Ratios of periods for tensor product motives

In this article we prove some period relations for the ratio of Deligne's periods for certain tensor product motives. These period relations give a motivic interpretation for certain algebraicity results for ratios of successive critical values for Rankin-Selberg L-functions for ${\rm GL}_n \times {\rm GL}_{n'}$ proved by G\"unter Harder and the second author.Comment: In this revised version, we have made some minor modifications according to the comments by the refere

Beware the animals that dance: conservation as an unintended outcome of cultural practices

The International Union for the Conservation of Nature (IUCN) World Parks Congress of 2003 and the Conference of Parties to the Convention on Biological Diversity (CBD) of 2004 call for the recognition and support of Community Conserved Areas, with the CBD Programme of Work on Protected Areas committing countries to take action by 2008. Both within protected areas and in the matrix of land beyond reserves, customs and beliefs of indigenous and local communities can yield conservation benefits. Identifying an intention to conserve by the custodians of customary conserved areas can be challenging as customary practices are embedded within a myriad of cosmologies and worldviews. However, the definition of Community Conserved Areas does not require an expressed intention to conserve nor does it specify the mechanisms by which nature or natural resources can be conserved. Thus, conservation as an unintended outcome of cultural practices is included within the scope of community conservation. Fieldwork was conducted in Sabah, Malaysian Borneo, from October 2010 to April 2011. Data for the case study of Gumantong comes from an interview with Porodong Mogilin,!Native Chief Representative of Matunggong Native Court in Bavanggazo, Kudat and meetings of community leaders from the 13 villages surrounding Gumantong. This paper 1) employs the case study of Gumantong in Sabah, Malaysian Borneo, to highlight the distinction between communities expressing an intention to conserve and conservation as an unintended outcome of cultural practices and 2) considers the implications of this distinction for the process of recognizing and supporting Community Conserved Areas

Confinement, DCSB, Bound States, and the Quark-Gluon Vertex

Aspects of the dressed-quark-gluon vertex and their role in the gap and Bethe-Salpeter equations are briefly surveyed using an intuitive model. The model allows one to elucidate why a linear extrapolation to the chiral limit of extant lattice data on the dressed-quark mass-function overestimates this function and hence the value of the vacuum quark condensate. The diagrammatic content of the vertex described is explicitly enumerable. This property is essential to the symmetry preserving study of bound state properties. It facilitates a realistic analysis of vector and pseudoscalar meson masses, and also allows the accuracy of standard truncations to be gauged. The splitting between vector and pseudoscalar meson masses is observed to vanish as the current-quark mass increases. That argues for the mass of the pseudoscalar partner of the Upsilon(1S) to be above 9.4GeV. Moreover, in this limit the rainbow-ladder truncation provides an increasingly accurate estimate of a bound state's mass.Comment: 6 pages, Contribution to the Proceedings of "QCD Down Under", Special Centre for the Subatomic Structure of Matter, University of Adelaide, 10-19/March/200