The additive logistic skew-normal distribution on the simplex

There is a dearth of suitable models with which to adequately model compositional data sets, especially those which exhibit skewness after additive logratio-transformation. In order to address this deficit we propose the additive logistic skew-normal distribution, an extension to the additive logistic normal model on the simplex derived from the skew-normal distribution in real space. The purpose of this paper is to outline the potential of this distribution in the modelling of compositional data. We present its most important properties and use an example to exhibit the potential of this distribution.     

Embryotoxicity of the antifouling biocide zinc pyrithione to sea urchin (Paracentrotus lividus) and mussel (Mytilus edulis)

The effects of the new antifouling compound zinc pyrithione (Zpt) on the embryonic development of sea urchin (Paracentrotus lividus) and mussel (Mytilus edulis) were investigated in laboratory toxicity tests. The median effective concentrations (EC50) were 7.7 nM for sea urchin embryos and 8 nM for mussel embryos. Toxic effects of Zpt on the larval growth of the sea urchin were detected at 0.5 nM. Predicted environmental concentrations of Zpt in pleasure craft harbours are higher than the predicted no effect concentrations for sea urchin and mussel embryos, indicating that Zpt may pose a threat to those species from exposure in the field.     

Equations for the Estimation of Strong Ground Motions from Shallow Crustal Earthquakes Using Data from Europe and the Middle East: Horizontal Peak Ground Acceleration and Spectral Acceleration

This article presents equations for the estimation of horizontal strong ground motions caused by shallow crustal earthquakes with magnitudes M_w 5 and distance to the surface projection of the fault less than 100km. These equations were derived by weighted regression analysis, used to remove observed magnitude-dependent variance, on a set of 595 strong-motion records recorded in Europe and the Middle East. Coefficients are included to model the effect of local site effects and faulting mechanism on the observed ground motions. The equations include coefficients to model the observed magnitude-dependent decay rate. The main findings of this study are that: short-period ground motions from small and moderate magnitude earthquakes decay faster than the commonly assumed 1/r, the average effect of differing faulting mechanisms is not large and corresponds to factors between 0.8 (normal and odd) and 1.3 (thrust) with respect to strike-slip motions and that the average long-period amplification caused by soft soil deposits is about 2.6 over those on rock sites. Disappointingly the standard deviations associated with the derived equations are not significantly lower than those found in previous studies.     

Exact cosmological solutions in Brans and Dicke's scalar-tensor theory,I

The exact solution is sought for the cosmological equations of Brans and Dicke's scalar-tensor theory when a power law exists between the gravitational constant and the radius of curvature of the universe. For the space of negative curvature no solution is possible. On the contrary for a closed space the gravitational constant and the radius of curvature increase linearly with respect to the age of the universe. The parameter of the scalar-tensor theory is necessarily negative and can be determined by the present values of the mass-density of the universe, the Hubble-constant and the gravitational constant. The solution has no analogy in Einstein's theory with vanishing cosmological constant, even when the deviations from Einstein's values of the solar relativistic effects are small.     

Spin-forbidden resonance multiplets in light elements

We present new laboratory data on the multiplets 2s ^{2 1} S -2s2p ³ P, 2s ²2p ² P - 2s2p ^{2 4} P, and 2s ²2p ^{2 3} P - 2s2p ^{3 5} S in nitrogen, oxygen and fluorine, and discuss theZ-dependence of their wave-numbers. These multiplets are very faint in laboratory light sources, but can become prominent in astrophysical sources of low density. Our results confirm the solar identifications of the nitrogen and oxygen multiplets made by Burtonet al. Predicted positions of the corresponding multiplets in neon are given.     

Corrections to Watts' datum from photoelectric occultations

Reduction and analysis of photoelectric observations of stars by the Moon made between 1955–1978 permit to obtain corrections to the Watts' reference surface, using the recent values for the correction of the equinox.     

Origin and evolution of the earth-moon system

The origin and evolution of the Earth-Moon system is studied by comparing it to the satellite systems of other planets. The normal structure of a system of secondary bodies orbiting around a central body depends essentially on the mass of the central body. The Earth with a mass intermediate between Uranus and Mars should have a normal satellite system that consists of about half a dozen satellites each with a mass of a fraction of a percent of the lunar mass. Hence, the Moon is not likely to have been generated in the environment of the Earth by a normal accretion process as is claimed by some authors.Capture of satellites is quite a common process as shown by the fact that there are six satellites in the solar system which, because they are retrograde, must have been captured. There is little doubt that the Moon is also a captured satellite, but its capture orbit and tidal evolution are still incompletely understood.The Earth and the Moon are likely to have been formed from planetesimals accreting in particle swarms in Kepler orbits (jet streams). This process leads to the formation of a cool lunar interior with an outer layer accreted at increasingly higher temperatures. The primeval Earth should similarly have formed with a cool inner core surrounded in this case by a very strongly heated outer core and with a mantle accreted slowly and with a low average temperature but with intense transient heating at each individual impact site.     

Masses for which triple collision is regularizable

We consider the regularization by continuity w.r.t. initial conditions (geometric or Easton method) which has a sense both in physical and computational aspects. Using the idea of triple collision manifold of McGehee we study the values of masses for which the invariant manifolds of equilibrium points coincide. Local analytical equations are continuated numerically. So one gets the masses satisfying a necessary condition. Again analytically we discuss the neighbourhood of t.c.m. at the equilibrium points. A necessary and sufficient condition in terms of integrals along invariant manifolds is found for the rectilinear case. This can be tested for the masses obtained above. Only a countable (symmetric) set of masses remains. Then, due to errors in physical measurements or numerical integrations we can never expect a regular behaviour. Extension to the planar case is also taken into account.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Etude géochimique des éléments condensés au cours du réfroidissement de la phase gazeuse volcanique: Etna 1976

On Mount Etna, in June 1976, sublimates were collected on the wall of a silicatube. Temperatures of deposition were recorded along the tube and the atomic composition has been analysed by neutronic activation. It is possible with this technique to know the temperature of condensation or sublimation for the different elements. These results should help to better understand the magma/gas relationship.     

Intercomparisons of earth gravity models by means of lumped coefficients: Terms for eccentricity and longitude

The comparisons of the Earth gravity field models by the order of their harmonic coefficients, performed with the basic lumped coefficients (Planet. Space Sci.29, 653, 1981, Paper I) are here extended to cover all harmonic coefficients (both odd and even degree). The lumped coefficients (the “e-terms” and “longitudinal” terms), corresponding to 18 Earth models, are compared mutually (Figs. 2–15). The large differences, observed for various models and orders, are of particular interest: they are gathered into Table 1. The result of Paper I was a little pessimistic. The same is true here: various inhomogeneities, sometimes very large, in the accuracy of the harmonic coefficients must exist—even for low orders. Most of our comments and objections, however, relate to the older Earth models, which have only a historical value now. Our comparisons are only relative ones; an actual test of the accuracy of the models (their calibration) is possible via data with independent status (Kloko?ník, 1982, 1983).