A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.
Even with the advances in signal processing and digital communications, robustness to uncertain channel statistics continues to be a fundamental issue in the design and performance analysis of today's communications, radar, and sonar systems. The variability of digital communications systems consistently challenges the communications system designer, while new applications have channels that almost defy accurate modeling. As a result, parametric detectors, which are excellent when model assumptions are satisfied, do not maintain the satisfactory performance necessary for detection. This core IEEE Press reissue is the only book devoted solely to nonparametric detection - the key to maintaining good performance over a wide range of conditions. Throughout, the authors employ the classical Neyman-Pearson approach, which is widely applicable to detection problems in communications, radar, sonar, acoustics, and geophysics. Topics covered include: nonparametric detection theory, basic detection theory, one-input and two-input detectors and performance, tied observations, dependent sample performance, and engineering applications.
This book describes systematic methods for winning in differential games of pursuit and evasion and illustrates the scope and application of the developed procedures.
This book deals with measures of information (the most important ones being called entropies), their properties, and, reciprocally, with questions concerning which of these properties determine known measures of information, and which are the most general formulas satisfying reasonable requirements on practical measures of information. Thisis the first book investigating this subject in depth.
A book on an advanced level that exposes the reader to the fascinating field of differential equations and provides a ready access to an up-to-date state of this art is of immense value. This book presents a variety of techniques that are employed in the theory of nonlinear boundary value problems. For example, the following are discussed: methods that involve differential inequalities; shooting and angular function techniques; functional analytic approaches; topological methods.