THE CARMICHAEL PRIZES.

The gowers prizes

Since 1950, the Council of the British Branch of the International League Against Epilepsy has been awarding the Gowers Prizes (named after William Gowers, the eminent British physician who in late Victorian times made contributions to the study of epilepsy that laid the foundation of our modem understanding of it). Initially awarded to young physicians for a dissertation on a topic related to ...

The Hodgkins Fund Prizes

Poster Prizes

The winners of the poster prizes are below Kelsey Mulder presenting her poster We present a climatology for tornadoes in the British Isles, defined here as England, Scotland, Wales, Northern Ireland, Republic of Ireland, Channel Islands, and the Isle of Man. The climatology includes the geographic distribution, annual and diurnal cycles, seasonality, intensities, and occurrence of outbreaks in ...

Optimal Prizes

Consider agents who undertake costly effort to produce stochastic outputs observable by a principal. The principal can award a prize to them with probabilities that depend on their outputs. His goal is to elicit maximal effort from the agents for the least prize. We show that, given a general class Π of probabilistic schemes for awarding the prize and a domain of agents’characteristics on which...

Carmichael numbers and pseudoprimes

We now establish a pleasantly simple description of Carmichael numbers, due to Korselt. First, we need the following notion. Let a and p be coprime (usually, p will be prime, but this is not essential). The order of a modulo p, denoted by ordp(a), is the smallest positive integer m such that a ≡ 1 mod p. Recall [NT4.5]: If ordp(a) = m and r is any integer such that a ≡ 1 mod p, then r is a mult...