Deligne's duality for de Rham realizations of 1-motives

We show that the pairing on de Rham realizations of 1-motives in "Theorie di Hodge III", IHES 44, can be defined over any base scheme and we prove that it gives rise to a perfect duality if one is working with a 1-motive and its Cartier dual. Furthermore we study universal extensions of 1-motives and their relation with $\natural$-extensions.Comment: 21 pages. Last section rewritten. New proof

Frontier at your fingertips

Between the nano- and micrometre scales, the collective behaviour of matter can give rise to startling emergent properties that hint at the nexus between biology and physics.Comment: Archival copy of Nature Connections Articl

A detailed analysis of the brachistochrone problem

If A and B are two points in the plane, with B lower and to the right of A, then we may consider the trajectory of an object travelling from A to B under the influence of gravity. The search for the trajectory minimising the time taken by the object gives rise to a mathematical optimisation problem involving an indefinite integral. Although the solution of this problem is known, a full detailed handling of the problem does not seem to be available. The aim of this article is to provide such a detailed study

Theology, Race and Libraries

Recent theological research into the origin of race and the presence of structural racism in library systems of knowledge organization will be presented. Using examples from the open access Anti-racism Digital Library and International Anti-racism Thesaurus participants will learn how to overcome current limitations in library catalog subject headings in order to offer anti-racist and just library service

The Problem of Doping

In this Essay, we examine Professor Michael J. Sandel and Judge Richard A. Posner\u27s thoughts on how to draw the line between substances and techniques that are fair game and those that constitute doping; whether there is a difference between sport and spectacle; and the nature of the public’s interest in sport as an institution and in doping as a practice that risks its integrity. Although we do not agree with all of their conclusions, they have made serious contributions to the ongoing discussion of these issues. Their linedrawing work in particular deserves considered attention from WADA and other stakeholders as they continue to work toward a useful and defensible definition of the spirit of sport