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The Table of Integrals, Series, and Products is the major reference source for integrals in the English language.It is designed for use by mathematicians, scientists, and professional engineers who need to solve complex mathematical problems. *Completely reset edition of Gradshteyn and Ryzhik reference book *New entries and sections kept in orginal numbering system with an expanded bibliography *Enlargement of material on orthogonal polynomials, theta functions, Laplace and Fourier transform pairs and much more.

One of the major concerns of theoretical computer science is the classifi cation of problems in terms of how hard they are. The natural measure of difficulty of a function is the amount of time needed to compute it (as a function of the length of the input). Other resources, such as space, have also been considered. In recursion theory, by contrast, a function is considered to be easy to compute if there exists some algorithm that computes it. We wish to classify functions that are hard, i.e., not computable, in a quantitative way. We cannot use time or space, since the functions are not even computable. We cannot use Turing degree, since this notion is not quantitative. Hence we need a new notion of complexity-much like time or spac~that is quantitative and yet in some way captures the level of difficulty (such as the Turing degree) of a function.

Spectral Techniques and Fault Detection focuses on the spectral techniques for the analysis, testing, and design of digital devices. This book discusses the error detection and correction in digital devices. Organized into 10 chapters, this book starts with an overview of the concepts and tools to evaluate the applicability of various spectral approaches and fault-detection techniques to the design. This text then describes the class of generalized Programmable Logic Array configurations called Encoded PLAs. Other chapters consider the two-sided Chrestenson Transform to the analysis of some pattern properties. This book describes as well a certain type of cellular arrays for highly parallel processing, namely, three-dimensional arrays. The final chapter deals with the system design methods that allow and encourage designers to incorporate the necessary distributed error correction throughout any digital system. This book is a valuable resource for graduate students and engineers working in the fields of logic design, spectral techniques, testing, and self-testing of digital devices.

This concise and self-contained introduction builds up the spectral theory of graphs from scratch, including linear algebra and the theory of polynomials. Covering several types of graphs, it provides the mathematical foundation needed to understand and apply spectral insight to real-world communications systems and complex networks.