This book presents the probabilistic methods around Hardy martingales for applications to complex, harmonic, and functional analysis.

This book focuses on the major applications of martingales to the geometry of Banach spaces, and a substantial discussion of harmonic analysis in Banach space valued Hardy spaces is also presented. It covers exciting links between super-reflexivity and some metric spaces related to computer science, as well as an outline of the recently developed theory of non-commutative martingales, which has natural connections with quantum physics and quantum information theory. Requiring few prerequisites and providing fully detailed proofs for the main results, this self-contained study is accessible to graduate students with a basic knowledge of real and complex analysis and functional analysis. Chapters can be read independently, with each building from the introductory notes, and the diversity of topics included also means this book can serve as the basis for a variety of graduate courses.

"Et moi, ..., si j'avait su comment en revenir, je One service mathematics bas rendered the human race. It bas put common sense back n'y serais point all .' where it belongs, on the topmost shelf next to lu1esVeme the dusty canister labelled 'discarded nonsense' Eric T. Bell 1be series is divergent; therefore we may be able to do something with it O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlineari- ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci- ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser- vice topology has rendered mathematical physics ... '; 'One service logic has rendered computer science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'etre of this series.

This volume presents the proceedings of the Seventh International Colloquium on Finite or Infinite Dimensional Complex Analysis held in Fukuoka, Japan. The contributions offer multiple perspectives and numerous research examples on complex variables, Clifford algebra variables, hyperfunctions and numerical analysis.

The 2nd Annual 2016 International Workshop on Materials Science and Engineering (IWMSE 2016) was held in Guangzhou, Guangdong, China on August 12 - August 14, 2016. The main aim of IWMSE 2016 was to provide a platform for scientists and engineers, to get together to share their research findings, exchange ideas and identify the future directions of R&D in materials science.In this conference, we have received over 272 high-quality papers, however, only 160 articles are included in the proceedings, covering topics such as ceramics and glasses, amorphous materials, nanomaterials and thin layers, soft magnetic materials, biomaterials, polymers, photovoltaic materials, steels, tool materials, composites, as well as functional and smart materials.

The Handbook presents an overview of most aspects of modern Banach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banach space theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.

Handbook of the Geometry of Banach Spaces