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Regularity Properties of Functional Equations in Several Variables
This book illustrates the basic ideas of regularity properties of functional equations by simple examples. It then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion. A long introduction highlights the basic ideas for beginners and several applications are also included.
Probabilistic Cellular Automata
This book explores Probabilistic Cellular Automata (PCA) from the perspectives of statistical mechanics, probability theory, computational biology and computer science. PCA are extensions of the well-known Cellular Automata models of complex systems, characterized by random updating rules. Thanks to their probabilistic component, PCA offer flexible computing tools for complex numerical constructions, and realistic simulation tools for phenomena driven by interactions among a large number of neighboring structures. PCA are currently being used in various fields, ranging from pure probability to the social sciences and including a wealth of scientific and technological applications. This situa...
Annual Report
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Theory of Numbers
Theory of Numbers: A Textbook is aimed at students of Mathematics who are graduates or even undergraduates. Very little prerequisites are needed. The reader is expected to know the theory of functions of a real variable and in some chapters complex integration and some simple principles of complex function theory are assumed. The entire book is self contained except theorems 7 and 9 of chapter 11 which are assumed. The most ambitious chapter is chapter 11 where the most attractive result on difference between consecutive primes is proved. References to the latest developments like Heath-Brown's work and the work of R.C. Baker, G. Harman and J. Pintz along with readable accounts of Brun's sieve and also of Apery's Theorem on irrationality of zeta (3) are given. Finally the reader is acquainted with Montgomery-Vaughan Theorem in the last chapter. It is hoped that the reader will enjoy the leisurely style of presentation of many important results.
IMS Bulletin
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