Compression of ephemerides

Approximations in the normL ₁ by Chebyshev polynomials are generated to represent astronomical ephemerides over large intervals of time.     

Lamé functions of the first kind generated by computer

The definitions of the Lamé functions and the ellipsoidal coordinates inherent to them are introduced. Proceeding from Lamé's differential equation the four classes of Lamé functions of the first kind are generated by computer with the aid of formula manipulation techniques. For this purpose algebraic expressions for the coefficients in the Lamé polynomials are constructed by virtue of recurrence formulae and presented in tabular as well as machine readable form for further processing. The determination of a parameter appearing in the polynomial coefficients leads to an algebraic eigenvalue problem. It is shown how this eigenvalue problem is amenable to numerical treatment. The polynomial coefficients together with the eigenvalues are characteristic for the Lamé functions and define them completely.     

Complex formation in the ternary system Mg(II)-CO2-H2O

The carbonato and hydrogencarbonato complexes of Mg²⁺ were investigated at 25 and 50° in solutions of the constant ClO₄^? molality (3 M) consisting preponderantly of NaClO₄. The experimental data could be explained assuming the following equilibria: Mg²⁺ + CO_2B + H₂O ag MgHCO⁺₃ + H⁺, $\text{log}{}^1\text{β}{}_1\text{= ?7.64}{}_4\text{± 0.01}{}_7\text{(25°), ?7.46}{}_2\text{± 0.01}{}_1\text{(50°)}$, Mg²⁺ + 2 CO_2g + 2 H₂Oag Mg(HCO₃)⁰₂ ± 2 H⁺, $\text{log}{}^1\text{β}{}_2\text{= ?15.00 ± 0.14 (25°)}$, ?15.37 ± 0.39 (50°), Mg²⁺ + CO_2g + H₂Oag MgCO⁰₃ + 2 H⁺, $\text{log}{}^1\text{k}{}_1\text{= ?15.64 ± 0.06 (25°)}$,?15.23 ± 0.02 (50°), with the assumption γ_MgCO3⁰ = γ_Mg(HCO3)⁰2, ΔG⁰(I = 0) for the reaction MgCO⁰₃ + CO_2g + H₂O = Mg(HCO₃)⁰₂ was estimated to be ?3.9₁ ± 0.8₆ and 0.6 ± 2.4 kJ/mol at 25 and 50°C, respectively. The abundance of carbonate linked Mg(II) species in fresh water systems is discussed.     

Association of spherical and ellipsoidal gravity coefficients of the Earth's potential

A comparison is drawn between the expansion of the potential in spherical harmonics on the one hand and in ellipsoidal harmonics on the other, with the objective of associating the spherical and ellipsoidal gravity coefficients of the Earth's potential.For this purpose the properties of orthogonality of the Lamé functions of the first kind have been tailored to this subject of investigation and become instrumental in establishing the mathematical expressions which relate the two classes of gravity coefficients to each other. In deriving the elements of the transition matrices elliptic integrals have been encountered whose reduction to the three kinds of canonical elliptic integrals is discussed.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 17–23, 1969.     

Evidence for climatic variability and its impact on human development during the Neolithic from Loughmeenaghan,County Sligo,Ireland

High‐resolution pollen and geochemical analyses conducted on a sediment profile from a small lake in County Sligo, Ireland, revealed that human development during the Neolithic was influenced by pronounced climatic oscillations. The primeval woodland around the lake experienced a considerable transformation coinciding with the elm decline at 3810 BC. The subsequent increase in summer temperatures and decrease in precipitation favoured wheat cultivation in the lake's catchment area, which was practised for approximately 140 years. A shift towards pastoral farming took place with the establishment of exceptionally dry conditions between 3650 and 3560 BC, when lake level and influx of allochthonous material were notably low. The onset of cool and wet conditions at the transition from the Early to Middle Neolithic possibly caused the initial decline of human activity in the area. Periods of particularly high precipitation during the Middle and early Late Neolithic contributed to the abandonment of the area by the first farmers. Comparison of the proxy record from the study site with other palynological and archaeological records from Ireland suggests that climatic variability on the decadal to centennial scale represented a primary control on the nature and duration of farming practices during the Neolithic. Copyright © 2012 John Wiley & Sons, Ltd.     

Nachweis der allgemeinen Gültigkeit des Gefrierkernspektrums

Zusammenfassung Durch weitere experimentelle Untersuchungen wird festgestellt, dass das an destillierten Wassertropfen ermittelte Gefrierkernspektrum von speziellen Versuchsbedingungen unabhängig ist und auch für Wasserarten mit verschiedenen natürlichen oder künstlichen Verunreinigungen gilt. Es kann ausserdem in allen bisher im Laboratorium und in der Atmosphäre durchgeführten Untersuchungen über die Eiskeimbildung nachgewiesen werden. Dieser Befund stützt als notwendige Bedingung die Deutung des Gefrierkernspektrums durch Strukturänderungen des Wassers und besagt, dass im Laboratorium und in der Atmosphäre dieselben Gefrierkerne vorhanden sind und dass bei der atmosphärischen Eiskeimbildung auch nur die aus Untersuchungen im Laboratorium bekannten Besonderheiten des Gefrieveorgangs (im unterkühlten Wasser) vorliegen.

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Summary Further experimental investigations demonstrate the «Gefrierkernspektrum», which was found for droplets from destilled water, to be independent from special experimental conditions and valid for sorts of water containing natural or artificial impurities, too. Furthermore it can be pointed out from all existing investigations on ice-nucleation, made in laboratory and in the atmosphere. This result supports, as a necessary condition, the interpretation of the «Gefrierkernspektrum» by means of changes in the structure of water itself and proves, that there are the same freezing nuclei both in the laboratory and the fre atmosphere and that ice-nucleation in the atmosphere holds but the same peculiarities of freezing (of supercooled water), known from laboratory work.

     

Theory of linear cosmological perturbations in flat space-time theory of gravitation

Covariant linear cosmological perturbations are considered in flat space-time theory of gravitation. The background metric is not altered. The perturbed energy-momentum is given. The basic equations for the propagation of the perturbations are presented. The perturbed equations for a homogeneous, isotropic universe are stated.     

Environmental Determinants of Emergent Macrophyte Vegetation in Pacific Northwest Estuarine Tidal Wetlands

We investigated whether within wetland environmental conditions or surrounding land cover measured at multiple scales were more influential in structuring regional vegetation patterns in estuarine tidal wetlands in the Pacific Northwest, USA. Surrounding land cover was characterized at the 100, 250, and 1,000 m, and watershed buffer scales. Vegetation communities were characterized by high species richness, lack of monotypic zonation, and paucity of invasive species. The number of species per site ranged between 4 and 20 (mean?±?standard deviation?=?10.2?±?3.1). Sites supported a high richness (mean richness of native species 8.7?±?2.8) and abundance of native macrophytes (mean relative abundance 85 %?±?19 %). Vegetation assemblages were dominated by a mix of grasses, sedges, and herbs with Sarcocornia pacifica and Distichlis spicata being common at sites in the oceanic zone of the estuary and Carex lyngbyei and Agrostis stolonifera being common at the fresher sites throughout the study area. The vegetation community was most strongly correlated with salinity and land cover within close proximity to the study site and less so with land cover variables at the watershed scale. Total species richness and richness of native species were negatively correlated with the amount of wetland in the buffer at all scales, while abundance of invasive species was significantly correlated to within wetland factors, including salinity and dissolved phosphorus concentrations. Landscape factors related to anthropogenic disturbances were only important at the 100-m buffer scale, with anthropogenic disturbances further from the wetland not being influential in shaping the vegetation assemblage. Our research suggests that the traditional paradigms of tidal wetland vegetation structure and environmental determinants developed in east coast US tidal wetlands might not hold true for Pacific Northwest wetlands due to their unique chemical and physical factors, necessitating further detailed study of these systems.     

Tracing the exhumation of the Eclogite Zone (Tauern Window,Eastern Alps) by <Superscript>40</Superscript>Ar/<Superscript>39</Superscript>Ar dating of white mica in eclogites

New radiometric ages from the Subpenninic nappes (Eclogite Zone and Rote Wand – Modereck Nappe, Tauern Window) show that phengites formed under eclogite-facies metamorphic conditions retain their initial isotopic signature, even when associated lithologies were overprinted by greenschist- to amphibolite-facies metamorphism. Different stages of the eclogite-facies evolution can be dated provided ⁴⁰Ar/³⁹Ar dating is combined with micro-structural analyses. An age of 39 Ma from the Rote Wand – Modereck Nappe is interpreted to be close to the burial age of this unit. Eclogite deformation within the Eclogite Zone started at the pressure peak along distinct shear zones, and prevailed along the exhumation path. An age of ca. 38 Ma is only observed for eclogites not affected by subsequent deformation and is interpreted as maximum age due to the possible influence of homogenously distributed excess argon. During exhumation deformation was localised along distinct mylonitic shear zones. This stage is mainly characterised by the formation of dynamically recrystallized omphacite2 and phengite. Deformation resulted in the resetting of the Ar isotopic system within the recrystallized white mica. Flat argon release spectra showing ages of 32 Ma within mylonites record the timing of cooling along the exhumation path, and the emplacement onto the Venediger Nappe. Ar-release patterns and ³⁶Ar/⁴⁰Ar vs.³⁹Ar/⁴⁰Ar isotope correlation analyses indicate no significant ⁴⁰Ar-loss after initial closure, and only a negligible incorporation of excess argon. From the pressure peak onwards, eclogitic conditions prevailed for almost 8–10 Ma.