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     

CCD Photometry and Long-Term Optical Variability of 3C 345

This paper presents evidence for long-term optical variability and colour behaviour of the blazar 3C 345 (1641+399, z=0.595). Our results show that the amplitude of the optical variations of 3C 345 has been only about 3 magnitudes from its photometric history; existent significant correlation between brightness and colours is found for 3C 345. Our recent CCD photometry of 3C 345 in May 1996 and May 1997 showed that they are in good agreement with our prediction of the optical variability period of about 10 years (see Zhang et al., 1998; Webb et al., 1988). This revised version was published online in July 2006 with corrections to the Cover Date.     

Nonstationary pearl pulsations as a signature of magnetospheric disturbances

We analyse long-lasting (several hours) Pc1 pearl pulsations with decreasing, increasing or constant central frequencies. We show that nonstationary pearl events (those with either decreasing or increasing central frequency) are observed simultaneously with increasing auroral magnetic activity at the nightside magnetosphere while the stationary events (constant central frequency) correspond to quiet magnetic conditions. Events with decreasing central frequency are observed mostly in the late morning and daytime whereas events with increasing central frequency appear either early in the morning or in the afternoon. We explain the diurnal distribution of the nonstationary pearl pulsations in terms of proton drifts depending on magnetic activity, and evaluate the magnetospheric electric field based on the variation of the central frequency of pearl pulsations.     

Additional Analytical Data for Gabbro, GOG-1

Additional data for gabbro, GOG-1, were determined by instrumental-neutron-activation analysis, atomic-absorption spectrometry, and semi-quantitative spectrographic analysis. F ratios calculated in the analysis of variance for 26 sets of data for elements determined by the three methods were not significant, and hence the elements are distributed homogeneously among the bottles. The agreement between our data and the averages previously published ranges from very good to poor. More analytical data are necessary to establish reliable estimates of the concentrations of elements in GOG-1 and in two other gabbros so that three gabbros may be available to geochemists for use as standards.     

Tectonic evolution of the ultrahigh-pressure (UHP) and high-pressure (HP) metamorphic belts from central China

Abstract In the Triassic suture between the Sino-Korean and Yangtze cratons, the Dabie metamorphic Complex in central China includes three tectonic units: the northern Dabie migmatitic terrane, the central ultrahigh-P coesite- and diamond-bearing eclogite belt, and the southern high-P blueschist-eclogite belt. This complex is bounded to the north by a north-dipping normal fault with a Paleozoic accretionary complex and to the south by a north-dipping reverse fault with Yangtze basement plus its foreland fold-and-thrust sequence. Great differences in metamorphic pressure suggests that these units reached different depths during metamorphism and their juxtaposition occurred by wedge extrusion of subducted old continental fragments. These units were subsequently subjected to (i) Barrovian type regional metamorphism and deformation at shallow depths; (ii) intrusion of Cretaceous granitic plutons; and (iii) doming and segmentation into several blocks by normal and strike-slip faults. A new speculative model of tectonic exhumation of UHP rocks is proposed.     

Modeling rhamnolipids production by Pseudomonas aeruginosa from immiscible carbon source in a batch system

A mathematical model to predict the rhamnolipids production by Pseudomonas aeruginosa from oleic acid in a two phase liquid-liquid batch reaction system, was developed in this study. The model was based on two theoretical assumptions: 1) the convective oleic acid mass transfer is coupled to a bioreaction in the aqueous liquid bulk, and 2) the volume of the immiscible oleic acid drops and the saturation concentration at the interface are a function of rhamnolipids production. The model was able to accurately predict the experimental growth of the Pseudomonas aeruginosa strain, and the rhamnolipids production data with oleic acid as carbon source. This mathematical approach indicated a high correspondence between the saturation dimensionless profiles of oleic acid at the interface and the experimental profiles of surface tension difference. This modeling approach may constitute a useful tool in the design and scaling-up of bioreactors applied to the production of biosurfactants with immiscible carbon sources.     

AIRFLOW PATTERNS FROM PHOTOGRAMMETRIC MEASUREMENTS OF WINDBLOWN TIMBER

Aerial photography may be used to quickly locate and measure the extent and severity of forest damage due to windblow. This paper describes such an application in a small area of semi-natural woodland in central Scotland after the “Great Gale” of 14th and 15th January, 1968. A 1 : 2000 scale map, showing the location and direction of fall of each windblown tree, suggests certain relationships between topography and the severity of woodland damage and gives considerable information on the airflow pattern existing over the area during the gale.     

Measurement of stress effects (scope for growth) and contaminant levels in mussels (Mytilus edulis) collected from the Irish Sea

The objective of this research was to quantify the impact of pollution along the coastlines of the Irish Sea. Pollution assessment was based on the combined measurement of scope for growth (SFG), and chemical contaminants in the tissues of mussels (Mytilus edulis) collected from 38 coastal sites around the Irish Sea during June-July in 1996 and 1997. On the UK mainland coast, the SFG showed a general trend with a significant decline in water quality in the Liverpool and Morecambe Bay region. High water quality was recorded along the west coast of Wales, as well as southwest England and northwest Scotland (clean reference sites outside the Irish Sea). Along the coast of Ireland there was a similar trend with reduced SFG within the Irish Sea region. SFG was generally low north of Duncannon and then improved north of Belfast. The poor water quality on both sides of the Irish Sea is consistent with the prevailing hydrodynamics and the spatial distribution of contaminants associated with urban/ industrial development. The decline in SFG of mussels on both sides of the Irish Sea was associated with a general increase in contaminant levels in the mussels. Certain contaminants, including PAHs, TBT, sigmaDDT, Dieldrin, gamma-HCH, PCBs, and a few of the metals (Cd, Se, Ag, Pb), showed elevated concentrations. Many of these contaminants were particularly elevated in the coastal margins of Liverpool Bay, Morecambe Bay and Dublin Bay. A quantitative toxicological interpretation (QTI) of the combined tissue residue chemistry and SFG measurements indicated that at the majority of coastal sites, c. 50 to > 80% of the observed decline in SFG was due to PAHs as a result of fossil fuel combustion and oil spills. TBT levels were highest at major ports and harbours, but these concentrations only made a minor contribution to the overall reduction in SFG. At no sites were individual metals accumulated to concentrations that could cause a significant effect on SFG. The study identified many sites where the observed reduction in SFG was far greater than predicted from the limited number of chemical contaminants analysed, thus indicating the presence of additional 'unknown toxicants'. Sewage (containing domestic, agricultural and industrial components) appears to be an important contributor to reduced SFG and linear alkylbenzenes (LABs) and As may provide suitable 'sewage markers'. There was a highly significant positive correlation between SFG and As (P < 0.001). This relationship may be due to reduced As uptake by algal food material and mussels at sites with elevated P04 concentrations (e.g. at sites with sewage inputs). Phosphate is a known competitive inhibitor of As accumulation, at least in algae. The results highlight that further research is required on 'sewage markers' in mussels. The SFG approach therefore provides a rapid, cost-effective and quantitative measure of pollution impact, as well as a means of identifying the causes through a QTI of tissue contaminants levels. It also serves to identify the presence of unidentified toxicants and areas that require further study.