Let $\mathfrak{g}$ be a real or complex (finite dimensional) simple Lie algebra and $\sigma\in\mathrm{Aut}\mathfrak{g}$. The authors study automorphisms of the twisted loop algebra $L(\mathfrak{g},\sigma)$ of smooth $\sigma$-periodic maps from $\mathbb{R}$ to $\mathfrak{g}$ as well as of the ``smooth'' affine Kac-Moody algebra $\hat L(\mathfrak{g},\sigma)$, which is a $2$-dimensional extension of $L(\mathfrak{g},\sigma)$. It turns out that these automorphisms which either preserve or reverse the orientation of loops, and are correspondingly called to be of first and second kind, can be described essentially by curves of automorphisms of $\mathfrak{g}$. If the order of the automorphisms is finite, then the corresponding curves in $\mathrm{Aut}\mathfrak{g}$ allow us to define certain invariants and these turn out to parametrize the conjugacy classes of the automorphisms. If their order is $2$ the authors carry this out in detail and deduce a complete classification of involutions and real forms (which correspond to conjugate linear involutions) of smooth affine Kac-Moody algebras. The resulting classification can be seen as an extension of Cartan's classification of symmetric spaces, i.e. of involutions on $\mathfrak{g}$. If $\mathfrak{g}$ is compact, then conjugate linear extensions of involutions from $\hat L(\mathfrak{g},\sigma)$ to conjugate linear involutions on $\hat L(\mathfrak{g}_{\mathbb{C}},\sigma_{\mathbb{C}})$ yield a bijection between their conjugacy classes and this gives existence and uniqueness of Cartan decompositions of real forms of complex smooth affine Kac-Moody algebras. The authors show that their methods work equally well also in the algebraic case where the loops are assumed to have finite Fourier expansions.

Finite Order Automorphisms and Real Forms of Affine Kac-Moody Algebras in the Smooth and Algebraic Category (Memoirs of the American Mathematical Society, Number 1030)

Science & Math

Groß, Christian

Heintze, Ernst

Mathematics

Amer Mathematical Society

This book is for anyone who wants to write good C# code―even if you have never programmed before. Writing good code can be a challenge―there are so many options, especially in a .NET language like C#. If you want to really get the best from a programming language, you need to know which features work best in which situations, and understand their strengths and weaknesses. It is this understanding that makes the difference between coding and coding well. Beginning C# 2008: From Novice to Professional, Second Edition has been written to teach you how to use the C# programming language to solve problems. From the earliest chapters and the first introductory concepts, you'll be looking at real–world programming challenges and learning how C# can be used to overcome them. As you progress through the book, the problems become more involved and interesting, while the solutions become correspondingly more complex and powerful as C# features interact to achieve the results that you want. This second edition has been revised and improved to now include the SQL Server 2008 release and explain how you can integrate SQL Server 2008 with your C# applications. By the time you've finished reading this book and worked through the sample exercises, you'll be a confident and very competent C# programmer. You will still have many explorations of the .NET Framework API to look forward to, but you will have a firm foundation to build from, and you will know exactly where to go to find the things that you need to progress confidently in your projects.

Beginning C# 2008: From Novice to Professional (Books for Professionals by Professionals)

Computers & Technology

Programming

Apress

Applied Software Engineering with Apache Jakarta Commons is a software engineering based guide to the Apache Jakarta Commons components (e.g., Betwixt, Digester, Discovery, Collections), other Apache projects such as Ant, the Axis Web Service toolkit, and the popular JUnit framework. The book emphasis focuses on solutions to complex problems using a simple task-driven approach. In this task-driven approach, the idea is to define a generic problem, for example Java class instantiation, and then provide solutions in multiple contexts, such as Collections-based factories, the Discovery package, or even the Launcher package. The book includes a companion CD-ROM with samples and source code.

Applied Software Engineering with Apache Jakarta (Programming Series)

Arts & Photography

Graphic Design

Charles River Media

This book introduces MicrosoftÂ® WindowsÂ® administrators to the world of Open Source applications in order to save time and money. It provides readers with information and techniques for using the appropriate Open Source applications in a variety of situations, such as anti-spam, databases, E-mail, Web content, file sharing, word processing, spreadsheets, and more. By using a component approach in which readers can pick and choose their technologies, the book, for example, enables a Windows administrator to use Apache as a Web server, while still electing Microsoft SQL Server as a database. The focus of the product coverage is to help the administrator to perform more efficiently. The discussion of each option includes: quality of documentation available, how to package for installation in a business setting, and solving common tasks using various techniques. Although it offers an Open Source equivalent to many Microsoft applications, it does not attempt to offer replacements for Windows applications but complements the Windows operational routines.

Open Source for Windows (Administrator's Advantage Series)

Computer Science

The focus of this book is to present object-oriented programming using .NET patterns. Patterns are currently being largely taught based on the assumption that the reader understands object oriented programming techniques. This has resulted in another gap as the techniques taught often clash with the techniques used by the reader. The pattern concept is also abstract and often fails to make the jump from theory to practical. The purpose of this book is to fix the object-oriented and pattern programming dilemma by "mixing" the two-that is, teaching object-oriented concepts using patterns. If a moment is taken to think about the problem, this is a very logical approach as it promotes a solutions-based approach. The solutions are "how to create an object", "how to define where one wants to go", "how might one define the implementation", and so on. This book is unique in that it is modeled after the author's successful speaking material that applies patterns in a very pragmatic and practical manner. The materials will be organized using tasks, presented using patterns, and illustrated using development problems and solutions. This book will reference open source projects that illustrate some of the development problems and solutions. The focus is to use practical solutions that developers encounter everyday, such as database manipulations, GUI development, or middle tier component development. There will be no focus on specific technologies; for example, to illustrate database manipulations, Microsoft SQL Server could be used, but the book will focus on using a generic database and the SQL programming language.

Foundations of Object-Oriented Programming Using .NET 2.0 Patterns

Web Development & Design

Ajax is unique because it combines technologies to make traditional web pages interactive. Ajax Patterns and Best Practices enables you to quickly write applications that work properly. This book is not just about the technical, low-level details of the APIs, but about making things happen on both the client and server sides. This book addresses the server side with the REST protocol. REST and Ajax blend elegantly together, but REST can also be used alone, with just a computer-to-computer solution. Like Ajax, REST can be used with today's existing technologies. Millions of client computers are now Ajax-ready, and millions of servers are REST-ready. This is an ideal book whether or not you have already created an Ajax application. Because the book outlines various patterns and best practices, you can quickly check and verify that you're building an efficient Ajax application.

Ajax Patterns and Best Practices (Expert's Voice)

Ajax and REST Recipes: A Problem-Solution Approach will serve all of your Ajax needs, by providing adaptable solutions for common tasks you'll want to implement on web sites using the next generation of Ajax and REST techniques. As a JavaScript developer, your time is precious, so you'll want to solve problems that present themselves in your work as quickly as possible. You can pick up the code provided in this book, adapt it, or plug it straight into your own applications. The book mainly focuses on illustrating and explaining how to build applications that use JavaScript, Ajax, and REST Web Services, along with some user interface issues. Specifically, the following topics are covered: implementing JavaScript unit tests; explaining the intent of Dynamic Languages, Web Services and SOA; defining and implementing contracts using REST; understanding why JavaScript Functions have state; implementing JavaScript "Generics", which are a mixture between real Generics and a replacement algorithm; using code blocks; using functions to make decisions; understanding the difference of JavaScript code that behaves like a value type or a reference type; implementing proxies, delegates, mixins, and overloaded functions; implementing a complete Ajax and Web Service architecture; defining a Web Service using REST; handling large or slow or real-time data sets; implementing shopping cart type architectures; and solving the back button problem using Ajax. Having read this book you will learn how to modularize your web application by decoupling the client from the server. The decoupling allows a client developer to focus on writing the best JavaScript and Ajax code, and a server developer to write the best business and data objects.

Ajax and REST Recipes: A Problem-Solution Approach (Expert's Voice)

What is good code? This book provides specific guidelines for well-written code in the .NET context. The contents are based on award-winning material the author has presented at conferences throughout the US and Europe. There is debate about good code because there is not a single good piece of code, but many good pieces of code, each depending on the context that it is used. The author, an acknowledged expert on the subject of .NET coding style and techniques, explains that good code results from using patterns, but that not all good pieces of code are patterns.

How to Code .NET: Tips and Tricks for Coding .NET 1.1 and .NET 2.0 Applications Effectively

This book is for anyone who wants to write good Visual Basic 2008 code - even if you have never programmed before. Writing good code can be a challenge, there are so many options, especially in a language like Visual Basic. If you want to really get the best from a programming language you need to know which features work best in which situations and understand their strengths and weaknesses. It is this understanding that makes the difference between coding and coding well. Beginning VB 2008 has been written to teach you how to use the Visual Basic programming language to solve problems. From the earliest chapters, and from the first introductory concepts, you'll be looking at real-world programming challenges and learning how Visual Basic can be used to overcome them. As you progress through the book the problems become more involved and interesting while the solutions become correspondingly more complex and powerful as Visual Basic features interact to achieve the results that you want. By the time you've finished reading this book and worked through the sample exercises, you'll be a confident and very competent Visual Basic programmer. You will still have many explorations of the .NET Framework API to look forward to in your future career, but you will have a firm foundation to build from and you will know exactly where to go to find the things that you need to progress confidently in your projects. Christian Gross is dedicated to helping his readers understand every detail of Beginning VB 2008 and so you can contact him via SKYPE (christianhgross) if you have bought this book and have a question about something Christian discusses. If Christian is available when you contact him, he will even try to answer you right away! What you'll learn Become skilled in the Visual Basic 2008 programming language. Learn everything you need to begin building your own applications in a solid, well-considered way: this book

Beginning VB 2008: From Novice to Professional (Expert's Voice in .NET)

This is the first book designed to help Windows developers decide not only which technologies to use but also how to use them. It teaches them to combine the wide variety of technologies that make up Windows DNA into effective solutions for their own enterprise application requirements. The author makes use of his long consulting experience in the client-server world to describe "best practices" that apply to building Windows DNA applications.

A Programmer's Introduction to Windows DNA (with CD-ROM for Windows 2000)

Networking & Cloud Computing

See the best price to sell, buy, or rent books by Groß, Christian. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Groß, Christian