Basalt depths in lunar basins using impact craters as stratigraphic probes: Evaluation of a method using orbital geochemical data

A rare look at the chemical composition of subsurface stratigraphy in lunar basins filled with mare basalt is possible at fresh impact craters. Mg/Al maps from orbital X-ray flourescence measurements of mare areas indicate chemical anomalies associated with materials ejected by large post-mare impacts. A method of constraining the wide-ranging estimates of mare basalt depths using the orbital MG/Al data is evaluated and the results are compared to those of investigators using different indirect methods. Chemical anomalies at impact craters within the maria indicate five locations where higher Mg/Al basalt compositions may have been excavated from beneath the surface layer. At eight other locations, low Mg/Al anomalies suggest that basin-floor material was ejected. In these two cases, the stratigraphic layers are interpreted to occur at depths less than the calculated maximum depth of excavation. In five other cases, there is no apparent chemical change between the crater and the surrounding mare surface. This suggests homogeneous basalt compositions that extend down to the depths sampled, i.e., no anorthositic material that might represent the basin floor was exposed

Evaluation of an application for dynamic feeding of dairy cows

Dynamic feeding is an innovative application for concentrate feeding of dairy cows. Daily individual settings are derived from the actual individual milk yield response to concentrate intake. This response is estimated using an adaptive dynamic linear model. Optimal daily individual settings for concentrate supply are directed to achieve the maximum gross margin milk returns minus concentrate costs. This response curve plays a key role in the application. The response curve is derived from a mechanistic model for milk production and can also be established empirically from daily milk yield development during early lactation when concentrate supply increase is linear. A test application for dynamic feeding ran for several months in 2008 and results from 145 cows at one farm on 17 December 2008 have been used to demonstrate the variation in individual response. The gross margin, milk returns minus concentrate costs, varied from 2.52 to 26.32 €/day. The estimated response parameters provide insight in variation between individuals concerning the effects of concentrate and base ration intake on daily milk yield. Economical and nutritional aspects can be evaluated for each individual. Individual dynamic feeding towards an economic optimum indicates that excessive changes in individual bodyweighti can be prevented

Orange Peels and Fresnel Integrals

There are two standard ways of peeling an orange: either cut the skin along meridians, or cut it along a spiral. We consider here the second method, and study the shape of the spiral strip, when unfolded on a table. We derive a formula that describes the corresponding flattened-out spiral. Cutting the peel with progressively thinner strip widths, we obtain a sequence of increasingly long spirals. We show that, after rescaling, these spirals tends to a definite shape, known as the Euler spiral. The Euler spiral has applications in many fields of science. In optics, the illumination intensity at a point behind a slit is computed from the distance between two points on the Euler spiral. The Euler spiral also provides optimal curvature for train tracks between a straight run and an upcoming bend. It is striking that it can be also obtained with an orange and a kitchen knife

Discussion of "Breakdown and groups" by P. L. Davies and U. Gather

Discussion of ``Breakdown and groups'' by P. L. Davies and U. Gather [math.ST/0508497]Comment: Published at http://dx.doi.org/10.1214/009053604000001138 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Phase behavior of three-component ionic fluids

We study the phase behavior of solutions consisting of positive and negative ions of valence z to which a third ionic species of valence Z>z is added. Using a discretized Debye-Hueckel theory, we analyze the phase behavior of such systems for different values of the ratio Z/z. We find, for Z/z>1.934, a three-phase coexistence region and, for Z/z>2, a closed (reentrant) coexistence loop at high temperatures. We characterize the behavior of these ternary ionic mixtures as function of charge asymmetry and temperature, and show the complete phase diagrams for the experimentally relevant cases of Z/z=2 and Z/z=3, corresponding to addition of divalent and trivalent ions to monovalent ionic fluids, respectively.Comment: 6 pages, 4 figures; to appear in the European Physical Journal