A set in complex Euclidean space is called C-convex if all its intersections with complex lines are contractible, and it is said to be linearly convex if its complement is a union of complex hyperplanes. These notions are intermediates between ordinary geometric convexity and pseudoconvexity. Their importance was first manifested in the pioneering work of André Martineau from about forty years ago. Since then a large number of new related results have been obtained by many different mathematicians. The present book puts the modern theory of complex linear convexity on a solid footing, and gives a thorough and up-to-date survey of its current status. Applications include the Fantappié transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.

Rainbow connections are natural combinatorial measures that are used in applications to secure the transfer of classified information between agencies in communication networks. Rainbow Connections of Graphs covers this new and emerging topic in graph theory and brings together a majority of the results that deal with the concept of rainbow connections, first introduced by Chartrand et al. in 2006.

We present here the mathematical papers of Hassler Whitney. This collection contains all the published papers, with the exception of some short announcements that Whitney did not wish to be included. We also include the introduction to his book Geometric Integration Theory, and one previously unpublished manuscript on the four-color problem. The papers are presented under some broad categories: graphs· and combinatorics, differentiable functions and singularities, analytic spaces, manifolds, bundles and characteristic classes, topology and algebraic topology, geometric integration theory. Whitney intended to write an introduction to this collection. Unfortunately he left us no manuscript at the time of his death, May 10, 1989. We had discussed the possibility of using his paper "Moscow 1935 - Topology moving toward America," written for the Centennial of the American Mathematical Society, as part of his introduction to this collection, an idea which he much liked. We therefore include this paper, which contains personal information as well as mathematical reflections, as Whitney's own introduction to these volumes. Whitney's mathematical style, like his personal style, was that of an explorer and pioneer. One of the pictures included in these volumes shows him as a mountain climber. In mathematics, he preferred to work on undeveloped areas: break new ground and build foundations. During the last twenty years of his life he concentrated his efforts on developing an educational system that builds on the natural tendency in children to be explorers.

A recent paper on subfactors of von Neumann factors has stimulated much research in von Neumann algebras. It was discovered soon after the appearance of this paper that certain algebras which are used there for the analysis of subfactors could also be used to define a new polynomial invariant for links. Recent efforts to understand the fundamental nature of the new link invariants has led to connections with invariant theory, statistical mechanics and quantum theory. In turn, the link invariants, the notion of a quantum group, and the quantum Yang-Baxter equation have had a great impact on the study of subfactors. Our subject is certain algebraic and von Neumann algebraic topics closely related to the original paper. However, in order to promote, in a modest way, the contact between diverse fields of mathematics, we have tried to make this work accessible to the broadest audience. Consequently, this book contains much elementary expository material.

Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.

Bondgraphs are a well-established technique for the modelling of complex engineering systems. The subject of this book is an integrated modelling and simulation of mechatronics systems in a visual computer environment. The modelling is based on system top-down and bottom-up approach. The mathematical models are generated in a form of differential-algebraic equations and solved using numerical and symbolic algebra methods. The authors carefully explain a systematic procedure for developing the models using simple visual commands and construct a bondgraph at every level of decomposition. The integrated approach they develop is applied to mechanical, electrical and control systems, multibody dynamics, and continuous systems. The book contains a powerful computer simulation package on the accompanying CD-ROM. The BondSim package supports top-down and bottom-up model development using component libraries.

Edmund Wylfing (ca. 844-870), a Saxon king of East Anglia, virgin and martyr, was the the first patron-saint of England. The Italian ensemble La Reverdie brings to life again his story through a medieval liturgical drama, in three parts: life, passion and miracles.

As the celebration of the 250th anniversary of Beethovens birth approaches, and following a much-admired version of the Diabelli Variations (Alpha 386 Gramophone Editors Choice), Martin Helmchen has decided to record his complete piano concertos in the company of musical partners with whom he has a special affinity, Andrew Manze and the Deutsches Symphonie-Orchester Berlin. They devote this first volume to the Concertos nos. 2 and 5, giving lovingly polished performances of these two masterpieces of the piano repertory. Composed even before Concerto no. 1, the Second Concerto was premiered in Vienna in 1795, when Beethoven was only twenty-five years old, but underwent several revisions before being published in its final version in 1801.

Atalanta (HWV 35) is a pastoral opera in three acts by George Frideric Handel composed in 1736. It is based upon the mythological female athlete, Atalanta, the libretto (which is in Italian) being derived from the book La Caccia in Etolia by Belisario Valeriani. The identity of the librettist is not known. Handel composed it for the London celebrations of the marriage in 1736 of Frederick, Prince of Wales, eldest son of King George II, to Princess Augusta of Saxe-Gotha. The first performance took place on 12 May 1736 in the Covent Garden Theatre.