The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., 42], 48], 77], 86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof...

This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for...

The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points.

Key features:

* New the Hardy - Friedrichs - Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.
* Precise exponents of...

General concepts and methods that occur throughout mathematics - and now also in theoretical computer science - are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric nature of the subject and explaining its connections to mathematical logic. The book should appeal to the inquisitive reader who has seen some basic topology and algebra and would like to learn and explore further.

The first part contains a detailed treatment of the fundamentals of Geometric Logic, which combines four central ideas: natural transformations, sheaves, adjoint...

The first volume of the Handbook of Public Economics contains eight essays on various topics in Public Economics by international leaders in the field. It begins with an historical perspective on the growth of the area as a whole, and subsequent essays focus on the theory and evidence about the impact of taxation on economic behavior.

The material presents an up-to-date survey of the field of public economics by those actually doing work on the frontier of the subject, and is written in a manner that renders it useful to the public finance specialist, whilst remaining understandable for...

Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem.

The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincare and Grothendieck with applications of Grothendieck's lemma to complex analysis, the imbedding theorem of Whitney and Thom's transversality theorem.

Chapter 3 includes characterizations of linear differentiable operators, due to Peetre and Hormander....

A number of monographs of various aspects of complex analysis in several variables have appeared since the first version of this book was published, but none of them uses the analytic techniques based on the solution of the Neumann Problem as the main tool.

The additions made in this third, revised edition place additional stress on results where these methods are particularly important. Thus, a section has been added presenting Ehrenpreis' fundamental principle'' in full. The local arguments in this section are closely related to the proof of the coherence of the sheaf of germs of...

"General-equilibrium" refers to an analytical approach which looks at the economy as a complete system of inter-dependent components (industries, households, investors, governments, importers and exporters). "Applied" means that the primary interest is in systems that can be used to provide quantitative analysis of economic policy problems in particular countries. Reflecting the authors' belief in the models as vehicles for practical policy analysis, a considerable amount of material on data and solution techniques as well as on theoretical structures has been included. The sequence of...

Scripting Languages form the basis of technologies on the World Wide Web. Office software suites such as Microsoft Office also rely heavily on them. They provide power and flexibility (even for non-expert programmers) for developing graphical user interfaces. This text surveys a variety of the most important Scripting Languages, illustrating their use in a wide variety of application domains, including Perl V, Tcl, Word Basic, Java Script, Visual Basic, and VB Script. It also explores object architectures such as COM, OLE and ActiveX and how thery rely on scripting.