Overcoming a difficult 'area'

One of the problems of the young teacher in the primary school is to find the middle-of-the-road course between what mathematics his pupils need to know and that mathematics which is prescribed in the syllabus for the examination. In an ideal setting there should be no conflict really and this is chiefly for two reasons: (a) the primary school teacher should teach mainly mathematical concepts and later someone else will teach the necessary arithmetic rules and techniques; (b) a satisfactory treatment of primary mathematics is achieved if the teacher has clearly in his mind the correct balance and treatment of the separate topics to which the prescribed syllabus is an approximation.peer-reviewe

Smallness and infinity in mathematics : an intuitive approach

The widespread availability of pocket calculators has widened the domain of possible investigations at certain levels in mathematics, in the secondary school classroom no less than in the university lecture-room. Most school boys and girls use the calculator and many of them may have asked what is the meaning of the letter e which appears on the key ex. This article is intended to explain the background which is necessary to understand the meaning of e and it is hoped that the numerical value of 2.718 assigned to e will no longer remain mysterious to readers who are non mathematicians. A knowledge of the realistic fractions e.g. that 1/6 is less than 1/4 , is the kind of mathematics required to follow the discussion.peer-reviewe

“Conceiving” the pill : the 45th birthday of the oral contraceptive pill in Europe

In 1961, the first combined oral contraceptive pill was introduced in Europe. This pill contained ethinylestradiol (0.05mg) and northisterone (4mg). Nowadays, monophasic pill preparations contain a low dose (20­35 g) of ethinylestradiol in combination with a progestogen. Progestogens include norethisterone and levonorgestrel (second generation); desogestrel and gestodene (third generation); and the newest progestogen, drospirenone (fourth generation). Risks of the combined oral contraceptive pill include venous thromboembolism and stroke. Benefits, such as protection from ovarian and endometrial cancer, apart from contraception, outweigh the risks if contraindications are observed, and low dose formulations used.peer-reviewe

Multi-Issue Allocation Games

This paper introduces a new class of transferable-utility games, called multi-issue allocation games.These games arise from various allocation situations and are based on the concepts underlying the bankruptcy model, as introduced by O'Neill (1982).In this model, a perfectly divisible good (estate) has to be divided amongst a given set of agents, each of whom has some claim on the estate.Contrary to the standard bankruptcy model, the current model deals with situations in which the agents' claims are multi-dimensional, where the dimensions correspond to various issues.It is shown that the class of multi-issue allocation games coincides with the class of (nonnegative) exact games.The run-to-the-bank rule is introduced as a solution for multi-issue allocation situations and turns out to be Shapley value of the corresponding game.Finally, this run-to-the-bank rule is characterised by means of a consistency property.game theory;allocation games

Skin ageing

Cutaneous ageing manifests itself as a progressive reduction in maximum function and reserve capacity of skin tissue. It is not a unique and uniform biological event. Skin comprises three layers: epidermis, dermis and subcutaneous tissue. Collagen atrophy is a major factor in skin ageing. There is a strong correlation between skin collagen loss and estrogen deficiency due to the menopause. Skin ageing, especially in the face, is associated with a progressive increase in extensibility and a reduction in elasticity. With increasing age, the skin also becomes more fragile and susceptible to trauma, leading to more lacerations and bruising. Furthermore, wound healing is impaired in older women. Estrogen use after the menopause increases collagen content, dermal thickness and elasticity, and it decreases the likelihood of senile dry skin. Large-scale clinical trials are necessary to help make informed recommendations regarding postmenopausal estrogen use and its role in the prevention of skin ageing.peer-reviewe

Job Scheduling, Cooperation and Control

This paper considers one machine job scheduling situations or sequencing problems, where clients can have more than a single job to be processed in order to get a final output.Moreover, a job can be of interest for different players. This means that one of the main assumptions in classic sequencing problems is dropped: the one to one correspondence between clients and jobs.It is shown that the corresponding cooperative games are balanced for specific types of cost criteria.scheduling;cooperation;game theory;cooperative games

Sequencing Games with Repeated Players

Two classes of one machine sequencing situations are considered in which each job corresponds to exactly one player but a player may have more than one job to be processed, so called RP(repeated player) sequencing situations.In max-RP sequencing situations it is assumed that each player's cost function is linear with respect to the maximum completion time of his jobs, whereas in min-RP sequencing situations the cost functions are linear with respect to the minimum completion times.For both classes, following explicit procedures to go from the initial processing order to an optimal order for the coalition of all players, equal gain splitting rules are defined.It is shown that these rules lead to core elements of the associated RP sequencing games.Moreover, it is seen that min-RP sequencing games are convex.cooperative game theory;sequencing;equal gain splitting;core;convexity

Composition and luminescence of AlInGaN layers grown by plasma-assisted molecular beam epitaxy

A study of AlInGaN epilayers, grown by plasma-assisted molecular beam epitaxy, was performed using spatially resolved x-ray microanalysis and luminescence spectroscopy in order to investigate competition between the incorporation of In, Al, and Ga as a function of the growth temperature in the 565-660 °C range and the nominal AlN mole fraction. The samples studied have AlN and InN mole fractions in the ranges of 4%-30% and 0%-16%, respectively. Composition measurements show the effect of decreasing temperature to be an increase in the incorporation of InN, accompanied by a small but discernible decrease in the ratio of GaN to AlN mole fractions. The incorporation of In is also shown to be significantly increased by decreasing the Al mole fraction. Optical emission peaks, observed by cathodoluminescence mapping and by photoluminescence, provide further information on the epilayer compositions as a function of substrate temperature, and the dependencies of peak energy and linewidth are plotted