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.     

Mean crustal velocity: a critical parameter for interpreting crustal structure and crustal growth

Mean crustal velocity is a critical parameter for genesis of continental crystalline crust because it is a function of mean crustal composition and therefore may be used to resolve continental crustal growth in space and time. Although the best values of mean crustal velocity are determined from wide-angle reflection measurements, most studied here necessarily come from vertical averages in crustal refraction determinations. The mode of 158 values of mean crustal velocity is 6.3 km/s, a velocity which corresponds to a mean crustal composition of granodiorite to felsic quartz diorite; Archean crust may be slightly more mafic. Mean crustal velocities range from 5.8 to 7.0 km/s. The lowest values invariably are found in thermally disturbed rift zones and the highest values correspond to velocities in gabbro. Velocities in island arcs may be as low as 6.0 km/s but are typically 6.5–6.9 km/s which corresponds to andesitic composition; estimates of island arc composition are andesitic. If values of mean crustal velocity are not biased, this observation suggests that continental crust did not grow simply by addition of island arc material. Possibilities are that crust formed from fusion of island arcs and was later changed to more felsic composition by addition of material from the mantle or that the late Archean episode of major crustal growth did not involve processes similar to younger island arcs. Some crustal blocks might be changed in composition and thickness by such processes as underplating, interthrusting, necking and sub-crustal erosion. Specially designed experiments are suggested to determine this parameter so critical for understanding genesis of continental crust.     

Paleolimnological investigations of anthropogenic environmental change in Lake Tanganyika: V. Palynological evidence for deforestation and increased erosion

Pollen spectra from seven short cores taken from deltaic sites in the central and northern parts of Lake Tanganyika provide information about vegetation changes around the lake during the last 5000 years. Pollen analysis was undertaken to understand the history and timing of catchment deforestation and its causal linkage to excess sedimentation and ecosystem change in Lake Tanganyika. The spectra are dominated by grass pollen at all levels in every core. Grass pollen percentage values range between 40 and 80%. Low values of arboreal pollen taxa (1–20%) were documented from most cores except core LT-98-2M. Core LT-98-2M represents the longest duration vegetation record of this study (close to 5000 years BP), and records the onset of increasingly arid conditions in the Late Holocene, especially after 500 A.D., with the probable replacement of forest by open grassland in the Mahale Mountains region. The pollen/spore content for other cores showed a consistent trend of a decrease in grass pollen and an increase in pteridophyte and forest indicator pollen taxa during the last few centuries, contemporaneous with other indications of increased watershed disturbance from forest clearing (especially isotopes and lake faunal change). The timing or strength of this trend is not tied to specific levels of watershed disturbance. However, increasing fern spore abundance does occur progressively later towards the south, where modern human population densities are lower. Although increasing fern spore abundance is consistent with a land-clearing hypothesis, the rising arboreal pollen percentages are seemingly counterintuitive. One possible explanation is that increasing arboreal pollen proportions reflects the recycling of abundant pollen of this type from rapidly eroding soils. Another likely explanation for this finding is that land clearing involved the replacement of miombo woodland, with its mixture of trees producing little pollen and understory grasses producing large amounts of pollen, by the present day cassava, banana, and legume agricultural systems, all of which are poor pollen producers. This shift in catchment vegetation would increase the relative contribution of Afromontane pollen transported long distances from the surrounding highland regions. This hypothesis is consistent with both the lack of correlation of palynological history with specific watershed deforestation attributes, as well as the broader historical record of human habitation in the Lake Tanganyika region. This study also highlights the need for both modern pollen transect data from the region and comparative cores from low elevation swamps or ponds (wetlands) in the region with smaller catchment areas.     

Crustal structure across the Grand Banks–Newfoundland Basin Continental Margin – II. Results from a seismic reflection profile

New multichannel seismic reflection data were collected over a 565 km transect covering the non-volcanic rifted margin of the central eastern Grand Banks and the Newfoundland Basin in the northwestern Atlantic. Three major crustal zones are interpreted from west to east over the seaward 350 km of the profile: (1) continental crust; (2) transitional basement and (3) oceanic crust. Continental crust thins over a wide zone (∼160 km) by forming a large rift basin (Carson Basin) and seaward fault block, together with a series of smaller fault blocks eastwards beneath the Salar and Newfoundland basins. Analysis of selected previous reflection profiles (Lithoprobe 85-4, 85-2 and Conrad NB-1) indicates that prominent landward-dipping reflections observed under the continental slope are a regional phenomenon. They define the landward edge of a deep serpentinized mantle layer, which underlies both extended continental crust and transitional basement. The 80-km-wide transitional basement is defined landwards by a basement high that may consist of serpentinized peridotite and seawards by a pair of basement highs of unknown crustal origin. Flat and unreflective transitional basement most likely is exhumed, serpentinized mantle, although our results do not exclude the possibility of anomalously thinned oceanic crust. A Moho reflection below interpreted oceanic crust is first observed landwards of magnetic anomaly M4, 230 km from the shelf break. Extrapolation of ages from chron M0 to the edge of interpreted oceanic crust suggests that the onset of seafloor spreading was ∼138 Ma (Valanginian) in the south (southern Newfoundland Basin) to ∼125 Ma (Barremian–Aptian boundary) in the north (Flemish Cap), comparable to those proposed for the conjugate margins.     

E (B-V) determination from an UV-visual two-colour diagram: O and B stars in the catalogue of stellar ultraviolet fluxes

We present here, for the O and B type stars in the Catalogue of Stellar Ultraviolet Fluxes, an approach which does not require a precise knowledge of spectral type and luminosity class for derivingE(B-V) colour excesses. The method is based on the use of an UV-visual two-colour diagram; galactic variations in the interstellar extinction law are analyzed and fully taken into account. Our results have been compared with those derived by using the differences between observed and intrinsic colours for stars with known spectral classification. The very good agreement in a large number of cases (94 per cent) demonstrates that our approach permits the derivation of reliable colour excess values for early type stars even if only a rough spectral classification is available.     

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).     

A note on the relationship between dip-slip fault parameters and plate parameters in the two-dimensional modelling of preseismic deformation

Preseismic lithospheric deformation at a subduction zone can be modelled as dip-slip dislocation on an inclined fault or as flexure of a thin plate. Both these models predict a region of positive topography known as forebulge or outer rise. By matching the location and the magnitude of the forebulge, we derive useful relations between the dip-slip fault parameters and the plate parameters. In particular, we determine the width of a long dip-slip fault of given dip corresponding to a semi-infinite plate of given thickness. The displacement profiles of the two models are also compared.     

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.