The quasi integrals

The usual Von Zeipel transformations of the Hamiltonian Mechanics are presented, they lead to state functions with extremely slow variations: the quasi-integrals.The Von Zeipel transformations are implicit: an explicit and direct construction of the quasi-integrals is also presented and the quasi-invariance property of these functions is demonstrated.These results are applied to the problem of the motion of artificial satellites perturbed by the zonal harmonics of the Earth potential, the quasi-integral is given, it is then so constant that the problem can be considered as integrable.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

A crystal-chemical classification of borate structures with emphasis on hydrated borates

The rules governing formation of hydrated borate polyanions that were proposed by C.L. Christ in 1960 are critically reviewed and new rules added on the basis of recent crystal structure determinations. Principles and classifications previously published by others are also critically reviewed briefly. The fundamental building blocks from which borate polyanions can be constructed are defined on the basis of the number n of boron atoms, and the fully hydrated polyanions are illustrated. Known structures are grouped accordingly, and a shorthand notation using n and symbols Δ = triangle, T = tetrahedron is introduced so that the polyanions can be easily characterized. For example, 3:Δ+2T describes [B₃O₃(OH)₅]^2?. Correct structural formulas are assigned borates with known structures whereas borates of unknown structure are grouped separately.     

The sliding bed facies in esker sands and gravels: a criterion for full-pipe (tunnel) flow?

The Guelph esker (Ontario, Canada) consists of a sinuous, steep-sided and segmented ridge which comprises poorly sorted, matrix-supported sands and gravels. These sands and gravels were probably deposited during the sliding bed stage which has been observed by others in closed-conduit hydraulic experiments. The poor sorting probably resulted from a high concentration of bed-material load in the lower part of a subglacial tunnel, sorting being restricted to that produced by particle collisions. Inclusive graphic standard deviation is characteristically large for the sands and gravels, indicating that virtually all sizes available were in transport. The overall grain size distribution shows a characteristic undulatory shape on arithmetic probability paper, mostly because of selective removal of pebble gravel and granule sizes. This poorly sorted fades is believed to be diagnostic of transport in a subglacial tunnel flowing full of water, and may be used to identify subglacial conditions in other eskers. Deltaic sands and gravels occur downcurrent of the esker and contain a greater diversity of structures; climbing-ripple cross-laminae, parallel laminae and massive structure, deposited in large-scale foresees at the end of a subglacial tunnel. These deltaic sands and gravels grade distally into outwash sands and gravels.     

Polyoxymethylene co-polymers on grains

Conditions prevalent in dense molecular clouds are shown to favour the polymerization of H₂CO molecules and the deposition of formaldehyde co-polymer mantles, with typical radii 10^–5 cm, on smaller refractory grains. If a significant fraction of such co-polymer coated grains are expelled with systematic gas flows into the general interstellar medium, these moderately refractory grains may be responsible for the bulk of interstellar extinction and polarization at optical wavelengths. Mie calculations for a mixture consisting of iron, graphite and POM particles are presented as an example where POM grains of radii 0.15 dominate the extinction at optical wavelengths, providing a satisfactory overall fit to a range of extinction data. A size distribution of POM needles with a mean radius 0.15 also provides good agreement with data on interstellar linear as well as circular polarization. Suitably end-capped and stabilized co-polymer-coated grains, with either silicate or graphite cores, may survive at temperatures 450 K under interstellar ambient conditions and be responsible for the 10 emission feature in many sources. Theoretically computed band profiles of the 10 -feature in POM coated grains, in general, provide better agreement with observations than most types of silicate grains considered so far. We also note that an unexplained dip at 10 in the 8–12 feature of the infrared source OH 231.8+4.2 may be a signature of POM grains; likewise, a persistent 3.3 emission feature in many different types of infrared source could be attributed to the CH stretching mode in formaldehyde co-polymer grains.     

Energy spectra of cosmic ray nuclei: 4≤Z≤26 and 0.3≤E≤2 GeV amu−1

Energy spectra of cosmic ray nuclei in the charge range 5Z26 have been derived from the response of an acrylic plastic erenkov detector. Data were obtained using a balloon-borne detector and cover the energy range 320E2200 MeV amu^–1. Spectra are derived from a formal deconvolution using the method of Lezniak (1975). Relative spectra of different elements are compared by observing the charge ratios. Secondary-primary ratios are observed to decrease with increasing energy, consistent with the effect previously observed at higher energy. Primary-to-primary ratios are constant for 6Z10 and 14Z26 but vary for 10Z14. This data is found to be consistent with existing data, where comparable, and lends strong support to the idea of two separate source populations contributing to the cosmic ray composition.Work supported by University of Maryland Grant NGR 21-002-316.     

Theoretical brightness temperature profiles of atmospheric pure H2 rotational quadrupole lines: Jupiter and Uranus

With the advent of high-resolution instruments and their use high above most of the telluric water vapor, we can expect to observe the hydrogen pure rotational quadrupole lines at 28, 17, and 12 μm from the atmospheres of the outer planets. We have calculated the best values for the line strengths, pressure-broadening coefficients, diffusion constants, and pressure shifts for these rotational transitions. We have used the collisionally narrowed Galatry profile to calculate brightness temperature line profiles for these H₂ transitions for the outer planets Jupiter and Uranus. We have also included the effect of the H₂ rotational-translational continuum and the NH₃ν₂ band.     

Energetic properties of interplanetary plasma at the earth's orbit following the August 4, 1972 flare

Solar wind and interplanetary magnetic field data were obtained by the PROGNOZ 1 and PROGNOZ 2 satellites during the period following the August 4, 1972 (0621 UT) solar flare. A thermalized plasma was recorded one hour after the shock followed two hours later by the plasma piston with a bulk velocity higher than 1700 km s^-1. The comparison between the PROGNOZ and PIONEER 9 solar wind data shows an attenuation of the plasma properties with the deflection from the flare's meridian.     

Auroral recombination of N and O: A possible source for emission in the γ and δ bands of NO

Radiative recombination of N and O provides a significant source for auroral emission in the γ and δ bands of NO with selective population of vibrational levels in the A²Σ⁺ and C²Π states. This mechanism may account for emissions detected near 2150 Å. Models are derived for the auroral ionosphere and include estimates for the concentrations of N and NO. The concentration of NO is estimated to have a value of about 10⁸ cm^?1 near 140 km in an IBC III aurora. The corresponding density for N is about 5 × 10⁷cm^?3 and the concentration ratio $\text{NO}{}^{\mathrm{+}}\text{O}{}_2{}^{\mathrm{+}}$ has a value of about 5.5.     

Transequatorial loops interconnecting McMath regions 12472 and 12474

We discuss the life-story of a transequatorial loop system which interconnected the newly born active region McMath 12474 with the old region 12472. The loop system was probably born through reconnection accomplished 1.5 to 5 days after the birth of 12474 and the loops were observed in soft X-rays for at least 1.5 days. Transient sharpenings of the interconnection and a striking brightening of the whole loop system for about 6 hr appear to be caused by magnetic field variations in the region 12474. A flare might have been related to the brightening, but only in an indirect way: the same emerging flux could have triggered the flare and at the same time strengthened the magnetic field at the foot-points of the loops. Electron temperature in the loop system, equal to 2.1 × 10⁶ K in its quiet phase, increased to 3.1 × 10⁶ K during the brightening. Electron density in the loop system was 1.3 × 10⁹ cm^–3 and it could be estimated to 7 × 10⁸ cm^–3 prior to the brightening. During the brightening the loops became twisted. There was no obvious effect whatsoever of the activity in 12474 upon the in erconnected old region. The final decay of the loop system reflected the decay of magnetic field in the region 12474.