The Geometric and the Bradford Distributions: A Comparison

Both the geometric and the Bradford probability distributions are used to describe collections of items of interest in information science. Each unit item has a productivity, an integer n measuring the amount of use of the item. The cumulative fraction Fn of items with productivity equal to n or greates may be expressed as a function of n or else as a function of the cumulative mean productivity Gn of items with productivity equal to n or greater. If Fn is an exponential function of n, the distribution is geometric; if it is an exponential function of Gn, it is a Bradford distribution. The exact solution of Fn as a function of n for the Bradford distribution is computed; the results are tabulated. Graphs are given, comparing the two distributions, and their relative usefulness is discussed.Supported in part by the U.S. Army Research Office (Durham) under Contract No. DAHC04-73-C-0032

Solution of the Retiring Search Problem

The well-known variational principle of the optimal distribution of search effort is applied to the case where the sought-for target has been located momentarily but the search cannot begin until a time T o later, during which interval the target may or may not move. The optimal search path, called the retiring search curve,, is a spiral starting at the point of original location, with the relationship between r and or L, the length of path, given by a differential equation derived from the variational principle. This equation is solved for a range of values of the parameters of greatest practical interest. The results are tabulated and also displayed in graphical form for use in practice. General conclusions emerge, of considerable practical value in searches of this kind

The Underlying Characteristics of the Bradford Distribution

Not Availabl

Contract N5ori 06001, Task Order I; proposal for extension beyond current expiration date for the period 1 July 1954 through 30 June 1955.

Proposal for the extension of Contract N5ori 06001 beyond its prior expiration date for the period 1 July 1954 through 30 June 1955. Includes budget breakdown of additional expenditures anticipated

Contract N5ori 06001, Task Order I; Proposal for extension beyond current expiration date for the period 1 July 1953 through 30 June 1954

Memorandum on a proposed Research and Training Project in Applied Mathematics, using large-scale computing equipment, particularly Whirlwind

Ionization in positive ion sheaths

It was found that the positive ion current to a plane auxiliary collector placed in a neon discharge had about twice the value expected from the equations of Langmuir and Mott-Smith. This increase must be due to an ionization within the sheath surrounding the electrode or to an emission of electrons from the surface of the electrode. Four different possible causes of the increase are analyzed and relations between the voltage drop V, total current to the collector i, and sheath thickness x are obtained. Comparison with data shows that the increase in i is probably caused by the ionization of the metastable atoms within the sheath by radiation from the discharge. The relations; V = A(Bx^(4/3) + Cx^(8/3)), and i = (i0 + I0x^2)/2 hold, and check fairly well with the three experimental curves. Considerations of atomic energy states of the metastable atoms show that this ionization would be most marked in the noble gases, and almost nonexistant in mercury vapor, which was the gas investigated by Langmuir and Mott-Smith

ISSUES IN REFORMING TARIFF-RATE IMPORT QUOTAS IN THE AGREEMENT ON AGRICULTURE IN THE WTO

Contents: The Economics of Tariff Rate Quotas and the Effects of Trade Liberalization; TRQs and GATT Rules; An Overview of Tariffs, Quotas and Imports Worldwide; TRQs in the European Union; U.S. TRQs for Sugar, Tobacco and Peanuts; Dairy TRQs in the United States; Tariff Rate Quota Implementation and Administration by Developing Countries; Management of Tariff Rate Quotas in Korea and Japan; Tariff Rate Quota Administration in Canadian Agriculture; The Case of Australia and New Zealand Facing TRQs; The 1999 WTO Panel Report on the EU's Common Market Organization for Bananas; AssessmentInternational Relations/Trade,

Sequence Effects on DNA Entropic Elasticity

DNA stretching experiments are usually interpreted using the worm-like chain model; the persistence length A appearing in the model is then interpreted as the elastic stiffness of the double helix. In fact the persistence length obtained by this method is a combination of bend stiffness and intrinsic bend effects reflecting sequence information, just as at zero stretching force. This observation resolves the discrepancy between the value of A measured in these experiments and the larger ``dynamic persistence length'' measured by other means. On the other hand, the twist persistence length deduced from torsionally-constrained stretching experiments suffers no such correction. Our calculation is very simple and analytic; it applies to DNA and other polymers with weak intrinsic disorder.Comment: LaTeX; postscript available at http://dept.physics.upenn.edu/~nelson/index.shtm

Creation of an incus recess for a middle-ear microphone using a drill or laser ablation : a comparison of equivalent noise level and middle ear transfer function

Purpose: Studies have assessed the trauma and change in hearing function from the use of otological drills on the ossicular chain, but not the effects of partial laser ablation of the incus. A study of the effectiveness of a novel middle-ear microphone for a cochlear implant, which required an incus recess for the microphone balltip, provided an opportunity to compare methods and inform a feasibility study of the microphone with patients. Methods: We used laser Doppler vibrometry with an insert earphone and probe microphone in 23 ears from 14 fresh-frozen cadavers to measure the equivalent noise level at the tympanic membrane that would have led to the same stapes velocity as the creation of the incus recess. Results: Drilling on the incus with a diamond burr created peak noise levels equivalent to 125.1–155.0 dB SPL at the tympanic membrane, whilst using the laser generated equivalent noise levels barely above the baseline level. The change in middle ear transfer function following drilling showed greater variability at high frequencies, but the change was not statistically significant in the three frequency bands tested. Conclusions: Whilst drilling resulted in substantially higher equivalent noise, we considered that the recess created by laser ablation was more likely to lead to movement of the microphone balltip, and therefore decrease performance or result in malfunction over time. For patients with greatly reduced residual hearing, the greater consistency from drilling the incus recess may outweigh the potential benefits of hearing preservation with laser ablation