Generalised prime systems with periodic integer counting function

We study generalised prime systems (both discrete and continuous) for which the `integer counting function' N(x) has the property that N(x) ¡ cx is periodic for some c > 0. We show that this is extremely rare. In particular, we show that the only such system for which N is continuous is the trivial system with N(x) ¡ cx constant, while if N has finitely many discontinuities per bounded interval, then N must be the counting function of the g-prime system containing the usual primes except for finitely many. Keywords and phrases: Generalised prime systems.

Collective Responsibility for Oppression

Many contemporary forms of oppression are not primarily the result of formally organized collective action nor are they an unintended outcome of a combination of individual actions. This raises the question of collective responsibility. I argue that we can only determine who is responsible for oppression if we understand oppression as a matter of social practices that create obstacles for social change. This social practice view of oppression enables two insights: First, that there is an unproblematic sense in which groups can bear irreducible collective responsibility for oppression. Second, that there are derived forms of individual responsibility for members of dominant groups

Review of A Family of Brothers: Soldiers of the 26th New Brunswick Battalion in the Great War by J. Brent Wilson

Review of A Family of Brothers: Soldiers of the 26th New Brunswick Battalion in the Great War by J. Brent Wilso

Asymptotic expansions for Taylor coefficients of the composition of two functions

We give an asymptotic expansion for the Taylor coe±cients of L(P(z)) where L(z) is analytic in the open unit disc whose Taylor coe±cients vary `smoothly' and P(z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences