We extend the concept of amenability of a Banach algebra A to the case that there is an extra A -module structure on A, and show that when S is an inverse semigroup with subsemigroup E of idempotents, then A = l(S) as a Banach module over A= l(E) is module amenable iff S is amenable. When S is a discrete group, l(E) = C and this is just the celebrated Johnson’s theorem.

We prove that the almost-entropic region of order four is not semialgebraic, we get as a corollary Matus’ Theorem, which asserts that the almost-entropic regions of order larger than four are not polyhedral. We discuss the algorithmic consequences of our result.

The authors analyzed self-reported SAT scores and actual SAT scores for five different samples of college students (N=650). Students overestimated their actual SAT scores by an average of 25 points (SD=81, d=0.31), with 10% under-reporting, 51% reporting accurately, and 39% over-reporting, indicating a systematic bias towards overreporting. The amount of over-reporting was greater for lower-sco...

We give a new simpler proof of a theorem of Jayne–Rogers.

The old-established growth method of Osborne, Mendel & Ferry (1919) for determining the protein efficiency ratio (PER) of protein sources has recently been suggested both in Canada (Chapman, Castillo & Campbell, 1959) and the USA (Derse, 1960) as a routine method for assessing the nutritive value of proteins. Njaa (1963) in a detailed study of the nitrogen balance sheet method for measurement o...

The Duggan-Schwartz theorem [Duggan and Schwartz, 1992] is a famous result concerning strategy-proof social choice correspondences, often stated as “A social choice correspondence that can be manipulated by neither an optimist nor a pessimist has a weak dictator”. However, this formulation is actually due to Taylor [2002], and the original theorem, at face value, looks rather different. In this...