What is the smallest prime?

What is the first prime? It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime.Comment: 11 pages, 5 figure

Professional practice in the new NHS: a study into the impact of the NHS reforms on the practice of doctors and nurses, and the effect on quality of patient care.

This study aims to examine the impact of the NHS Reforms on doctors and nurses in two North London hospitals, in relation to both changes to the nature of professional practice, and the effect on quality of care offered by professionals to their patients. A case study approach is utilised, combining quantitative and qualitative methodologies to explore the consequence of the policy implementation. A survey was carried out to examine the nature and scope of the effects on professional practice, of the NHS Reforms, and to collate examples of improvements and deteriorations in quality of care offered to patients. In-depth interviews were carried out with senior managers in both hospitals and also their purchasing Health Authority, to identify key features of the policy implementation process. In-depth interviews were also carried out with doctors and nurses in both hospitals, working in a range of clinical specialities to explore the experience of professional practice within a changing policy environment. It emerged that there was a shared experience, across both hospitals and professions, of increasing levels of stress, increasing workload and increasing levels of conflict with managers. There is evidence of both improvements and deteriorations in the quality of care offered to patients, but whereas improvements were largely related to the quality element of structure, the deteriorations were closely related to the process element. Analysis of the interview data revealed three distinct responses by professionals to the NHS Reforms, and these related to the differing values and belief systems which were held. Two groups of professionals – the Traditional and the Transformed - have adapted to the changing milieu of the NHS, but the third - the Transitional - have become disenfranchised from the system within which they practice

Whales, dolphins, and porpoises of the western North Atlantic: a guide to their identification

This is an identification guide for cetaceans (whales, dolphins, and porpoises). It was designed to assist laypersons in identifying cetaceans encountered in the western North Atlantic Ocean and was intended for use by ongoing cetacean observer programs. This publication includes sections on identifying cetaceans at sea as well as stranded animals on shore. Species accounts are divided by body size and presence or lack of a dorsal fin. Appendices cover tags used on cetacean species; how to record and report cetacean observations at see and for stranded cetaceans; and a list of contacts for reporting cetacean strandings. (Document pdf contains 183 pages - file takes considerable time to open

Spectral Variations in Early-Type Galaxies as a Function of Mass

We report on the strengths of three spectral indicators - Mg_2, Hbeta, and Hn/Fe - in the integrated light of a sample of 100 field and cluster E/S0 galaxies. The measured indices are sensitive to age and/or and metallicity variations within the galaxy sample. Using linear regression analysis for data with non-uniform errors, we determine the intrinsic scatter present among the spectral indices of our galaxy sample as a function of internal velocity dispersion. Our analysis indicates that there is significantly more intrinsic scatter in the two Balmer line indices than in the Mg_2 index, indicating that the Balmer indices provide more dynamic range in determining the age of a stellar population than does the Mg_2 index. Furthermore, the scatter is much larger for the low velocity dispersion galaxies, indicating that star formation has occurred more recently in the lower mass galaxies.Comment: 4 pages, 1 figure, 1 table, to appear in the Astrophysical Journal Letter

Plasma Wakefield Acceleration with a Modulated Proton Bunch

The plasma wakefield amplitudes which could be achieved via the modulation of a long proton bunch are investigated. We find that in the limit of long bunches compared to the plasma wavelength, the strength of the accelerating fields is directly proportional to the number of particles in the drive bunch and inversely proportional to the square of the transverse bunch size. The scaling laws were tested and verified in detailed simulations using parameters of existing proton accelerators, and large electric fields were achieved, reaching 1 GV/m for LHC bunches. Energy gains for test electrons beyond 6 TeV were found in this case.Comment: 9 pages, 7 figure

Effect of plasma inhomogeneity on plasma wakefield acceleration driven by long bunches

Effects of plasma inhomogeneity on self-modulating proton bunches and accelerated electrons were studied numerically. The main effect is the change of the wakefield wavelength which results in phase shifts and loss of accelerated particles. This effect imposes severe constraints on density uniformity in plasma wakefield accelerators driven by long particle bunches. The transverse two stream instability that transforms the long bunch into a train of micro-bunches is less sensitive to density inhomogeneity than are the accelerated particles. The bunch freely passes through increased density regions and interacts with reduced density regions.Comment: 7 pages, 10 figure