Inverse problems arise whenever one tries to calculate a required quantity from given measurements of a second quantity that is associated to the first one.
Since the injective envelope and projective cover were defined by Eckmann and Bas in the 1960s, they have had great influence on the development of homological algebra, ring theory and module theory.
This book contains the notes of five short courses delivered at the "e;Centro Internazionale Matematico Estivo"e; session "e;Integral Geometry, Radon Transforms and Complex Analysis"e; held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems.
This book presents the first comprehensive treatment of the blocking technique which consists in transforming norms in section form into norms in block form, and vice versa.
The first part of these lecture notes is an introduction to potential theory to prepare the reader for later parts, which can be used as the basis for a series of advanced lectures/seminars on potential theory/harmonic analysis.
This monograph describes the stochastic behavior of the solutions to the classic problems of Euclidean combinatorial optimization, computational geometry, and operations research.
In the fall of 1994, Edward Witten proposed a set of equations which give the main results of Donaldson theory in a far simpler way than had been thought possible.
This book provides a classification of all three-dimensional complex manifolds for which there exists a transitive action (by biholomorphic transformations) of a real Lie group.
This is a research monograph covering the majority of known results on the problem of constructing compact symplectic manifolds with no Kaehler structure with an emphasis on the use of rational homotopy theory.
The lecture courses of the CIME Summer School on Probabilistic Models for Nonlinear PDE's and their Numerical Applications (April 1995) had a three-fold emphasis: first, on the weak convergence of stochastic integrals; second, on the probabilistic interpretation and the particle approximation of equations coming from Physics (conservation laws, Boltzmann-like and Navier-Stokes equations); third, on the modelling of networks by interacting particle systems.
These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data.
This book contains two of the three lectures given at the Saint-Flour Summer School of Probability Theory during the period August 18 to September 4, 1993.
Starting from basic knowledge of nilpotent (Lie) groups, an algebraic theory of almost-Bieberbach groups, the fundamental groups of infra-nilmanifolds, is developed.
Most books devoted to the theory of the integral have ignored the nonabsolute integrals, despite the fact that the journal literature relating to these has become richer and richer.
Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties.
The book, based on a course of lectures by the authors at the Indian Institute of Technology, Guwahati, covers aspects of infinite permutation groups theory and some related model-theoretic constructions.
The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface.
This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, and its representation theoretic aspect involving vertex operator super-algebras.
While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce.
