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     

Solving the problem of shock wave attenuation in an obstacle during a contact explosion of a high-energy material charge

A problem of estimation of shock wave attenuation in an obstacle under an explosion of a high-energy material (explosive) charge on its surface is considered. An algorithm for its solution is proposed using the analytical and semiempirical dependences generally recognized in explosion physics.     

Stochastic variability in the atmospheric activity of Jupiter

The atmospheric activity of Jupiter exhibits quasi-periodic character attributed to the stochastic nature of the involved mechanisms. Periodicities between 4–33 years are obtained employing four spectrum analysis methods, (power spectrum employing the Blackman-Tukey window, maximum entropy, Fourier, autocorrelation), whilst, their significance and their stationarity has been established with the application of general statistical tests (Kolmogorov-Smirnov, one sample and two sample test, randomness test, chi-square, various orders of autoregressive process, analysis of truncated records).Deceased.     

The marine Lockne impact structure, Jämtland, Sweden: a review

The Lockne impact structure in Jämtland (63°00'20"N, 14°49'30"E) formed in the Middle Ordovician at approximately 455 Ma. The structure is a concentric crater with a total diameter of 13.5 km. The impact took place in a marine environment. Seawater played an important role in the cratering process and in crater morphology and the amount of melt remaining in the structure. Seawater rushed back into the crater in a resurge, eroding and redepositing the ejecta among the resurge deposit. Seawater furthermore facilitated the hydrothermal system, which was driven by the residual heat in the structure. The Lockne structure hosts shocked quartz and an iridium anomaly. The rim wall round the crater collapsed in the modification stage of the crater and was annihilated by the resurge. The fractured basement and the impact breccia were initially rich in open cavities. These became partly filled with dominantly calcite. The filling contributed to a low-density contrast, generating a negative gravity anomaly of 22 gu. The gravity model indicates a central uplift and a NW-directed tilt of the structure. This tilt is also seen in the magnetic models. The apparent absence of any impact melt is probably real and related to the environment of impact.     

Search for variable sources using data of “Cold” surveys

We search for variable sources, using the data of the surveys conducted on the RATAN-600 radio telescope in 1980–1994 at 3.94 GHz. To test the radio sources of the RCR (RATAN Cold Refined) catalog for variability, we estimated the long-term variability indices V of the studied objects, their relative variability amplitudes V _χ , and the χ ² probabilities p. Out of about two hundred considered sources, 41 proved to have positive long-term variability indices, suggesting that these sources may be variable. Fifteen objects can be considered to be reliably variable according to the χ ² criterion p > 0.98, three of these sources have χ ² probabilities p ≥ 0.999. The corresponding probabilities for six sources lie in the 0.95 < p < 0.98 interval, and those of the remaining 20 objects in the 0.73 ≤ p < 0.95 interval. Twenty four of 41 objects are variable or possibly variable in the optical range, and five objects are known variable radio sources. We construct the light curves and spectra for the sources with positive long-term variability indices.     

Cluster–subcluster mergers and the formation of narrow-angle tailed radio sources

We examine the ROSAT PSPC X-ray properties of a sample of 15 Abell clusters containing 23 narrow-angle tailed (NAT) radio galaxies. We find that clusters with NATs show a significantly higher level of substructure than a similar sample of radio-quiet clusters, indicating that NAT radio sources are preferentially located in dynamically complex systems. Also, the velocity distribution of the NAT galaxies is similar to that of other cluster members; these velocities are inadequate for producing the ram pressure necessary to bend the radio jets. We therefore propose a new model for NAT formation, in which NATs are associated with dynamically complex clusters undergoing merger events. The U -shaped NAT morphology is produced in part by the merger-induced bulk motion of the ICM bending the jets.     

Phase transformations of enstatite in spherical shock waves

The analysis of available theoretical evaluations and experimental data reveals discrepancies and makes it possible to formulate the goals for the comprehensive study of the behavior of enstatite MgSiO₃ in shock isentropic waves of various scale and intensity. The paper presents the layout and results of an explosion experiment on the compression of an enstatite sphere with spherical shock waves and the subsequent recovery of the experimental material and its examination in discrete zones (along the sphere radius) that were produced by shock waves in the material. The latter were examined with the application of scanning electron microscopy, Raman spectroscopy, and X-ray diffraction analysis. The comparison of the systematic variations in the texture, chemistry, and phase composition of enstatite along the sphere radius with calculated pressure P(R, t) and temperature T(R, t) values led us to the following conclusions: enstatite starts melting on an isentrope upon pressure relief after shock wave compression at ?? _xx ?? 80 GPa and melts on the front of the spherically converging shock wave at ?? _xx ?? 160 GPa and T ?? 6300 K. Our laboratory experiments with shock waves were the world??s first in which enstatite was loaded with spherical converging shock isentropic waves and which provided evidence that shock wave-loaded MgSiO₃ shows certain morphological and mineralogical features never before detected in this mineral loaded with plane shock wave of smaller amplitude and duration. Goals are formulated for the further studying of shock wave-loaded materials, and the necessity is discussed for conducting an explosion experiment with a five to seven times greater spherical system in order to increase the duration of the shock wave loading impulse.     

Formation of iron sulfide nodules during anaerobic oxidation of methane

The biomarker compositions of iron sulfide nodules (ISNs; upper Pliocene Valle Ricca section near Rome, Italy) that contain the ferrimagnetic mineral greigite (Fe₃S₄) were examined. In addition to the presence of specific terrestrial and marine biomarkers, consistent with formation in coastal marine sediments, these ISNs contain compounds thought to originate from sulfate reducing bacteria (SRB). These compounds include a variety of low-molecular-weight and branched alkanols and several non-isoprenoidal dialkyl glycerol diethers (DGDs). In addition, archaeal biomarkers, including archaeol, macrocyclic isoprenoidal DGDs and isoprenoidal glycerol dialkyl glycerol tetraethers are also present. Both SRB and archaeal lipid δ¹³C values are depleted in ¹³C (δ¹³C values are typically less than −50‰), which suggests that the SRB and archaea consumed ¹³C depleted methane. These biomarker and isotopic signatures are similar to those found in cold seeps and marine sediments where anaerobic oxidation of methane (AOM) occurs with sulfate serving as the terminal electron acceptor. Association of AOM with formation of greigite-containing ISNs could provide an explanation for documented remagnetization of the Valle Ricca sediments. Upward migration of methane, subsequent AOM and associated authigenic greigite formation are widespread processes in the geological record that have considerable potential to compromise paleomagnetic records.     

Se and Te mineralization in albitites and prospects of the metasomatites for Au,Salla-Kuolajarvi belt,Northern Karelia

On the basis of the complex of geological features, the eastern flank of the Salla-Pana-Kuolajarvi belt is a prospect structure for gold mineralization in the U-bearing albitites and related acid and mafic metasomatites. Visible tellurides and selenides, which are typical of gold deposits of the Fe-Co-Au-U group in the adjacent territory of Finland within the Salla-Pana-Kuolajarvi belt, were found in the Ozerny occurrence as a result of studies. Native gold is found in association with tellurides. Molybdenite from the occurrence has a high Re content up to 0.3%.