Letters from William Burnside to Robert Fricke: Automorphic Functions, and the Emergence of the Burnside Problem

Two letters from William Burnside have recently been found in the Nachlass of Robert Fricke that contain instances of Burnside's Problem prior to its first publication. We present these letters as a whole to the public for the first time. We draw a picture of these two mathematicians and describe their activities leading to their correspondence. We thus gain an insight into their respective motivations, reactions, and attitudes, which may sharpen the current understanding of professional and social interactions of the mathematical community at the turn of the 20th century.Comment: documentclass amsart, 17 page

Cavity QED analog of the harmonic-oscillator probability distribution function and quantum collapses

We establish a connection between the simple harmonic oscillator and a two-level atom interacting with resonant, quantized cavity and strong driving fields, which suggests an experiment to measure the harmonic-oscillator's probability distribution function. To achieve this, we calculate the Autler-Townes spectrum by coupling the system to a third level. We find that there are two different regions of the atomic dynamics depending on the ratio of the: Rabi frequency Omega (c) of the cavity field to that of the Rabi frequency Omega of the driving field. For Omega (c

A New Omomyid Primate from the Earliest Eocene of Southern England: First Phase of Microchoerine Evolution

Hooker, J.J. 2012. A new omomyid primate from the earliest Eocene of southern England: First phase of microchoerin

Diversity and palaeoecology of Australia's southern‐most sauropods, Griman Creek Formation (Cenomanian), New South Wales, Australia

Predominately, occurances of Australian sauropods from the Early to mid-Cretaceous of Queensland and Western Australia, lie between ~45° and 55°S palaeolatitude. The Cenomanian Griman Creek Formation, which straddles the New South Wales-Queensland border, preserves arguably one of the richest Cretaceous terrestrial faunas in Australia. Although sauropod postcranial elements are notably absent or as yet unidentified, isolated sauropod teeth are relatively well represented from exposures near Lightning Ridge (New South Wales), offering insights into the diversity and palaeoecology of these animals at ~60°S palaeolatitude. From a sample of 25 teeth, we identify five dental morphotypes from the Griman Creek Formation. Some of this variation is attributed to heterodonty; however, other distinctive morphologies partly agree with previous indications of at least two taxa of non-titanosaur titanosauriforms together with a third, possible titanosaur in the Griman Creek Formation. An investigation of dental microwear found two teeth with identifiable wear features, but differences in these features suggest separate feeding strategies consistent with the hypothesis of ecological tiering between sympatric species. The presence of at least two non-titanosaur titanosauriforms and a third species of titanosaur in the Griman Creek Formation is reminiscent of the roughly coeval Winton Formation in central Queensland, which preserves three titanosauriform species, and implies that diverse sauropod communities persisted during this interval into their most southern recorded range in Australia