Bøger i Lecture Notes in Mathematics serien

Starting with convex functions on the line, this title leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational principles and perturbed optimization.

This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa.

A graph complex is a finite family of graphs closed under deletion of edges. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology.

Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. It is shown that these notions lead to nonautonomous Morse decompositions.

Partly based on new and unpublished sources, and featuring fresh biographical material, this volume explores numerous features of the lives and work of the three mathematicians, from their central theorems to their place in early 20th century French society.

We consider Levi non-degenerate tube hypersurfaces in complex linear space which are "spherical", that is, locally CR-equivalent to the real hyperquadric. For example, every such hypersurface is real-analytic and extends to a closed real-analytic spherical tube hypersurface in complex space.

This work introduces tools, from the field of category theory, that make it possible to tackle until now unsolvable representation problems (determination of the range of a given functor). The basic idea is: if a functor lifts many objects, then it also lifts many (poset-indexed) diagrams.

This stands in marked contrast to the seemingly countless, complex proof techniques offered by the extant body of papers and books. It also includes numerous explanatory figures that enable readers to progressively and intuitively understand the most important notions and proofs in the area of factors and factorization.

This volume deals with the theory of finite topological spaces and itsrelationship with the homotopy and simple homotopy theory of polyhedra.

This monograph discusses the existence and regularity properties of local times associated to a continuous semimartingale, as well as excursion theory for Brownian paths.

This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems.

The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike.

Focusing on two central conjectures of Asymptotic Geometric Analysis, the Kannan-Lovasz-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the treated topics.

Collects the notes of the CIME course Nonlinear PDE's and applications held in Cetraro (Italy) on June 23-28, 2008. This book explores the fundamental connections between topics such as optimal transport, Hamilton-Jacobi equations, Riemannian geometry, and more.

Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings.

The new theory of Jacobi forms over totally real number fields introduced in this monograph is expected to give further insight into the arithmetic theory of Hilbert modular forms, its L-series, and into elliptic curves over number fields.

We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems.

Recent years have seen dramatic progress in shape recognition algorithms applied to ever-growing image databases. The book describes a complete method that starts from a query image and an image database and yields a list of the images in the database containing shapes present in the query image.

In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others.

Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. This book includes boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis.

Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry.

This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement.

This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables.

Probabilistic Group Theory, Combinatorics and Computing is based on lecture courses held at the Fifth de Brun Workshop in Galway, Ireland in April 2011.