Atlantis Press – förlag

This monograph treats normally hyperbolic invariant manifolds, with a focus on noncompactness. These objects generalize hyperbolic fixed points and are ubiquitous in dynamical systems.First, normally hyperbolic invariant manifolds and their relation to hyperbolic fixed points and center manifolds, as well as, overviews of history and methods of proofs are presented. Furthermore, issues (such as uniformity and bounded geometry) arising due to noncompactness are discussed in great detail with examples.The main new result shown is a proof of persistence for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. This extends well-known results by Fenichel and Hirsch, Pugh and Shub, and is complementary to noncompactness results in Banach spaces by Bates, Lu and Zeng. Along the way, some new results in bounded geometry are obtained and a framework is developed to analyze ODEs in a differential geometric context.Finally, the main result is extended to time and parameter dependent systems and overflowing invariant manifolds.

A new high-level book for professionals from Atlantis Press providing an overview of nanotechnologies now and their applications in a broad variety of fields, including information and communication technologies, environmental sciences and engineering, societal life, and medicine, with provision of customized treatments.

The book shows where nanotechnology is now - a fascinating time when the science is transitioning into complex systems with impact on new products. Present and future developments are addressed, as well as a larger number of new industrial and research opportunities deriving from this domain. An overview for professionals, researchers and policy-makers of this very rapidly expanding field. Brief chapters and colour figures with a contained overall length make the book attractive at an attractive price - a must for every professional’s shelf.

Mihail C. Roco, National Science Foundation and National Nanotechnology Initiative, wrote the preface underlying the importance and weight of the present book to this exciting and epoch-awakening field of research and applications:

“Nanotechnology is well recognized as a science and technology megatrend for the beginning of the 21st century. This book aims to show where nanotechnology is now - transitioning to complex systems and fundamentally new products - and communicates the societal promise of nanotechnology to specialists and the public. Most of what has already made it into the marketplace is in the form of “First Generation” products, passive nanostructures with steady behaviour. Many companies have “Second Generation” products, active nanostructures with changing behaviour during use, and embryonic “Third Generation” products, including 3-dimensional nanosystems. Concepts for “Fourth Generation” products, including heterogeneous molecular nanosystems, are only in research.”

The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.

The book covers a wide range of topics, yet essential, in Computational Finance (CF), understood as a mix of Finance, Computational Statistics, and Mathematics of Finance. In that regard it is unique in its kind, for it touches upon the basic principles of all three main components of CF, with hands-on examples for programming models in R. Thus, the first chapter gives an introduction to the Principles of Corporate Finance: the markets of stock and options, valuation and economic theory, framed within Computation and Information Theory (e.g. the famous Efficient Market Hypothesis is stated in terms of computational complexity, a new perspective). Chapters 2 and 3 give the necessary tools of Statistics for analyzing financial time series, it also goes in depth into the concepts of correlation, causality and clustering. Chapters 4 and 5 review the most important discrete and continuous models for financial time series. Each model is provided with an example program in R. Chapter 6 covers the essentials of Technical Analysis (TA) and Fundamental Analysis. This chapter is suitable for people outside academics and into the world of financial investments, as a primer in the methods of charting and analysis of value for stocks, as it is done in the financial industry. Moreover, a mathematical foundation to the seemly ad-hoc methods of TA is given, and this is new in a presentation of TA. Chapter 7 reviews the most important heuristics for optimization: simulated annealing, genetic programming, and ant colonies (swarm intelligence) which is material to feed the computer savvy readers. Chapter 8 gives the basic principles of portfolio management, through the mean-variance model, and optimization under different constraints which is a topic of current research in computation, due to its complexity. One important aspect of this chapter is that it teaches how to use the powerful tools for portfolio analysis from  the  RMetrics R-package. Chapter 9 is a naturalcontinuation of chapter 8 into the new area of research of online portfolio selection. The basic model of the universal portfolio of Cover and approximate methods to compute are also described.