Wenrong Li

This book offers a systematic platform for the theory of Boolean matrix and its application in logical dynamical systems. As a special kind of non-negative matrix, Boolean matrix has wide applications in graph theory, discrete-event system, game theory, clustering analysis, and so on. Due to the special operations between Boolean matrices, there exist some special mathematical properties for Boolean polynomial and Boolean vector space, which necessitate a general theory of Boolean matrix. Furthermore, logical dynamical systems have received recent attention from systems biology, information security, artificial intelligence, etc. The development of logical dynamical systems needs the mathematical foundation of Boolean matrix and logical matrix. Therefore, it is necessary to explore the relation between Boolean matrix theory and logical dynamical systems. To our best knowledge, there are no published books available on both Boolean matrix theory and logical dynamical systems. This book aims to provide some recent insightful results to meet this gap. It can serve as a textbook for scholars and students of mathematics, cybernetics, biology and artificial intelligence. Especially, the book is an important reference for readers who are interested in Boolean matrix theory and logical dynamical systems.

This book presents a self-contained and unified introduction to the properties of analytic functions. Based on recent research results, it provides many examples of functional equations to show how analytic solutions can be found. Unlike in other books, analytic functions are treated here as those generated by sequences with positive radii of convergence. By developing operational means for handling sequences, functional equations can then be transformed into recurrence relations or difference equations in a straightforward manner. Their solutions can also be found either by qualitative means or by computation. The subsequent formal power series function can then be asserted as a true solution once convergence is established by various convergence tests and majorization techniques. Functional equations in this book may also be functional differential equations or iterative equations, which are different from the differential equations studied in standard textbooks since composition of known or unknown functions are involved.