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Georgian
The Caucasus for its size can boast more languages than any other region on earth. Of the 40 or so native tongues Georgian is the most widely spoken (by up to 5 million, of whom 3 million are ethnic Georgians). With its own unique script, Georgian has been written since the 4th century and has a rich literature of all genres. Outside Georgia, however, it has remained virtually unknown and unstudied, its grammatical intricacies being discussed by a small but ever growing succession of foreign specialists. The present work represents the first Reference Grammar of this challenging language to appear in English and is the summation of 20 years of intensive study by its author.
Random Summation
This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of its applications to solving practical problems in hardware and software reliability, insurance, finance, and more. The authors show how practice interacts with theory, and how new mathematical formulations of problems appear and develop. Attention is mainly focused on transfer theorems, description of the classes of limit laws, and criteria for convergence of distributions of sums for a random number of random variables. Theoretical background is given for the choice of approximations for the dis...
High-dimensional Knot Theory
High-dimensional knot theory is the study of the embeddings of n-dimensional manifolds in (n+2)-dimensional manifolds, generalizing the traditional study of knots in the case n=1. The main theme is the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory. Many results in the research literature are thus brought into a single framework, and new results are obtained. The treatment is particularly effective in dealing with open books, which are manifolds with codimension 2 submanifolds such that the complement fibres over a circle. The book concludes with an appendix by E. Winkelnkemper on the history of open books.
