Linearization: Laplace vs. Stiefel

The method for processing perturbed Keplerian systems known today as the linearization was already known in the XVIII^th century; Laplace seems to be the first to have codified it. We reorganize the classical material around the Theorem of the Moving Frame. Concerning Stiefel's own contribution to the question, on the one hand, we abandon the formalism of Matrix Theory to proceed exclusively in the context of quaternion algebra; on the other hand, we explain how, in the hierarchy of hypercomplex systems, both the KS-transformation and the classical projective decomposition emanate by doubling from the Levi-Civita transformation. We propose three ways of stretching out the projective factoring into four-dimensional coordinate transformations, and offer for each of them a canonical extension into the moment space. One of them is due to Ferrándiz; we prove it to be none other than the extension of Burdet's focal transformation by Liouville's technique. In the course of constructing the other two, we examine the complementarity between two classical methods for transforming Hamiltonian systems, on the one hand, Stiefel's method for raising the dimensions of a system by means of weakly canonical extensions, on the other, Liouville's technique of lowering dimensions through a Reduction induced by ignoration of variables.     

A Logistic Regression Model Applied to Evaluate the Influence of Operating Time of AgI Ground Acetonic Generators on the Size and Hardness of Hail

In this paper we study the effect of operating time of AgI ground acetonic generatorsbefore hailing on the hail characteristics (size and hardness), and hailfall crop damages.The study was carried out in a large area of northern Spain over an area of 12,000 km².Data are available from 1,984 hailstorms that occurred from May to September in theperiod 1982–1987. By using several Stepwise Logistic Regression Models, a statisticalsignificant (p < 0.05) decrease shows up in hailfall crop damage due to hail prevention.This effect is due to the influence of ground seeding on the hardness and mainly on thesize of hailstones.     

The role of GPR techniques in determining ice cave properties: Peña Castil ice cave,Picos de Europa

The structure and ice content of ice caves are poorly understood. Ground penetrating radar (GPR) can provide useful insights but has only rarely been applied to ice caves. This paper interprets GPR images (radargrams) in terms of internal structure, stratification, compaction, thickness and volume of the ice block in the Peña Castil ice cave (Central Massif of Picos de Europa, northern Spain), providing the endokarst geometry of the ice cave in GPR data reflections. Eight radargrams were obtained by applying a shielded ground‐coupled antenna with a nominal frequency of 400 MHz. Although the radargrams do not depict the ice–basal bedrock interface, they suggest that the ice block is at least 54 m deep and similarly thick. Some curved reflection signatures suggest a potential vertical displacement in the block of ice, and thus certain dynamics in the ice body. Other images show numerous interbedded clasts and thin sediment layers imaged as banded reflections. In this particular cave a direct visual inspection of the ice stratigraphy is a difficult task but GPR provides clear reflectivity patterns of some of its internal features, making GPR a suitable instrument for this and future studies to achieve a better and broader understanding of the internal behavior of ice caves.     

A Ta,Ti–rich oxide mineral assemblage from the Nancy beryl–columbite–phosphate granitic pegmatite,San Luis,Argentina

Mineralogy and Petrology - An assemblage of tantalite-(Mn), tantalian rutile, tapiolite-(Fe), titanowodginite, ferrotitanowodginite, and hydroxycalciomicrolite occurs in the Nancy granitic...     

On the use of Bayesian networks as a meta-modelling approach to analyse uncertainties in slope stability analysis

In this paper, we report on the use of Bayesian networks, BNs, learnt from data generated by physical and numerical models, to overcome to a certain degree a number of complications in traditional slope stability analyses that jointly consider the mechanical and hydraulic properties of soils. Discrete Bayesian networks resulted to be useful and efficient to acquire knowledge from simulated data and to identify significant factors by the combined use of backward inference and global sensitivity analysis. Further, BNs enable decision thresholds to be estimated quickly. Along with this, backward inference and global sensitivity analysis are performed in BNs at low computation costs. Moreover, under conditions in which knowledge is scarce, we show how a practitioner can be better informed using the proposed approach. All these previously under-reported modelling features in the specialised literature encourage the further application of the proposed approach to enhance slope stability analysis.     

Impacts of milkfish (Chanos chanos) aquaculture on carbon and nutrient fluxes in the Bolinao area,Philippines

Sediment oxygen consumption, TCO2 production and nutrient fluxes across the sediment-water interface were measured in sediments within and along a transect from four fish pens with production of milkfish (Chanos chanos) in the Bolinao area, The Philippines. The four fish pens were each representing a specific period in the production cycling. There was a positive linear relationship between the rates of sedimentation inside the fish pens and the sediment oxygen consumption indicating that the benthic processes were controlled by the input of organic matter from fish production. The nutrient fluxes were generally higher inside the fish pens, and nitrate was taken up (1.7-5.8 mmol m(-2) d(-1)) whereas ammonium (1-22 mmol m(-2) d(-1)) and phosphate (0.2-4.7 mmol m(-2) d(-1)) were released from the sediments. The sediments were enriched in organic matter with up to a factor 4 compared to outside. A mass balance for one crop of milkfish was constructed based on production data and on measured fluxes of nutrients in the fish pens to assess the loss of carbon and nutrients to the environment. There was a loss to the surroundings of carbon and nitrogen of 51-68% of the total input, whereas phosphorus was buried in the sediments inside the fish pens which acted as net sinks of phosphorus. The results obtained suggest that fish pen culture as practiced in the Bolinao area, leads to even greater impacts on benthic carbon and nutrient cycling than those found in suspended cage cultures.     

SIMS analyses on trace and rare earth elements in coexisting clinopyroxene and mica from minette mafic enclaves in potassic syenites crystallized under high pressures

Trace and rare earth element contents were determined by SIMS technique in clinopyroxene and mica crystals from minette lamprophyric enclaves in a potassic syenite host. This co-mingled system was crystallized at high pressures, which varied about 3–5 GPa, as indicated by the presence of K-clinopyroxenes and pyrope-rich garnet with measurable amounts of K₂O and Na₂O, among the near-liquidus phases. Major and trace element composition of these lamprophyric enclaves is quite similar to those observed in silica-rich lamproites, suggesting that similar sources were involved in their origin. In a general view, the concentrations of most trace and rare earth elements in clinopyroxene of the studied enclaves are higher than those referred to by other authors. Clinopyroxene/melt partition coefficient for most trace elements are close to determinations in alkali-basalts and lamproites from Leucite Hills, with considerable differences relative to Gaussberg lamproites. Furthermore, these partition data are completely different from those determined for potassic lavas crystallized under crustal pressures. Spidergrams for clinopyroxenes exhibit negative-Sr anomalies relative to LREE, which have been associated by most authors to crystallization under low-pressures, out of garnet stability field. The presence of pyrope together with K-clinopyroxene excludes such hypotheses for the studied enclaves. Y and HREE are concentrated in clinopyroxene, whilst the other trace elements have Kd<1. LIL elements, except Rb, have incompatible (Kd<1) behavior in phlogopite. The high partition coefficient for Nb (Kd>3) determined in the studied phlogopite is unusual in lamproites, lamprophyres, and basalts, but frequently observed in phlogopite from metasomatic mantle samples, as well as in acid magmas. This partition value may indicate the lack of other mineral phase with high partition for this element during crystallization, and may be enhanced by the liquid composition progressively closer to alkali feldspar, an unsuitable structure for six-coordinated cations. Ce/Yb, Rb/Sr, and Zr/Hf ratios in clinopyroxene and mica suggest that the minettic magma could produce the host Piquiri potassic syenite by fractional crystallization. This hypothesis is not consistent with Ba concentrations in clinopyroxene and mica, which suggest that a Ba-bearing phase (e.g. alkali feldspar) should be among the fractionated phases in order to produce the potassic syenites.     

Harrington's Hamiltonian in the stellar problem of three bodies: Reductions,relative equilibria and bifurcations

We study Harrington's Hamiltonian in the Hill approximation of the stellar problem of three bodies in order to clarify and sharpen a qualitative analysis made by Lidov and Ziglin. We show how the orbital space after four reductions is a two-dimensional sphere, Harrington's Hamiltonian defining a biparametric dynamical system. We produce the diagrams corresponding to each type of phase flow according to a complete discussion of all possible local and global bifurcations determined by the four integrals of the system.     

Origin and distribution of biomarkers in the sulphur rich Utrillas coal basin – Teruel mining district – Spain

The Utrillas coal facies are located in the Maestrazgo basin in NE Spain. This mining district of Teruel contains sub-bituminous deposits from the Middle Albian (Lower Cretaceous 105 Ma) in areas near a delta estuary with abundant sulphur. The high sulphur content is due to an influx of sulphate caused by the geological recycling of Triassic gypsum from the catchment area into the delta estuary. In some outcrops, the weathered coal reveals leonardite deposits. The depositional environment of the basin originated coals, some of which are currently mined. The organic matter of the coals has been the object of scattered reports. Studies have focused on bulk pyrolysis parameters and microscopic observation in Utrillas samples, as well as the inorganic and insoluble organic fraction.We analysed the organic soluble extract of the Utrillas coals using GC–MS in order to characterize their aliphatic, aromatic and organosulphur compounds. The biomarker distribution allowed us to recognize different inputs, assess their depositional palaeoenvironment and finally determine their degree of maturity. In particular, homologous series of hopanes related to eubacteria were present. Biomarkers characteristic of higher plant inputs were also widely distributed (e.g. phyllocladane or C₂₉ steranes). The presence of linear alkylbenzenes allowed us to recognize the palaeodepositional reducing environments where they were deposited. Specifically, thienylhopanes were associated with sulphur-reducing environments. Finally, the abundance of unsaturated biomarkers such as diacholestenes indicated low-maturity coals. Various aromatic ratios such as the methylphenanthrene index also suggested diagenesis in the initial stage.     

Application of the Engineering-Geological Conditions in Land-Use Plans in the Petrvald Region(Czech Republic)

The objective of this paper is to demonstrate necessity to inform relevant parties about engineering-geological conditions for various practical purposes,especially including appropriate land-use planning.However,the relationship between relevant geological information and the geological environment is vital for foundation engineering purposes,especially where demanding structures are involved.This information is most conveniently structured when accumulated information concerning engineering-geological zones is utilized.This necessarily includes knowledge of rock workability and also of the pre-Quaternary bedrock,and these characteristics were then related to the current built-up area and future development according to the land-use plans in a case study are from the Petrvald Region(Czech Republic).The geological environment of area has been severely influenced by anthropogenic effects of deep black coal mining.Results of this research showed that future development should be founded on spoil banks,dumps,and settling basins. According to the land-use plan,this zone occupies 44.9%of the area of interest,and its materials predominantly emanate from mining in the Ostrava-Karvina Coal District.For future foundation structures planned there,it is imperative to consult detailed engineering-geological study.However, attention to and reliance on this necessity is not reflected in the existing land-use plan.