We say that two elliptic curves E1, E2 over a number field K are n-Selmer companions for a positive integer n if for every quadratic character χ of K, there is an isomorphism Seln(E χ 1 /K) ∼= Seln(E 2 /K) between the nSelmer groups of the quadratic twists E 1 , E χ 2 . We give sufficient conditions for two elliptic curves to be n-Selmer companions, and give a number of examples of non-isogenou...

Sun-like stars have stellar, brown dwarf and planetary companions. To help constrain their formation and migration scenarios, we analyse the close companions (orbital period < 5 years) of nearby Sun-like stars. By using the same sample to extract the relative numbers of stellar, brown dwarf and planetary companions, we verify the existence of a very dry brown dwarf desert and describe it quanti...

Reading is an essential skill for functioning in modern society, fundamental to achievement and success. Yet, an alarming proportion of students have significant difficulties with reading. Research indicates that computer assisted instruction (CAI) can provide an effective educational tool to help poor readers. This case study investigates the effectiveness of a CAI reading tutorial in helping ...

Early research on imaginary companions viewed the phenomenon negatively. Imaginary companions were often associated with psychopathology and an inability to distinguish between fantasy and reality. The prevailing view on imaginary companions has shifted in recent years with many studies focusing on the positive attributes exhibited by children with imaginary friends. Methodological issues which...

Affect sensitivity is an important requirement for artificial companions to be capable of engaging in social interaction with human users. This paper provides a general overview of some of the issues arising from the design of an affect recognition framework for artificial companions. Limitations and challenges are discussed with respect to other capabilities of companions and real world scenar...

We analyze a 19 night photometric search for transiting extrasolar planets in the open cluster NGC 1245. An automated transit search algorithm with quantitative selection criteria finds six transit candidates; none are bona fide planetary transits.We characterize the survey detection probability viaMonte Carlo injection and recovery of realistic limb-darkened transits. We use this to derive upp...

In the context of abstract coinduction in complete lattices, the notion of compatible function makes it possible to introduce enhancements of the coinduction proof principle. The largest compatible function, called the companion, subsumes most enhancements and has been proved to enjoy many good properties. Here we move to universal coalgebra, where the corresponding notion is that of a final di...

357 June 2013, Vol. 103, No. 6 SAMJ Feline companions and demography To the Editor: In A Moveable Feast by Ernest Hemingway, the author goes to visit Gertrude Stein and, sitting downstairs, hears from above the following by Ms Stein: ‘Don’t, pussy. Don’t. Don’t, please don’t. I’ll do everything, pussy, pussy, but please don’t do it. Please don’t. Please don’t, pussy.’ Hemingway immediately leav...