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.     

Degradation of plastic carrier bags in the marine environment

There is considerable concern about the hazards that plastic debris presents to wildlife. Use of polymers that degrade more quickly than conventional plastics presents a possible solution to this problem. Here we investigate breakdown of two oxo-biodegradable plastics, compostable plastic and standard polyethylene in the marine environment. Tensile strength of all materials decreased during exposure, but at different rates. Compostable plastic disappeared from our test rig between 16 and 24 weeks whereas approximately 98% of the other plastics remained after 40 weeks. Some plastics require UV light to degrade. Transmittance of UV through oxo-biodegradable and standard polyethylene decreased as a consequence of fouling such that these materials received ～ 90% less UV light after 40 weeks. Our data indicate that compostable plastics may degrade relatively quickly compared to oxo-biodegradable and conventional plastics. While degradable polymers offer waste management solutions, there are limitations to their effectiveness in reducing hazards associated with plastic debris.     

Using amphibole phenocrysts to track vapor transfer during magma crystallization and transport: An example from Mount St. Helens,Washington

In order to evaluate and further constrain models for volatile movement and vapor enrichment of magma stored at shallow levels, amphibole phenocrysts from 2004–2005 Mount St. Helens dacite were analyzed for major and selected trace elements (Li, Cu, Zn, Mn, and REE) and Li isotopes. Several recent studies have examined fluid-mobile trace element abundances in phencryst phases and melt inclusions as a means of tracking volatile movement within subvolcanic magmatic systems, and high Li contents in plagioclase phenocrysts from 1980 and 2004 Mount St. Helens dacites have been interpreted as evidence that shallow magma was fluxed by a Li-bearing vapor phase prior to eruption.     

Singularity and Nonnormality in the Classification of Compositional Data

Geologists may want to classify compositional data and express the classification as a map. Regionalized classification is a tool that can be used for this purpose, but it incorporates discriminant analysis, which requires the computation and inversion of a covariance matrix. Covariance matrices of compositional data always will be singular (noninvertible) because of the unit-sum constraint. Fortunately, discriminant analyses can be calculated using a pseudo-inverse of the singular covariance matrix; this is done automatically by some statistical packages such as SAS. Granulometric data from the Darss Sill region of the Baltic Sea is used to explore how the pseudo-inversion procedure influences discriminant analysis results, comparing the algorithm used by SAS to the more conventional Moore–Penrose algorithm. Logratio transforms have been recommended to overcome problems associated with analysis of compositional data, including singularity. A regionalized classification of the Darss Sill data after logratio transformation is different only slightly from one based on raw granulometric data, suggesting that closure problems do not influence severely regionalized classification of compositional data.