Expansion of the principal functions of Keplerian motion using complex variables

A special system of canonical variables is considered. An algorithm for expanding the principal functions of Keplerian motion in new elements is presented. The advantage of the proposed system is a relatively small number of terms in the classical expansions of the unperturbed two-body problem. A method for expanding the time derivatives of the rectangular coordinates is proposed. Some estimates of the number of terms in the presented expansions have been obtained through numerical experiments.     

Evolution of disk galaxies regulated by supernova remnants

Assuming that a disk galaxy is composed of an ambient pervasive gas, small clouds, molecular clouds and stars, its evolution is studied through examining the interchange processes among them. Main results obtained are: (1) The star formation rate is directed by the formation process of molecular clouds. (2) Depending upon the parameters there may be three or four types of evolution of disk galaxies: the no star formation case, the active in the past and inactive at present star formation case, the burst-like star formation case and the very active in star formation case.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan between 30 September–6 October, 1984.     

Existence of transverse waves in anisotropic poroelastic media

Out of the four waves in an anisotropic poroelastic medium, two are termed as quasi-transverse waves. The prefix 'quasi' refers to their polarizations being nearly, but not exactly, perpendicular to direction of propagation. In this composite medium, unlike perfectly elastic medium, the propagation of a longitudinal wave along a phase direction may not be accompanied by transverse waves. The existence of a transverse wave in anisotropic poroelastic media is ensured by the two equations restricting the choice of elastic coefficients of porous aggregate as well as fluid–solid coupling. Necessary and sufficient conditions for the existence of transverse waves along the coordinate axes and in the coordinate planes for general anisotropy are discussed. The discussion is extended to the case of orthotropic materials and existence for few specific phase directions is also explored. The conditions for the transverse waves decided on the basis of their apparent polarizations, that is, particle motion being perpendicular to ray direction, are also discussed. For a particular numerical model, the existence of these apparent transverse waves is solved numerically for phase directions in coordinate planes. For general directions of phase propagation, the existence of these transverse waves is checked graphically for the chosen numerical model.     

First Byurakan Spectral Sky Survey. Stars of Late Spectral Types. XI. Zone -7° ≤ δ ≤ -3°

The eleventh list of faint late M and carbon type stars detected on the plates of the First Byurakan Spectral Survey in zone -7° -3° and covering about 1000 square degrees is presented. From 126 detected stars, 88 are newly discovered objects: they are 6 carbon stars, 8 carbon star candidates, and 74 M-type stars; among the latter 38 (26 PSC + 12 FSC) are unclassified IRAS sources, and one object is an unclassified ROSAT source. Distances to the 6 newly discovered early-type carbon stars are estimated. Equatorial coordinates, red magnitudes, and spectral classes determined from the Palomar E-charts are provided. The lack of optical counterparts on Palomar O and E maps for two detected late M-type stars indicates a large variability in brightnesses of these objects (amplitude not smaller than 7.0 magnitude).     

Impacts of primary deforestation upon limestone slopes in northern Vancouver Island, British Columbia

Effects of deforestation upon slopes in limestones and in volcanic rocks in the Benson River valley, northern Vancouver Island, have been investigated quantitatively. Postlogging soil erosion and vegetal regeneration success were assessed by measuring soil depth, percent bare rock and moss cover, and the numbers and diversity of trees, shrubs, and plants on 25 sampling sites, each containing ten measuring quadrats selected at random. Sixteen sites were on the Quatsino Formation, a well-karstified limestone, and nine on the Karmutsen Formation of basaltic lavas. Eight sites were of virgin forest, 16 were logged between 1970 and 1983, and one (on limestone) was logged in 1911. Both bedrock types were significantly affected by the cutting. There was greater loss of soil and an increase in bare rock on the limestones. Erosion was increased significantly by burning on the limestones but not on the volcanics. Within-group comparisons on the limestones determined that steeper slopes and harder burned areas suffered the most and are slowest to regenerate. Volume of timber on the 1911 site was 19 percent of that in similar uncut forest sites. It appears that complete recovery on the barren limestone slopes will require at least some centuries.     

Distinct metamorphic evolution of alternating silica-saturated and silica-deficient microdomains within garnet in ultrahigh-temperature granulites: An example from Sri Lanka

Here we report the occurrence of garnet porphyroblasts that have overgrown alternating silica-saturated and silica deficient microdomains via different mineral reactions. The samples were collected from ultrahigh-temperature (UHT) metapelites in the Highland Complex, Sri Lanka. In some of the metapelites, garnet crystals have cores formed via a dehydration reaction, which had taken place at silica-saturated microdomains and mantle to rim areas formed via a dehydration reaction at silica-deficient microdomains. In contrast, some other garnets in the same rock cores had formed via a dehydration reaction which occurred at silica-deficient microdomains while mantle to rim areas formed via a dehydration reaction at silica-saturated microdomains. Based on the textural observations, we conclude that the studied garnets have grown across different effective bulk compositional microdomains during the prograde evolution. These microdomains could represent heterogeneous compositional layers (paleobedding/laminations) in the precursor sediments or differentiated crenulation cleavages that existed during prograde metamorphism. UHT metamorphism associated with strong ductile deformation, metamorphic differentiation and crystallization of locally produced melt may have obliterated the evidence for such microdomains in the matrix. The lack of significant compositional zoning in garnet probably due to self-diffusion during UHT metamorphism had left mineral inclusions as the sole evidence for earlier microdomains with contrasting chemistry.     

Lunar Gravity-Assist Maneuver As a Way of Reducing the Orbit Amplitude in the Spectrum–Röntgen–Gamma Project

Spectrum–Röntgen–Gamma (SRG) is a space observatory designed to observe astrophysical objects in the X-ray range of the electromagnetic spectrum. SRG is planned to be launched in 2019 by a Proton-M launch vehicle with a DM3 upper stage. The spacecraft will be delivered to an orbit around the Sun–Earth collinear libration point L2 located at a distance of ~1.5 million km from the Earth. Although the SRG launch scheme has already been determined at present, in this paper we consider an alternative spacecraft transfer scenario using a lunar gravity-assist maneuver. The proposed scenario allows a oneimpulse transfer from a low Earth orbit to a small-amplitude orbit around the libration point to be performed while fulfilling the technical constraints and the scientific requirements of the mission.