Transfinite Cantor's Mature Theory

This book is an evolution from my book A First Course in Information Theory published in 2002 when network coding was still at its infancy. The last few years have witnessed the rapid development of network coding into a research ?eld of its own in information science. With its root in infor- tion theory, network coding has not only brought about a paradigm shift in network communications at large, but also had signi?cant in?uence on such speci?c research ?elds as coding theory, networking, switching, wireless c- munications,distributeddatastorage,cryptography,andoptimizationtheory. While new applications of network coding keep emerging, the fundamental - sults that lay the foundation of the subject are more or less mature. One of the main goals of this book therefore is to present these results in a unifying and coherent manner. While the previous book focused only on information theory for discrete random variables, the current book contains two new chapters on information theory for continuous random variables, namely the chapter on di?erential entropy and the chapter on continuous-valued channels. With these topics included, the book becomes more comprehensive and is more suitable to be used as a textbook for a course in an electrical engineering department.

This book is a timely and practical guide to conducting qualitative research with a socio-technical approach. It covers the foundations of research including research design, research philosophy, and literature review; describes qualitative data collection, qualitative data preparation and filtering; explains qualitative data analysis using the techniques of socio-technical grounded theory (STGT); and presents the advanced techniques of qualitative theory development using emergent or structured modes. It provides guidance on evaluating qualitative research application and outcomes; and explores the possible role of Artificial Intelligence (AI) in qualitative research in the future.

The motivations that suggested the publication of this book in 1969 are still largely valid. In this revised edition I have updated the literature on the subjects that were covered in the original version; I have also added an appendix to Chapter VI, explaining the technique for solving singular integral equations and systems of such equations. In addition I have tried to give an introduction to the important developments concerning the purely mathematical theory (existence and uniqueness theorems). This part of kinetic theory has reached a mature stage in the last few years and is relevant for both the physical foundations of the subject (validity of the Boltzmann equation) and the application of kinetic theory to rarefied gas dynamics (numerical and simulation methods).

This book is a timely and practical guide to conducting qualitative research with a socio-technical approach. It covers the foundations of research including research design, research philosophy, and literature review; describes qualitative data collection, qualitative data preparation and filtering; explains qualitative data analysis using the techniques of socio-technical grounded theory (STGT); and presents the advanced techniques of qualitative theory development using emergent or structured modes. It provides guidance on evaluating qualitative research application and outcomes; and explores the possible role of Artificial Intelligence (AI) in qualitative research in the future.

Special relativity and quantum mechanics are likely to remain the two most important languages in physics for many years to come. The underlying language for both disciplines is group theory. Eugene P. Wigner's 1939 paper on the Unitary Representations of the Inhomogeneous Lorentz Group laid the foundation for unifying the concepts and algorithms of quantum mechanics and special relativity.

The sliding mode control paradigm has become a mature technique for the design of robust controllers for a wide class of systems including nonlinear, uncertain and time-delayed systems. This book is a collection of plenary and invited talks delivered at the 12th IEEE