WZW Commutants, Lattices, and Level 1 Partition Functions

A natural first step in the classification of all `physical' modular invariant partition functions \sum N_{LR}\,\c_L\,\C_R lies in understanding the commutant of the modular matrices $S$ and $T$. We begin this paper extending the work of Bauer and Itzykson on the commutant from the $SU(N)$ case they consider to the case where the underlying algebra is any semi-simple Lie algebra (and the levels are arbitrary). We then use this analysis to show that the partition functions associated with even self-dual lattices span the commutant. This proves that the lattice method due to Roberts and Terao, and Warner, will succeed in generating all partition functions. We then make some general remarks concerning certain properties of the coefficient matrices $N_{LR}$, and use those to explicitly find all level 1 partition functions corresponding to the algebras $B_n$, $C_n$, $D_n$, and the 5 exceptionals. Previously, only those associated to $A_n$ seemed to be generally known.Comment: 26 page

Multiple primary neoplasms of the ovary and uterus

Multiple primary neoplasms arising in the ovary and uterus were analyzed in 55 patients: 49 synchronous and 6, metachronous. When they occurred synchronously, 74.5% of the ovarian carcinomas and 93.6% of the uterine carcinomas were stage I lesions. The endometrial carcinomas were invariably well differentiated and superficial. It was the stage of the ovarian carcinomas that determined the prognosis of these patients. Ways of their identification as separate neoplasms are discussed. The potential to develop further neoplasms in the gastrointestinal tract and breasts should be borne in mind.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23917/1/0000161.pd

Inference on the Nature and the Mass of Earth's Late Veneer from Noble Metals and Gases

Noble metals and gases are very sensitive to the late accretion to the Earth of asteroids and comets. We present mass balance arguments based on these elements that indicate that 0.7E22-2.7E22 kg of extraterrestrial bodies struck the Earth after core formation and that comets comprised less than 1E-5 by mass of the impacting population. These results imply that the dynamics of asteroids and comets changed drastically with time and that biogenic elements and prebiotic molecules were not delivered to the Earth by comets but rather by carbonaceous asteroids.Comment: 10 pages, 2 figures, 1 table, submitted to JG

Comparing Notes: Recording and Criticism

This chapter charts the ways in which recording has changed the nature of music criticism. It both provides an overview of the history of recording and music criticism, from the advent of Edison’s Phonograph to the present day, and examines the issues arising from this new technology and the consequent transformation of critical thought and practice

Wider Still and Wider: British Music Criticism since the Second World War

This chapter provides the first historical examination of music criticism in Britain since the Second World War. In the process, it also challenges the simplistic prevailing view of this being a period of decline from a golden age in music criticism