Exact properties of Frobenius numbers and fraction of the symmetric semigroups in the weak limit for n=3

We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester's formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit

The Origin of Black Hole Entropy in String Theory

I review some recent work in which the quantum states of string theory which are associated with certain black holes have been identified and counted. For large black holes, the number of states turns out to be precisely the exponential of the Bekenstein-Hawking entropy. This provides a statistical origin for black hole thermodynamics in the context of a potential quantum theory of gravity.Comment: 18 pages (To appear in the proceedings of the Pacific Conference on Gravitation and Cosmology, Seoul, Korea, February 1-6, 1996.

Changing social contracts in climate-change adaptation

Risks from extreme weather events are mediated through state, civil society and individual action 1 , 2 . We propose evolving social contracts as a primary mechanism by which adaptation to climate change proceeds. We use a natural experiment of policy and social contexts of the UK and Ireland affected by the same meteorological event and resultant flooding in November 2009. We analyse data from policy documents and from household surveys of 356 residents in western Ireland and northwest England. We find significant differences between perceptions of individual responsibility for protection across the jurisdictions and between perceptions of future risk from populations directly affected by flooding events. These explain differences in stated willingness to take individual adaptive actions when state support retrenches. We therefore show that expectations for state protection are critical in mediating impacts and promoting longer-term adaptation. We argue that making social contracts explicit may smooth pathways to effective and legitimate adaptation

Safety and efficacy of fluticasone propionate in the topical treatment of skin diseases

Fluticasone propionate - the first carbothioate corticosteroid - has been classified as a potent anti-inflammatory drug for dermatological use. It is available as 0.05% cream and 0.005% ointment formulations for the acute and maintenance treatment of patients with dermatological disorders such as atopic dermatitis, psoriasis and vitiligo. This glucocorticoid is characterized by high lipophilicity, high glucocorticoid receptor binding and activation, and a rapid metabolic turnover in skin. Although skin blanching following fluticasone propionate exceeds that of corticosteroids of medium strength, several clinical trials demonstrate a low potential for cutaneous and systemic side-effects, even in difficult-to-treat areas like the face, the eyelids and intertriginous areas. Even among paediatric patients with atopic dermatitis, fluticasone propionate proved to be safe and effective. These pharmacological and clinical properties are reflected by the high therapeutic index of this glucocorticoid

Risk factors for race-day fatality in flat racing Thoroughbreds in Great Britain (2000 to 2013)

A key focus of the racing industry is to reduce the number of race-day events where horses die suddenly or are euthanased due to catastrophic injury. The objective of this study was therefore to determine risk factors for race-day fatalities in Thoroughbred racehorses, using a cohort of all horses participating in flat racing in Great Britain between 2000 and 2013. Horse-, race- and course-level data were collected and combined with all race-day fatalities, recorded by racecourse veterinarians in a central database. Associations between exposure variables and fatality were assessed using logistic regression analyses for (1) all starts in the dataset and (2) starts made on turf surfaces only. There were 806,764 starts in total, of which 548,571 were on turf surfaces. A total of 610 fatalities were recorded; 377 (61.8%) on turf. In both regression models, increased firmness of the going, increasing racing distance, increasing average horse performance, first year of racing and wearing eye cover for the first time all increased the odds of fatality. Generally, the odds of fatality also increased with increasing horse age whereas increasing number of previous starts reduced fatality odds. In the ‘all starts’ model, horses racing in an auction race were at 1.46 (95% confidence interval (CI) 1.06–2.01) times the odds of fatality compared with horses not racing in this race type. In the turf starts model, horses racing in Group 1 races were at 3.19 (95% CI 1.71–5.93) times the odds of fatality compared with horses not racing in this race type. Identification of novel risk factors including wearing eye cover and race type will help to inform strategies to further reduce the rate of fatality in flat racing horses, enhancing horse and jockey welfare and safety

Factors associated with failed treatment : an analysis of 121,744 women embarking on their first IVF cycles

Peer reviewedPublisher PD

A Tonnetz Model for pentachords

This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same $T/I$ class. It is a generalization of the well known \"Ottingen-Riemann torus for triads of neo-Riemannian theories. Two pentachords are near if they differ by a particular set of contextual inversions and the whole contextual group of inversions produces a Tiling (Tessellation) by pentagons on the surfaces. A description of the surfaces as coverings of a particular Tiling is given in the twelve-tone enharmonic scale case.Comment: 27 pages, 12 figure