Hopf algebras of dimension pq, II

Let H be a Hopf algebra of dimension pq over an algebraically closed field of characteristic zero, where p, q are odd primes with p < q < 4p+12. We prove that H is semisimple and thus isomorphic to a group algebra, or the dual of a group algebra.Comment: 14pp, Late

About quantum fluctuations and holographic principle in (4+n)-dimensional spacetime

In the article we present explicit expressions for quantum fluctuations of spacetime in the case of $(4+n)$-dimensional spacetimes, and consider their holographic properties and some implications for clocks, black holes and computation. We also consider quantum fluctuations and their holographic properties in ADD model and estimate the typical size and mass of the clock to be used in precise measurements of spacetime fluctuations. Numerical estimations of phase incoherence of light from extra-galactic sources in ADD model are also presented.Comment: 5 page

Academic reflections between Polynesian tattooing and reflective practice

In Polynesian culture stories which may be generations old are told via tattoo art: the Tahitian word ‘tatu’ or ‘ta-tu’ means to strike something and links directly to the ancient art of tattooing to preserve an ancestral lineage and/or record a particular event or story that has been handed down from generation to generation via the same method (Villequette, 1998). Some scholars such as Gell (1993), and Schrader (2000) and Jones (2000) in Schildkrout (2004), write of tattoos being associated with “subsidiary selves, spirits, ancestors, rulers and victims” that are resident within the tattooed individual, while some write of ethnographic work being inscribed on bodies (Sparkes, 2000, p. 21 and Schildkrout, 2004, p. 322). Auto-ethnographic study (the study of ourselves) is a relatively new field and is often associated with qualitative analysis; as such it has stimulated the author to introduce the term ‘internal’ reflection. I believe that this may describe a ‘personal’ or ‘internal’ reflection that is transmitted to the outside world in the form of a tattoo. Drawing on the work of Sparkes, an auto-ethnography is a narrative of self, although this research offers tattoos as a viable alternative to narrative and suggests that auto-ethnographic tattoos are not only commonplace but that they can also be very real transcripts of the narrative equivalent. Further, this research shows that different cultures reflect in different ways and that the tattoo is a popular and essential method of ethnographic captur