Donaldson Type Invariants For Algebraic Surfaces
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| Author | : Takuro Mochizuki |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 404 |
| Release | : 2009-03-26 |
| Genre | : Mathematics |
| ISBN | : 3540939121 |
We are defining and studying an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface.We are interested in relations among the invariants, which are natural generalizations of the "wall-crossing formula" and the "Witten conjecture" for classical Donaldson invariants. Our goal is to obtain a weaker version of these relations, by systematically using the intrinsic smoothness of moduli spaces. According to the recent excellent work of L. Goettsche, H. Nakajima and K. Yoshioka, the wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case!
| Author | : Christian Pötzsche |
| Publisher | : Springer |
| Total Pages | : 422 |
| Release | : 2010-08-24 |
| Genre | : Mathematics |
| ISBN | : 3642142583 |
Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.
| Author | : Thomas Duquesne |
| Publisher | : Springer |
| Total Pages | : 216 |
| Release | : 2010-09-02 |
| Genre | : Mathematics |
| ISBN | : 3642140076 |
Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.
| Author | : Catherine Donati Martin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 511 |
| Release | : 2010-10-28 |
| Genre | : Mathematics |
| ISBN | : 3642152163 |
This is a new volume of the Séminaire de Probabilités which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis on Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journées de Probabilités held in Poitiers in June 2009.
| Author | : Wen Yuan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 295 |
| Release | : 2010-09-18 |
| Genre | : Mathematics |
| ISBN | : 3642146058 |
During the last 60 years the theory of function spaces has been a subject of growing interest and increasing diversity. Based on three formally different developments, namely, the theory of Besov and Triebel-Lizorkin spaces, the theory of Morrey and Campanato spaces and the theory of Q spaces, the authors develop a unified framework for all of these spaces. As a byproduct, the authors provide a completion of the theory of Triebel-Lizorkin spaces when p = ∞.
| Author | : Alexander Y. Khapalov |
| Publisher | : Springer |
| Total Pages | : 296 |
| Release | : 2010-05-19 |
| Genre | : Mathematics |
| ISBN | : 3642124135 |
This monograph addresses the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The methodology is illustrated with a variety of model equations.
| Author | : Thomas Lorenz |
| Publisher | : Springer |
| Total Pages | : 526 |
| Release | : 2010-05-29 |
| Genre | : Mathematics |
| ISBN | : 3642124712 |
Ordinary differential equations play a central role in science and have been extended to evolution equations in Banach spaces. For many applications, however, it is difficult to specify a suitable normed vector space. Shapes without a priori restrictions, for example, do not have an obvious linear structure. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals. Here are some of the examples: - Feedback evolutions of compact subsets of the Euclidean space - Birth-and-growth processes of random sets (not necessarily convex) - Semilinear evolution equations - Nonlocal parabolic differential equations - Nonlinear transport equations for Radon measures - A structured population model - Stochastic differential equations with nonlocal sample dependence and how they can be coupled in systems immediately - due to the joint framework of Mutational Analysis. Finally, the book offers new tools for modelling.
| Author | : Markus Banagl |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 237 |
| Release | : 2010-07-08 |
| Genre | : Mathematics |
| ISBN | : 3642125883 |
The present monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality.
| Author | : Alberto Parmeggiani |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 260 |
| Release | : 2010-04-22 |
| Genre | : Mathematics |
| ISBN | : 3642119212 |
This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
| Author | : Pandelis Dodos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 180 |
| Release | : 2010-05-10 |
| Genre | : Mathematics |
| ISBN | : 3642121527 |
This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.
