A General size-biased distribution

We generalize a size-biased distribution related to the Riemann xi function using the work of Ferrar. Some analysis and properties of this more general distribution are offered as well

Gendered Language and the Science of Colonial Silk

This article uses pronominal resilience to suggest how we can identify women's contributions to the colonial silk industry. By comparing different editions of silkworm treatises, all of which were published between 1650-1655 and circulated within the Hartlib Circle's circum-Atlantic network of readers (Bermuda, Germany, England, Ireland, Virginia), I find a pattern in the gendered language of the texts. Books that describe worms grown by women use feminine pronouns (she/her) to classify worms throughout the lifecycle, while books that describe worms grown by men begin with masculine pronouns (he/his) and become feminine (she/her) when the worms become reproductive in the third stage of the lifecycle

Milichiella lacteipennis (Loew, 1866) is associated with beeswax (Diptera, Milichiidae)

The Milichiidae (Diptera, Schizophora) is a family of acalypterate Diptera of worldwide distribution. Some 240 species are recognised (Brake, 2000). The most comprehensive account on the biology and breeding habits of the family may be found in Ferrar (1987) from which most of the following information is taken.peer-reviewe

A new proof of the Vorono\"i summation formula

We present a short alternative proof of the Vorono\"i summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics as a trace formula for a Schr\"odinger operator on a non-compact quantum graph \mathfrak{G} [S. Egger n\'e Endres and F. Steiner, J. Phys. A: Math. Theor. 44 (2011) 185202 (44pp)]. As a byproduct we give a new proof of a non-trivial identity for a particular Lambert series which involves the divisor function d(n) and is identical with the trace of the Euclidean wave group of the Laplacian on the infinite graph \mathfrak{G}.Comment: Enlarged version of the published article J. Phys. A: Math. Theor. 44 (2011) 225302 (11pp

Application LANDSAT imagery to geologic mapping in the ice-free valleys of Antarctica

The author has identified the following significant results. Studies in the Ice-Free Valleys are resulted in the compilation of a sizeable library of maps and publications. Rock reflectance measurements were taken during the Antarctic summer of 1973. Spectral reflectance of rocks (mostly mafic lava flows) in the McMurdo and Ice-Free Valleys areas were measured using a filter wheel photometer equipped to measure reflectances in the four Landsat bands. A series of samples were collected at regular intervals across a large differentiated, mafic sill near Lake Vida. Chemical analyses of the sample suggest that the tonal variations in this sill are controlled by changes in the iron content of the rock. False color images were prepared for a number of areas by the diazo method and with an optical multispectral biviewer. These images were useful in defining boundaries of sea ice, snow cover, and in the study of ablating glaciers, but were not very useful for rock discrimination

Natural age dispersion arising from the analysis of broken crystals, part I. Theoretical basis and implications for the apatite (U-Th)/He thermochronometer

Over the last decade major progress has been made in developing both the theoretical and practical aspects of apatite (U-Th)/He thermochronometry and it is now standard practice, and generally seen as best practice, to analyse single grain aliquots. These individual prismatic crystals are often broken and are fragments of larger crystals that have broken during mineral separation along the weak basal cleavage in apatite. This is clearly indicated by the common occurrence of only 1 or no clear crystal terminations present on separated apatite grains, and evidence of freshly broken ends when grains are viewed using a scanning electron microscope. This matters because if the 4He distribution within the whole grain is not homogeneous, because of partial loss due to thermal diffusion for example, then the fragments will all yield ages different from each other and from the whole grain age. Here we use a numerical model with a finite cylinder geometry to approximate 4He ingrowth and thermal diffusion within hexagonal prismatic apatite crystals. This is used to quantify the amount and patterns of inherent, natural age dispersion that arises from analysing broken crystals. A series of systematic numerical experiments were conducted to explore and quantify the pattern and behaviour of this source of dispersion using a set of 5 simple thermal histories that represent a range of plausible geological scenarios. In addition some more complex numerical experiments were run to investigate the pattern and behaviour of grain dispersion seen in several real data sets. The results indicate that natural dispersion of a set of single fragment ages (defined as the range divided by the mean) arising from fragmentation alone varies from c. 7% even for rapid (c. 10 ∘C/Ma), monotonic cooling to over 50% for protracted, complex histories that cause significant diffusional loss of 4He. The magnitude of dispersion arising from fragmentation scales with the grain cylindrical radius, and is of a similar magnitude to dispersion expected from differences in absolute grain size alone (spherical equivalent radii of 40 to 150 μm). This source of dispersion is significant compared with typical analytical uncertainties on individual grain analyses (c. 6%) and standard deviations on multiple grain analyses from a single sample (c. 10-20%). Where there is a significant difference in the U and Th concentration of individual grains (eU), the effect of radiation damage accumulation on 4He diffusivity (assessed using the RDAAM model of Flowers et al. (2009)) is the primary cause of dispersion for samples that have experienced a protracted thermal history, and can cause dispersion in excess of 100% for realistic ranges of eU conentration (i.e. 5-100 ppm). Expected natural dispersion arising from the combined effects of reasonable variations in grain size (radii 40-125 μm), eU concentration (5-150 ppm) and fragmentation would typically exceed 100% for complex thermal histories. In addition to adding a significant component of natural dispersion to analyses, the effect of fragmentation also acts to decouple and corrupt expected correlations between grain ages and absolute grain size and to a lesser extent between grain age and effective uranium concentration (eU). Considering fragmentation explicitly as a source of dispersion and analysing how the different sources of natural dispersion all interact with each other provides a quantitative framework for understanding patterns of dispersion that otherwise appear chaotic. An important outcome of these numerical experiments is that they demonstrate that the pattern of age dispersion arising from fragmentation mimics the pattern of 4He distribution within the whole grains, thus providing an important source of information about the thermal history of the sample. We suggest that if the primary focus of a study is to extract the thermal history information from (U-Th)/He analyses then sampling and analytical strategies should aim to maximise the natural dispersion of grain ages, not minimise it, and should aim to analyse circa 20-30 grains from each sample. The key observations and conclusions drawn here are directly applicable to other thermochronometers, such as the apatite, rutile and titanite U-Pb systems, where the diffusion domain is approximated by the physical grain size