Ferdinand F. Leimkuhler

A relationship between Lotka's Law, Bradford's Law, and Zipf's Law

A common functional relationship among Lotkas law, Bradfords law, and Zipfs law is derived. The proof takes explicit account of the sequences of observed values of the variables by means of an index. This approach results in a more realistic and precise formulation of each law.

Bradford's law: An index approach

A rigorous analysis of Bradfords law is made using an index for the observed values of the variables. Three important properties relating size and frequency are identified. Using this approach, the shape of Bradford-type curves can be described in terms of three distinct regions and two shape parameters.

Analysis of Zipf's law: an index approach

Abstract A rigorous analysis of Zipfs law is made using an index for the sequence of observed values of the variables in a Zipf-type relationship. Three important properties relating rank, count, and frequency are identified. Using this approach, the shape of Zipf-type curves can be described in terms of three distinct regions and two parameters of the Mandelbrot-Zipf law. This result has considerable practical significance, since it provides rigorous foundations for the application of Zipfs law.

A type-token identity in the Simon-Yule model of text

There are three significant results in this paper. First, we establish a type‐token identity relating the type‐token ratio and the bilogarithmic type‐token ratio. The plays of Shakespeare and other interesting texts serve as demonstrative examples. Second, the Simon‐Yule model of Zipfs law is used to derive the type‐token identity and provide a promising statistical model of text generation. Third, a realistic refinement of the Simon‐Yule model is made to allow for a decreasing entry rate of new words. Simulation methods are used to show that the type‐token identity is preserved with this change in assumptions.

Booth's law of word frequency

Booths results are based on Zipfs (1949) well-known relationship between the probability of occurrence, p(r), and the corresponding rank, r, of a word. Booths (1967) law is widely used to model the incidence of low frequency words in English text. Fedorowicz (1981, 1982) used it below to study automated bibliographic systems. Pao (1978) used it to derive a transition point in automatic text analysis. The present communication confirms this usage, corrects a deficiency in the original derivation, and makes the results more general

Economic Analysis of Computer Integrated Manufacturing Systems

Computer integrated manufacturing systems provide important economic advantages over less flexible and less controllable forms of manufacturing. Increased flexibility is particularly advantageous in the short run for small-batch production of mixed parts on the same system, and for longer run changes in product specifications and volume requirements. Increased controllability is particularly advantageous in sychronizing the flow of parts and tools over a greater part of the total production cycle, in maintaining greater and more uniform dimensional accuracy, and in stabilizing production during design and schedule changes. These advantages are realized in the form of lower direct labor requirements, lower in-process inventories, greater machine utilization, shorter lead times, and improved quality. On the other hand, such advantages require larger initial capital investments, more intensive use of such facilities, training in new labor skills, organizational changes, and the use of new planning and control methods.

ASIS Distinguished Lecture—1972: Operations Research and Information Science—A Common Cause

Operations research and information science were started in the 1940’s as expedient ways of solving societal problems by expanding the scope and application of scientific methodology. During the last two decades of public support for high technology and national science, both fields developed rapidly and won acceptance as new disciplines of study and professional practice. Today, however, the rise of technological disillusionment, scientific recession, and concern with the limits of growth are forcing both fields to re-examine their premises and their promises of a Utopian future. It is an appropriate time to reflect on the common origins of operations research and information science, and to recall the enthusiasm, spirit, and vision that motivated the pioneers, who were not idle dreamers. Indeed, there was an atmosphere of desperation and hardheaded practicality surrounding their efforts to bring these two disciplines into prominence.

The Practice of Operations Research in Libraries

The application of operations research methods to library-type problems has a long history which predates the formation of the Operations Research Society. Its practice continues today but much of its emphasis has shifted from concern with the specific problems of a librarian or a library manager to the more general problems of designing large information networks and satisfying the information needs of large classes of users through a variety of services. By moving in these directions, the operations researcher is largely following the course of the application of computers to library-type problems, since much of the motivation on the part of the librarians for the practice of operations research is in preparation for or defense against the relentless onslaught of computer-based automation of information activities. In many respects, it seems that these developments have resulted more in a change of the scale of the problems encountered rather than a change in the substance of the problems, since all of ...