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     

Are crystalline C-(H-O-N) carbons the elusive meteoritic carbynes?

Abstract I present an internally consistent reinterpretation of carbyne diffraction data making a few plausible assumptions. The results support that carbynes could be crystalline, randomly interstratified (or mixed-layered) carbons with variable C/(C+H+O+N) ratios rather than thermodynamically stable carbon allotropes. The metastable carbynes are likely the result of incomplete, kinetically-inhibited, low-temperature pyrolysis of precursor material. A renewed interest in meteoritic carbynes should seek to combine light-element chemistry and crystallography of these elusive carbons.     

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.     

Detection and extraction of signals from the epoch of reionization using higher-order one-point statistics

Detecting redshifted 21-cm emission from neutral hydrogen in the early Universe promises to give direct constraints on the epoch of reionization (EoR). It will, though, be very challenging to extract the cosmological signal (CS) from foregrounds and noise which are orders of magnitude larger. Fortunately, the signal has some characteristics which differentiate it from the foregrounds and noise, and we suggest that using the correct statistics may tease out signatures of reionization. We generate mock data cubes simulating the output of the Low Frequency Array (LOFAR) EoR experiment. These cubes combine realistic models for Galactic and extragalactic foregrounds and the noise with three different simulations of the CS. We fit out the foregrounds, which are smooth in the frequency direction, to produce residual images in each frequency band. We denoise these images and study the skewness of the one-point distribution in the images as a function of frequency. We find that, under sufficiently optimistic assumptions, we can recover the main features of the redshift evolution of the skewness in the 21-cm signal. We argue that some of these features – such as a dip at the onset of reionization, followed by a rise towards its later stages – may be generic, and give us a promising route to a statistical detection of reionization.     

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.     

Possible meteoroid streams associated with (69230) Hermes and 2002 SY50

The orbits of (69230) Hermes and 2002 SY₅₀ are similar and the Earth approaches both of them twice: at the end of October the local orbital minimum distances are smaller than 0.007 AU, and at the end of April the distances are smaller than 0.04 AU. This gives us opportunities to observe the meteors associated with these asteroids. Using the geocentric parameters of the orbital close encounters (the theoretical radiants) and our D _N distance function (Valsecchi et al. Mon. Not. R. Astron. Soc. 304 (1999) 743), we searched for meteoroids originated by Hermes and 2002 SY₅₀. A search among 1830 good quality photographic meteors gave negative results: we found no meteor dynamically similar to Hermes or 2002 SY₅₀. In a second search, done in a set of 62150 radio meteors, we applied two methods (M1, M2) and in both cases we found two streams; the streams found with the M1 method had 43 and 30 members, those found with the M2 method had 39 and 14 members. However, these results do not look convincing, due to the small number of common members in the corresponding streams. We therefore conclude that amongst the IAU meteors used in our search there are no compact streams associated with Hermes and 2002 SY₅₀.     

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.     

Time-dependent convection at high latitudes

A fully time-dependent ionospheric convection model, in which electric potentials are derived by an analytic solution of Laplaces equation, is described. This model has been developed to replace the empirically derived average convection patterns currently used routinely in the Sheffield/SEL/UCL coupled thermosphere/ionosphere/plasmasphere model (CTIP) for modelling disturbed periods. Illustrative studies of such periods indicate that, for the electric field pulsation periods imposed, long-term averages of parameters such as Joule heating and plasma density have significantly different values in a time-dependent model compared to those derived under the same mean conditions in a steady-state model. These differences are indicative of the highly non-linear nature of the processes involved.