Tangent power sums and their applications

For integer $m, p,$ we study tangent power sum $\sum^m_{k=1}\tan^{2p}\frac{\pi k}{2m+1}.$ We prove that, for every $m, p,$ it is integer, and, for a fixed p, it is a polynomial in $m$ of degree $2p.$ We give recurrent, asymptotical and explicit formulas for these polynomials and indicate their connections with Newman's digit sums in base $2m.$Comment: 14 pages. Addition of reference: A.M. and I.M. Yaglom (1953

Analytical technique for determining the polarization dependence of optical matrix elements in quantum wires with band-coupling effects

We present an analytical technique for determining polarization-dependent optical transition matrix elements in quantum wires which rigorously incorporates the effects of band coupling. Using this technique, we examine the polarization anisotropy of the two lowest energy optical transitions in a GaAs quantum wire. Contrary to assumptions employed in previous studies, we show that the valence states involved in these transitions are a strong admixture of light and heavy hole character. The lowest energy transition is found to be four times stronger for electric fields oriented parallel to the wire than for the perpendicular orientation. In contrast, the next highest transition does not interact with optical waves polarized along the wire axis. We discuss sources of error which arise in simpler one-band models of this phenomenon in addition to the neglect of band coupling and show that the coupled band model presented here is essential for predicting these effects

The George C. Davis Site, Cherokee County, Texas: Spring 1980 Archeological Investigations

The results of archeological investigations in portions of the George C. Davis Site are presented in this report prepared by Ross Fields and J. Peter Thurmond . Stringent contract requirements and the provisions of Texas Antiquities Permit No. 237 dictate that this report be brief and descriptive in nature. Requirements such as inclusion of a detailed site investigation history and environmental data were excluded and extensive excavations were stressed in preference to detailed analyses and comparisons. Field investigations were limited by contract to 20 working days and the analysis/write-up to 10 working days. The governing research design was prepared by the Texas Antiquities Committee staff to reflect agreements between the Committee and the Texas Forest Service. Sighificant findings include the general delineation of extensive, and in places intensive, Archaic and Late Prehistoric occupations. Of primary importance is the lack of an identifiable Alto Focus occupation within the northern portion of the Davis Site. This suggests that the small left bank tributary to Bowles Creek existed during Alto Focus times and served as a natural boundary for the village area during that period of site usage. There are hints that significant variations in the selection and use of lithic resources through time are identifiable. It is indeed ! unfortunate that time limitations precluded pursuit of this line of investigation. Ross and Pete have successfully accomplished a most challenging task under less than ideal conditions. They and their field crew are commended for their outstanding work at the Davis Site

Was human evolution driven by Pleistocene climate change?

Modern humans are probably a product of social and anatomical preadaptations on the part of our Miocene australopithecine ancestors combined with the increasingly high amplitude, high frequency climate variation of the Pleistocene. The genus Homo first appeared in the early Pleistocene as ice age climates began to grip the earth. We hypothesize that this co-occurrence is causal. The human ability to adapt by cultural means is, in theory, an adaptation to highly variable environments because cultural evolution can better track rapidly changing environments than can genes. High resolution ice and sediment cores published in the early 1990s showed the last ice age was characterized by high amplitude millennial and submillenial scale variation, exactly the sort of variation mathematical models suggest should favor a costly capacity for culture. More recent cores suggest that over the last several 100 thousand year glacial cycles the amount of millennial scale variation has increased rather dramatically in parallel with increases in hominin brain size and sophistication of the artifacts they made

Response of Saddled Prominent (Lepidoptera: Notodontidae) Pupae to Desiccation, Cold Treatment, and Post-Cold Treatment Incubation Temperature

Saddled prominent, Heterocampa guttivitta, pupae were placed at 1.5oC for 50 to 200 days, then incubated at one of four post-cold temperatures ranging from 10° to 26.7°C. Adults emerged from pupae exposed to all cold treatment periods. A few adults also emerged from pupae that were not exposed to cold. The time required for adult emergence following cold treatment declined with longer periods of cold treatment and higher post-cold incubation temperature. The interaction between these two main effects was also significant. Adult morphogenesis begins immediately after pupation, and continues until interrupted by cold temperature. When pupae were subjected to desiccating conditions prior to cold treatment, weight loss due to desiccation was accompanied by increased mortality. Desiccation occurred faster at IS.6° than at 18.0°C. Our results identify a physical factor which might contribute to pupal overwintering mortality: prolonged excessive drought conditions between time of pupation and the onset of cold

System identification, time series analysis and forecasting:The Captain Toolbox handbook.

CAPTAIN is a MATLAB compatible toolbox for non stationary time series analysis, system identification, signal processing and forecasting, using unobserved components models, time variable parameter models, state dependent parameter models and multiple input transfer function models. CAPTAIN also includes functions for true digital control