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The document is a tutorial Monograph describing various aspects of time and frequency (T/F). Included are chapters relating to elemental concepts of precise time and frequency; basic principles of quartz oscillators and atomic frequency standards; historical review, recent progress, and current status of atomic frequency standards; promising areas for developing future primary frequency standards; relevance of frequency standards to other areas of metrology including a unified standard concept; statistics of T/F data analysis coupled with the theory and construction of the NBS atomic time scale; an overview of T/F dissemination techniques; and the standards of T/F in the USA. The Monograph addresses both the specialist in the field as well as those desiring basic information about time and frequency. The authors trace the development and scope of T/F technology, its improvement over periods of decades, its status today, and its possible use, applications, and development in days to come.
The Code of Federal Regulations is the codification of the general and permanent rules published in the Federal Register by the executive departments and agencies of the Federal Government.
Special edition of the Federal Register, containing a codification of documents of general applicability and future effect ... with ancillaries.

Hearings

United States. Congress. House. Committee on Interstate and Foreign Commerce

Published: 1966

Total Pages: 1570


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This book gives a lively development of the mathematics needed to answer the question, “How many times should a deck of cards be shuffled to mix it up?” The shuffles studied are the usual ones that real people use: riffle, overhand, and smooshing cards around on the table. The mathematics ranges from probability (Markov chains) to combinatorics (symmetric function theory) to algebra (Hopf algebras). There are applications to magic tricks and gambling along with a careful comparison of the mathematics to the results of real people shuffling real cards. The book explores links between shuffling and higher mathematics—Lie theory, algebraic topology, the geometry of hyperplane arrangements, stochastic calculus, number theory, and more. It offers a useful springboard for seeing how probability theory is applied and leads to many corners of advanced mathematics. The book can serve as a text for an upper division course in mathematics, statistics, or computer science departments and will be appreciated by graduate students and researchers in mathematics, statistics, and computer science, as well as magicians and people with a strong background in mathematics who are interested in games that use playing cards.
This book highlights the fundamental physics of orbit theory, dynamical models, methods of orbit determination, design, measurement, adjustment, and complete calculations for the position, tracking, and prediction of satellites and deep spacecraft. It emphasizes specific methods, related mathematical calculations, and worked examples and exercises. Therefore, technicians and engineers in the aerospace industry can directly apply them to their practical work. Dedicated to undergraduate students and graduate students, researchers, and professionals in astronomy, physics, space science, and related aerospace industries, the book is an integrated work based on the accumulated knowledge in satellite orbit dynamics and the author’s more than five decades of personal research and teaching experience in astronomy and aerospace dynamics.