Mathematics : Applied

As individual needs have arisen in the fields of physics, electrical engineering and computational science, each has created its own theories of information to serve as conceptual instruments for advancing developments. This book provides a coherent consolidation of information theories from these different fields. The author gives a survey of current theories and then introduces the underlying notion of symmetry, showing how information is related to the capacity of a system to distinguish itself. A formal methodology using group theory is employed and leads to the application of Burnside's Lemma to count distinguishable states. This provides a versatile tool for quantifying complexity and information capacity in any physical system. Written in an informal style, the book is accessible to all researchers in the fields of physics, chemistry, biology, computational science as well as many others. more...

Price: $109.00

Asymptotics and Mellin-Barnes Integrals provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. more...

Price: $120.00

The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called “liftings.” This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2,?) in SL(4, ?). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to Langlands’ program in the area of automorphic representations. It includes a proof of known cases of Artin’s conjecture. more...

Price: $95.00

The purpose of this book is to address the challenging problem of Autonomous Navigation in Dynamic Environments, and to present new ideas and approaches in this newly emerging technical domain. The book surveys the state-of-the-art, discusses in detail various related challenging technical aspects, and addresses upcoming technologies in this field. The aim of the book is to establish a foundation for a broad class of mobile robot mapping and navigation methodologies for indoor, outdoor, and exploratory missions. Three main topics located on the cutting edge of the state of the art are addressed, from both the theoretical and technological point of views: Dynamic world understanding and modelling for safe navigation, Obstacle avoidance and motion planning in dynamic environments, and Human-robot physical interactions. Several models and approaches are proposed for solving problems such as Simultaneous Localization and Mapping (SLAM) in dynamic environments, Mobile obstacle detection and tracking, World state estimation and motion prediction, Safe navigation in dynamic environments, Motion planning in dynamic environments, Robust decision making under uncertainty, and Human-Robot physical interactions. more...

Price: $99.00

The aim of this book is to provide a comprehensive introduction to cryptography without using complex mathematical constructions. The themes are conveyed in a form that only requires a basic knowledge of mathematics, but the methods are described in sufficient detail to enable their computer implementation. The book describes the main techniques and facilities of contemporary cryptography, proving key results along the way. The contents of the first five chapters can be used for one-semester course. more...

Price: $70.00