coherence of the overall enterpreise but also become prepared to pursue research in several specific areas by studying the relevant sections.
Researchers and graduate students in set theory, including set-theoretic topology
infinitary combinatorics
large cardinals
new axioms for set theory
relative consistency results
set theory
Series: Trends in Mathematics
2009, Approx. 300 p., Hardcover
ISBN: 978-3-7643-9892-7
Due: January 2009
This book contains selected papers from the ISAAC conference 2007 and invited contributions. The topics covered represent the main streams of research in hypercomplex analysis as well as "state of the art" expository articles.
The book will be of interest to researchers and postgraduate students in various areas of mathematical analysis, e.g. one and several complex variables; PDE; hypercomplex analysis; operator theory; theoretical and mathematics physics.
Graduates, postgraduates and researchers in analysis, differential geometry and mathematical physics
Clifford algebra
Clifford analysis
hypercomplex analysis
quaternionic analysis
Series: Publications of the Scuola Normale Superiore
Subseries: Theses (Scuola Normale Superiore) , Vol. 10
2009, Approx. 130 p., Softcover
ISBN: 978-88-7642-336-9
Due: December 2008
The book is devoted to study the relationships between Stochastic Partial Differential Equations and the associated Kolmogorov operator in spaces of continuous functions.
In the first part, the theory of a weak convergence of functions is developed in order to give general results about Markov semigroups and their generator.
In the second part, concrete models of Markov semigroups deriving from Stochastic PDEs are studied. In particular, Ornstein-Uhlenbeck, reaction-diffusion and Burgers equations have been considered. For each case the transition semigroup and its infinitesimal generator have been investigated in a suitable space of continuous functions.
The main results show that the set of exponential functions provides a core for the Kolmogorov operator. As a consequence, the uniqueness of the Kolmogorov equation for measures has been proved.
Graduate students and researchers in stochastic analysis
1. Introduction.- 2. Preliminaries.- 3. Measure valued equations for stochastically continuous Markov semigroups.- 4. Measure equations for Ornstein-Uhlenbeck operators.- 5. Bounded perturbations of Ornstein-Uhlenbeck operators.- 6. Lipschitz perturbations of Ornstein-Uhlenbeck operators.- 7. The reaction-diffusion operator.- 8. The Burgers equation.- Bibliography.- Index.
Series: Progress in Mathematics , Vol. 273
2009, Approx. 250 p., Hardcover
ISBN: 978-3-7643-9903-0
Due: February 2009
Introduction of the new “upper triangular technology” method
Detailed application of upper triangular technology to operations in algebraic K-theory and to the Arf-Kervaire invariant problem.
An account of the relation of the book’s classical stable homotopy theory results to the important, new motivic stable homotopy theory of Morel-Voevodsky
This monograph describes important techniques of stable homotopy theory, both classical and brand new, applying them to the long-standing unsolved problem of the existence of framed manifolds with odd Arf-Kervaire invariant. Opening with an account of the necessary algebraic topology background, it proceeds in a quasi-historical manner to draw from the author’s contributions over several decades. A new technique entitled “upper triangular technology” is introduced which enables the author to relate Adams operations to Steenrod operations and thereby to recover most of the important classical Arf-Kervaire invariant results quite simply. The final chapter briefly relates the book to the contemporary motivic stable homotopy theory of Morel-Voevodsky.
Preface.- 1. Algebraic Topology Background.- 2. The Arf-Kervaire Invariant via QX 43.- 3. The Upper Triangular Technology.- 4. A Brief Glimpse of Algebraic K-theory.- 5. The Matrix Corresponding to $1\wedge\psi^3$.- 6. Real Projective Space.- 7. Hurewicz Images, BP-theory and the Arf-Kervaire Invariant.- 8. Upper Triangular Technology and the Arf-Kervaire Invariant.- 9. Futuristic and Contemporary Stable Homotopy.- Bibliography.- Index.
Series: Lecture Notes in Mathematics , Vol. 1971
2009, Approx. 210 p., Softcover
ISBN: 978-3-540-92846-1
Due: April 15, 2009
The aim of this book is to present some mathematical results describing the transition from kinetic theory, and, more precisely, from the Boltzmann equation for perfect gases to hydrodynamics.
Different fluid asymptotics will be investigated, starting always from solutions of the Boltzmann equation which are only assumed to satisfy the estimates coming from physics, namely some bounds on mass, energy and entropy.
Researchers and graduate students
Boltzmann equation
hydrodynamic limits
moment method
relative entropy method
1 Introduction.- 2 The Boltzmann equation and its formal hydrodynamic limits.- 3 Mathematical tools for the derivation of hydrodynamiclimits.- 4 The incompressible Navier-Stokes limit.- 5 The incompressible Euler limit.- 6 The compressible Euler limit.