"Analyzes the behavior, design, and implementation of artificial recurrent neural networks. Offers methods of synthesis for associative memories. Evaluates the qualitative properties and limitations of neural networks. Contains practical applications for optimal system performance."

This volume offers a systematic, comprehensive investigation of field extensions, finite or not, that possess a Cogalois correspondence. The subject is somewhat dual to the very classical Galois Theory dealing with field extensions possessing a Galois correspondence. Solidly backed by over 250 exercises and an extensive bibliography, this book presents a compact and complete review of basic field theory, considers the Vahlen-Capelli Criterion, investigates the radical, Kneser, strongly Kneser, Cogalois, and G-Cogalois extensions, discusses field extensions that are simultaneously Galois and...

Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analyzes packings and coverings with congruent convex bodies, arrangements on the sphere, line transversals, Euclidean and spherical tilings, geometric graphs, polygons and polyhedra, and fixing systems for convex figures. This text also offers research...

This reference details valuable results that lead to improvements in existence theorems for the Loewner differential equation in higher dimensions, discusses the compactness of the analog of the Caratheodory class in several variables, and studies various classes of univalent mappings according to their geometrical definitions. It introduces the infinite-dimensional theory and provides numerous exercises in each chapter for further study. The authors present such topics as linear invariance in the unit disc, Bloch functions and the Bloch constant, and growth, covering and distortion results...

An ambitious, comprehensive book covering subject matter typically taught over the course of two or three years, Abstract Algebra offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to automatically smooth the trajectory of learning algebra from zero to one - and includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory.

Presents hyperspace fundamentals, offering a basic overview and a foundation for further study. Topics include the topology for hyperspaces, examples of geometric models for hyperspaces, 2x and C(X) for Peano continua X, arcs in hyperspaces, the shape and contractability of hyperspaces, hyperspaces and the fixed point property, and Whitney maps. The text contains examples and exercises throughout, and provides proofs for most results.

Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.