On a relation among lie series

In this paper we discuss the relation between the structures of the series expansion for the Dragt and Finn composition of Lie transforms and for a transformation introduced by Giorgilli and Galgani. A recursive algorithm is presented which is used to generate the series expansion for the composition of Lie transforms. This algorithm strongly resembles the algorithm of Giorgilli and Galgani, and differs from it only in an ordering property. The relation with the algorithms of Kamel and Henrard for Deprit's direct and inverse series is also discussed.     

Geodetic calculus with block-averages observations on the sphere

The calculus of spherical harmonic representation of fields of geodetic interest is often performed by applying integral formulas to block-averaged quantities. Due to the dependence of the block areas on latitude, it is difficult to perform a rigorous computation; in this paper the effects of approximations related to the loss of orthogonality in the discretization and averaging procedures are numerically studied; a simple numerical approach to improve the efficiency of the estimates is presented.     

A numerical experiment of integrated geodesy

The paper has two main targets: to prove by numerical experiment on simulated data (exact solution a priori known) that the integrated approach gives superior results that can’t be achieved neither by pure (“incorrect”) λ.s. adjustment nor by a λ.s. adjustment of observations corrected by some a priori long wave length gravity model; to find among many strategies for approximate solutions, one which preserves most of the features of the exact one, although with a much simpler numerical structure.     

Some problems related to satellite gradiometry

Observation equations for a gradiometer in inertial flight are described, and the effects of orbit and attitude errors are modelled, showing that, when high precision direction observations are missing, the use of rotation invariant equations is advantageous. The invariant form of the equations is analysed by demonstrating the necessity of using as observables the eigenvalues of the gravitational tensor instead of classic invariants. The singularity of the problem in spherical approximation is shown, and consequently the necessity of taking into accountJ ₂ in the reference field used in the linearization.     

Soil-erosion assessment at basin scale through 137Cs content analysis based on pedo-morphological units

Soil loss evaluation by means of radioisotopic content measurements represents a promising technique, half-way between field surveys and theoretical models, which still suffers from its practical limits when applied at basin scale. A main limit is represented by the costs of field investigations and laboratory investigations on the high number of soil samples required by a traditional sampling scheme, such as regular grid or transects. A non-conventional soil sampling scheme was tested with the aim to consider a relative scanty number of soil samples and to verify the feasibility of this technique on large areas. This scheme was based on the hypothesis that land analysis and classification could point out areas characterised by homogeneous behaviour with respect to the ¹³⁷Cs deposition and transmission model. A Geographic Information System (GIS)-aided procedure allowed to classify the selected basin area in pedo-morphological units, representative of the different pedologic, morphologic and land-use conditions, to locate few sampling points for each unit. Outcomes pointed out a low correlation between ¹³⁷Cs contents and soil physical and compositional characteristics. Nevertheless, the isotopic methodology allowed to estimate a total soil loss value at basin scale almost consistent with both observed data, given by reservoir sedimentation measurements and estimates from the application of the RUSLE model. Thus, the results can be considered encouraging and they allow to deem that the isotopic methodology can be refined in order to account for erosion and deposition processes even at river basin scale and with a limited number of soil samples.     

Resource partitioning among air‐breathing marine predators: are body size and mouth diameter the major determinants?

Although the body size of consumers may be a determinant factor in structuring food webs, recent evidence indicates that body size may fail to fully explain differences in the resource use patterns of predators in some situations. Here we compared the trophic niche of three sympatric and sexually dimorphic air‐breathing marine predators (the South American sea lion, Otaria flavescens, the South American fur seal, Arctocephalus australis, and the Magellanic penguin, Spheniscus magellanicus) in three areas of the Southwestern Atlantic Ocean (Río de la Plata and adjoining areas, Northern Patagonia and Southern Patagonia), in order to assess the importance of body size and mouth diameter in determining resource partitioning. Body weight and palate/bill breadth were used to characterize the morphology of each sex and species, whereas the trophic niche was assessed through the use of stable isotope ratios of carbon and nitrogen. The quantitative method Stable Isotope Bayesian Ellipses in R (SIBER) was used to compute the area of the Bayesian ellipses and the overlap of the isotopic niches. The results showed that morphological similarity was significantly correlated with isotopic distance between groups within the δ¹³C–δ¹⁵N bi‐plot space in the Río de la Plata area, but not in Northern and Southern Patagonia. Furthermore, resource partitioning between groups changed regionally, and some morphologically distinct groups exhibited a large trophic overlap in certain areas, such as the case of male penguins and male sea lions in Southern Patagonia. Conversely, female sea lions always overlapped with the much larger males of the same species, but never overlapped with the morphologically similar male fur seals. These results indicate that body size and mouth diameter are just two of the factors involved in resource partitioning within the guild of air‐breathing predators considered here, and for whom – under certain environmental conditions – other factors are more important than morphology.