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Geometrical concepts play a significant role in the analysis of physical systems. Apart from the intrinsic interest, the knowledge of differentiable manifolds has become useful — even mandatory — in an ever-increasing number of areas of mathematics and its applications. Many results/concepts in analysis find their most natural (generalized) setting in manifold theory. An interrelation of geometry and analysis can be found in this volume.The book presents original research, besides a few survey articles by eminent experts from all over the world on current trends of research in differential and algebraic geometry, classical and modern analysis including the theory of distributions (linear and nonlinear), partial differential equations and wavelets.
Boundary value problems for partial differential equations playa crucial role in many areas of physics and the applied sciences. Interesting phenomena are often connected with geometric singularities, for instance, in mechanics. Elliptic operators in corresponding models are then sin gular or degenerate in a typical way. The necessary structures for constructing solutions belong to a particularly beautiful and ambitious part of the analysis. Cracks in a medium are described by hypersurfaces with a boundary. Config urations of that kind belong to the category of spaces (manifolds) with geometric singularities, here with edges. In recent years the analysis on such (in general, stratified) spac...
Nuu-chah-nulth “family histories” are actually tribal histories since their idea of family encompasses the tribe. Eighteen such histories are presented here, chronicling the origins and resources of a number of tribal families. In lieu of written records, these oral traditions stood as Nuu-chah-nulth history and were recited formally in public on ceremonial occasions. Several accounts give long lists of foods. Others describe the acquisition of important technological advances, such as a salmon trap. Half of the texts are short, focusing on a particular item like a mask or a house decoration. One text lists hundreds of Nuu-chah-nulth place names given mythically by Swan Women to the Port Alberni region, which was previously Salish in population and language. Generally, these histories explain how the world came to be and set forth family claims to material and spiritual resources. Each account belonged to the family, which had the exclusive right to tell it publicly. Summary outlines are provided in the introduction.
Combinatorial design theory is a source of simply stated, concrete, yet difficult discrete problems, with the Hadamard conjecture being a prime example. It has become clear that many of these problems are essentially algebraic in nature. This book provides a unified vision of the algebraic themes which have developed so far in design theory. These include the applications in design theory of matrix algebra, the automorphism group and its regular subgroups, the composition of smaller designs to make larger designs, and the connection between designs with regular group actions and solutions to group ring equations. Everything is explained at an elementary level in terms of orthogonality sets a...
The main objective of this book is to give a systematic exposition of the main results and techniques of the factorization theory of abelian groups. The necessary background materials are presented along with some of the most important applications in geometry, combinatorics, coding theory, and number theory. A large part of the text is accessible to students, requiring only basic knowledge in group theory and algebra. Helpful exercises are provided in every chapter.
Reprint of the original, first published in 1881.
Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure.This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-order nondifferentiability (the usual sense of nonsmooth optimization) second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization.