Posts Tagged Theory
Safety and Reliability in Cooperating Unmanned Aerial Systems Reviews
This book provides a comprehensive overview of recent advances in the analysis and design of health management systems for cooperating unmanned aerial vehicles. Such systems rely upon monitoring and fault adaptation schemes. Motivation for their study comes from the fact that, despite the use of fault-tolerant control software and hardware embedded onboard air vehicles, overall fleet performance may still be degraded after the occurrence of anomalous events such as systems faults and failures. Cooperative health management (CHM) systems seek to provide adaptation to the presence of faults by capitalizing on the availability of interconnected computing, sensing and actuation resources.This monograph complements the proposed CHM concepts by means of case studies and application examples. It presents fundamental principles and results encompassing optimization, systems theory, information theory, dynamics, modeling and simulation. Written by pioneers in cooperative control, health management and fault-tolerant control for unmanned systems, this book is a unique source of information for designers, researchers and practitioners interested in the field.
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The Fabulous Fibonacci Numbers
The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature?from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world.
With admirable clarity, math educators Alfred Posamentier and Ingmar Lehmann take us on a fascinating tour of the many ramifications of the Fibonacci numbers. The authors begin with a brief history of their distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the “golden ratio.” And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal?s triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.
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Computing and Combinatorics: 8th Annual International Conference, COCOON 2002, Singapore, August 15-17, 2002 Proceedings
This book constitutes the refereed proceedings of the 8th Annual International Computing and Combinatorics Conference, COCOON 2002, held in Singapore in August 2002.
The 60 revised full papers presented together with three invited contributions were carefully reviewed and selected from 106 submissions. The papers are organized in topical sections on complexity theory, discrete algorithms, computational biology and learning theory, radio networks, automata and formal languages, Internet networks, computational geometry, combinatorial optimization, and quantum computing.
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Calculus
Spivak’s celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.
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Coding Theory and Number Theory
This introductory book, which grew out of lectures given at the Mathematics Institute of Würzburg University, proposes a combination of coding theory and number theory. Chapter 1 gives a standard course of linear codes. The next two chapters treat a link between coding theory and number theory. Chapter 4 is a systematic study of algebraic-geometric codes and in Chapter 5 a connection between binary linear codes and theta functions is discussed.
The book is designed to teach undergraduates and graduates the basic ideas and techniques of coding theory and number theory.
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