Triangle based interpolation

Triangle based interpolation is introduced by an outline of two classical planar interpolation methods, viz. linear triangular facets and proximal polygons. These are shown to have opposite local bias. By applying cross products of triangles to obtain local gradients, a method designated slant-top proximal polygon interpolation is introduced that is intermediate between linear facets and polygonal interpolation in its local bias. This surface is not continuous, but, by extending and weighting the gradient planes, a C¹ surface can be obtained. The gradients also allow a roughness index to be calculated for each data point in the set. This index is used to control the shape of a blending function that provides a weighted combination of the gradient planes and linear interpolation. This results in a curvilinear, C¹,interpolation of the data set that is bounded by the linear interpolation and the weighted gradient planes and is tangent to the slant-top interpolation at the data points. These procedures may be applied to data with two, three, or four independent variables.     

Compositional evidence regarding the influx of interplanetary materials onto the lunar surface

Siderophilic element/Ir ratios are higher in mature lunar soils from highlands sites than in those from mare sites. We infer that the population of materials responsible for the early intense bombardment of the Moon had high ratios, and that the population responsible for the essentially constant flux has low ratios. No group of chondrites has siderophile/Ir ratios identical to those in the mare or highlands soils; CM chondrites are the most similar, and CM-like materials may account for a major fraction of Earth-crossing materials during the past 3.7 b.y.Siderophile/Ir ratios may be used to determine the amount of highlands regolith in soils or breccias from the mare-highlands interface areas (Apollo 15 and 17), and to infer the time of formation of highlands breccias whose sideropbiles originated in mature soils. Arguments are summarized against the viewpoint that the siderophiles in most highlands breccias originated in basin-forming projectiles. Differences in mature soil siderophile concentrations at Apollo 14 and 16 indicate a substantially greater concentration at the latter site immediately following the Imbrium event.Siderophile concentrations are used to estimate mean regolith depths at the landing sites; as relative values these are more precise than estimates based on seismic or crater observations. The longlived flux is calculated to be 2.9 g cm^–2 b.y.^–1 averaged over the past 3.7 b.y. A consideration of the relationship between mass fluence and time indicates that the mass flux decreased with a half-life of about 40 m.y. immediately following the Imbrium event.     

Fisheries aid: low in development league

Fisheries have tended to be a relatively neglected aspect of aid to developing countries. In the article below, Philip Appleyard gives some reasons for this and indicates ways in which future fisheries aid could be usefully employed.     

The surfaces of Larissa and Proteus

Topographic models of Neptune's small inner satellites Larissa and Proteus were derived from the shapes of limbs and terminators in Voyager images, modified locally to accomodate large craters and ridges. The models are presented here in tabular and graphic form, including the first map of Larissa and the first detailed relief map of Proteus. The shape of Larissa is approximated by a triaxial ellipsoid with axes of 208, 192 and 178 km, but is only weakly constrained by the single available view. The volume is estimated to be 3.5 ± 1.0 × 10⁶ km³. The surface is heavily cratered and may be crossed by one or two poorly seen linear ridges. Proteus is approximated by a triaxial ellipsoid with axes of 424, 390 and 396 km (the latter being the rotation axis dimension). The volume is estimated to be 3.4 ± 0.4 × 10⁷ km³. Its surface appears to be very heavily cratered and extensive evidence for linear fractures is observed despite very low image quality.     

Migrants,manufacturing and metropolitan labour markets in Australia

While the experience of migrants in the Australian labour market has received considerable attention, few researchers have asked how uniform this experience has been across the country's major metropolitan labour markets. This paper shows that migrants employed in the manufacturing sector exhibit noticeable differences in their relative access to jobs in different parts of the country. This evidence raises a number of questions about the appropriate scale within which to consider the labour participation and occupational selection experience of migrant men and women.     

<Superscript>40</Superscript>Ar/<Superscript>39</Superscript>Ar dating of the eruptive history of Mount Erebus,Antarctica: summit flows,tephra, and caldera collapse

Eruptive activity has occurred in the summit region of Mount Erebus over the last 95 ky, and has included numerous lava flows and small explosive eruptions, at least one plinian eruption, and at least one and probably two caldera-forming events. Furnace and laser step-heating ⁴⁰Ar/³⁹Ar ages have been determined for 16 summit lava flows and three englacial tephra layers erupted from Mount Erebus. The summit region is composed of at least one or possibly two superimposed calderas that have been filled by post-caldera lava flows ranging in age from 17 ± 8 to 1 ± 5 ka. Dated pre-caldera summit flows display two age populations at 95 ± 9 to 76 ± 4 ka and 27 ± 3 to 21 ± 4 ka of samples with tephriphonolite and phonolite compositions, respectively. A caldera-collapse event occurred between 25 and 11 ka. An older caldera-collapse event is likely to have occurred between 80 and 24 ka. Two englacial tephra layers from the flanks of Mount Erebus have been dated at 71 ± 5 and 15 ± 4 ka. These layers stratigraphically bracket 14 undated tephra layers, and predate 19 undated tephra layers, indicating that small-scale explosive activity has occurred throughout the late Pleistocene and Holocene eruptive history of Mount Erebus. A distal, englacial plinian-fall tephra sample has an age of 39 ± 6 ka and may have been associated with the older of the two caldera-collapse events. A shift in magma composition from tephriphonolite to phonolite occurred at around 36 ka.Editorial responsibility: Julie Donnelly-Nolan