Closed-form solution of P4P or the three-dimensional resection problem in terms of Möbius barycentric coordinates

 The perspective 4 point (P4P) problem - also called the three-dimensional resection problem - is solved by means of a new algorithm: At first the unknown Cartesian coordinates of the perspective center are computed by means of M?bius barycentric coordinates. Secondly these coordinates are represented in terms of observables, namely space angles in the five-dimensional simplex generated by the unknown point and the four known points. Substitution of M?bius barycentric coordinates leads to the unknown Cartesian coordinates (2.8)–(2.10) of Box 2.2. The unknown distances within the five-dimensional simplex are determined by solving the Grunert equations, namely by forward reduction to one algebraic equation (3.8) of order four and backward linear substitution. Tables 1.–4. contain a numerical example. Finally we give a reference to the solution of the 3 point (P3P) problem, the two-dimensional resection problem, namely to the Ansermet barycentric coordinates initiated by C.F. Gau? (1842), A. Schreiber (1908) and A.␣Ansermet (1910). Received: 05 March 1996; Accepted: 15 October 1996     

Die Radialgeschwindigkeit des Am Sternes 68 Tau

The radial velocity of the star 68 Tau is searched in dependence on the light variation period. No variations have been proved. The mean radial velocity of 22 spectra is 40.4 km/sec ± 0.7 km/sec.     

Resolving mechanisms of toxicity while pursuing ecotoxicological relevance?

In this age of modern biology, aquatic toxicological research has pursued mechanisms of action of toxicants. This has provided potential tools for ecotoxicologic investigations. However, problems of biocomplexity and issues at higher levels of biological organization remain a challenge. In the 1980s and 1990s and continuing to a lesser extent today, organisms residing in highly contaminated field sites or exposed in the laboratory to calibrated concentrations of individual compounds were carefully analyzed for their responses to priority pollutants. Correlation of biochemical and structural analyses in cultured cells and tissues, as well as the in vivo exposures led to the production and application of biomarkers of exposure and effect and to our awareness of genotoxicity and its chronic manifestations, such as neoplasms, in wild fishes. To gain acceptance of these findings in the greater environmental toxicology community, “validation of the model” versus other, better-established often rodent models, was necessary and became a major focus. Resultant biomarkers were applied to heavily contaminated and reference field sites as part of effects assessment and with investigations following large-scale disasters such as oil spills or industrial accidents.

Over the past 15 years, in the laboratory, small aquarium fish models such as medaka (Oryzias latipes), zebrafish (Danio rerio), platyfish (Xiphophorus species), fathead minnow (Pimephales promelas), and sheepshead minnow (Cyprinodon variegatus) were increasingly used establishing mechanisms of toxicants. Today, the same organisms provide reliable information at higher levels of biological organization relevant to ecotoxicology. We review studies resolving mechanisms of toxicity and discuss ways to address biocomplexity, mixtures of contaminants, and the need to relate individual level responses to populations and communities.     

∼3,850 Ma tonalites in the Nuuk region,Greenland: geochemistry and their reworking within an Eoarchaean gneiss complex

The Eoarchaean (>3,600 Ma) Itsaq Gneiss Complex of southern West Greenland is dominated by polyphase orthogneisses with a complex Archaean tectonothermal history. Some of the orthogneisses have c. 3,850 Ma zircons, and they vary from rare single phase metatonalites to more common complexly banded migmatites. This is due to heterogeneous strain, in situ anatexis and granitic veining superimposed during younger tectonothermal events. In the single-phase tonalites with c. 3,850 Ma zircon, oscillatory-zoned prismatic zircon is all 3,850 Ma old, but shows patchy ancient loss of radiogenic Pb. SHRIMP spot analyses and laser ablation ICP-MS depth profiling show that thin (usually < 10 μm) younger (3,660–3,590 Ma and Neoarchaean) shells of lower Th/U metamorphic zircon are present on these 3,850 Ma zircons. Several samples with this simple zircon population occur on islands near Akilia. In contrast, migmatites usually contain more complex zircon populations, with often more than one generation of igneous zircon present. Additional zircon dating of banded gneisses across the Complex shows that samples with c. 3,850 Ma igneous zircon are not just a phenomenon restricted to Akilia and adjacent islands. For example, migmatites from Itilleq (c. 65 km from Akilia) contain variable amounts of oscillatory-zoned 3,850 Ma and 3,650 Ma zircon, interpreted, respectively, as the rock age and the time of crustal melting under Eoarchaean metamorphism. With only 110–140 ppm Zr in the tonalites and likely magmatic temperatures of >850°C, zircon solubility–melt composition relationships show that they were only one-third saturated in zircon. Any zircon entrained in the precursor magmas would thus have been highly soluble. Combined with the cathodoluminesence imaging, this demonstrates that the c. 3,850 Ma oscillatory zoned zircon crystallised out of the melt and hence gives a magmatic age. Thus the rare well-preserved tonalites and palaeosome in migmatites testify that c. 3,850 Ma quartzo–feldspathic rocks are a widespread (but probably minor) component in the Itsaq Gneiss Complex. C. 3,850 Ma zircon with negative Eu anomalies (showing growth in felsic systems) also occurs as detrital grains in rare c. 3,800 Ma metaquartzites and as inherited grains in some 3,660 Ma granites (sensu stricto). These demonstrate that still more c. 3,850 Ma rocks were present, but were recycled into Eoarchaean sediments and crustally derived granites. The major and trace element characteristics (e.g. LREE enrichment, HREE depletion, low MgO) of the best-preserved c. 3,850 Ma rocks are typical of Archaean TTG suites, and thus argue for crust formation processes involving important contributions from melting of hydrated mafic crust to the earliest Archaean. Five c. 3,850 Ma tonalites were selected as the best preserved on the basis of field criteria and zircon petrology. Four of these samples have overlapping initial ɛ_Nd (3,850 Ma) values from +2.9 to +3.6± 0.5, with the fourth having a slightly lower value of +0.6. These data provide additional evidence for a markedly LREE-depleted early terrestrial mantle reservoir. The role of c. 3,850 Ma crust should be considered in interpreting isotope signatures of the younger (3,800–3,600 Ma) rocks of the Itsaq Gneiss Complex. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A rational interpretation of the role of particle size in flotation

From the examination of data from detailed plant surveys and associated laboratory batch testing, the principal effects of particle size in flotation have been identified. The current state of knowledge concerning the role of this variable is discussed in terms of the evidence presented. It is concluded that the minimum degree of hydrophobicity necessary for the flotation of a particle depends upon its size and as a result, recovery-size curves are a valuable diagnostic aid to the assessment of flotation performance. Entrainment is shown to be an important contributory mechanism to the recovery of fine particles which, when coupled with a low rate of genuine flotation, can account for much of the observed behaviour of such fines. The significance of particle size and its consequences in flotation research, in plant operations and in control schemes has been under-rated. The separate conditioning or flotation or both of separate size fractions seems inevitable as ores become increasingly difficult to concentrate.     

Mars: Experimental study of albedo changes caused by dust fallout

An experimental study was undertaken to determine how the spectral and photometric properties of representative Martian areas are affected by fallout of atmospheric dust suspended during dust forms. A laboratory apparatus was used to simulate the uniform fallout and deposition of particles 1 to 5 μm in diameter. Spectral measurements from 0.4- to 1.2-μm wavelengths and photometric measurements at several wavelengths were made for a number of Mars-analog materials before and after deposition of 6 × 10^?5 to 1.5 × 10^?3 g/cm² of simulated fallout. These results indicate that the spectral and photometric properties of Martian regions can be affected significantly even by minute amounts of fallout. For instance, the reflectance at 0.56 μm of an average dark area will increase by 35% after deposition of only 9 × 10^?5 g/cm², and by 70% after deposition of 1.5 × 10^?4 g/cm². Thus the fallout from even one dust storm season (～2 × 10^?3 g/cm²) is sufficient to change significantly the spectral and photometric characteristics of the substrate material, if the fallout were ubiquitous over the surface and if no competing processes of dust removal from surface grains occured.