Motion of rigid bodies in a set of redundant variables

In this article we study the conditions for obtaining canonical transformationsy=f(x) of the phase space, wherey(y ₁,y ₂,...,y _2n ) andx(x ₁,x ₂,...,x _2m ) in such a way that the number of variables is increased. In particular, this study is applied to the rotational motion in functions of the Eulerian parameters (q ₀,q ₁,q ₂,q ₃) and their conjugate momenta (Q ₀,Q ₁,Q ₂,Q ₃) or in functions of complex variables (z ₁,z ₂,z ₃,z ₄) and their conjugate momenta (Z ₁,Z ₂,Z ₃,Z ₄) defined by means of the previous variables. Finally, our article include some properties on the rotational motion of a rigid body moving about a fixed point.     

The Stellar Content of Active Galaxies

We present the results of a long-slit spectroscopic study of 38 active and four normal galaxies. Stellar absorption features, continuum colours and their radial variations are analysed in an effort to characterize the stellar population in these galaxies and detect the presence of a featureless continuum underlying the starlight spectral component. Spatial variations of the equivalent widths of conspicuous absorption lines and continuum colours are detected in most galaxies. Star-forming rings, in particular, leave clear fingerprints in the equivalent widths and colour profiles. We find that the stellar populations in the inner regions of active galaxies present a variety of characteristics, and cannot be represented by a single starlight template. Dilution of the stellar lines by an underlying featureless continuum is detected in most broad-lined objects, but little or no dilution is found for most of the 20 type 2 Seyferts in the sample. Colour gradients are also ubiquitous. In particular, all but one of the observed Seyfert 2s are redder at the nucleus than in its immediate vicinity. Possible consequences of these findings are briefly outlined.     

Emission-line properties of Seyfert 2 nuclei

This is the third paper of a series devoted to the study of the global properties of Joguet's sample of 79 nearby galaxies observable from the southern hemisphere, of which 65 are Seyfert 2 galaxies. We use the population synthesis models of Paper II to derive 'pure' emission-line spectra for the Seyfert 2 galaxies in the sample, and thus explore the statistical properties of the nuclear nebular components and their relation to the stellar populations. We find that the emission-line clouds suffer substantially more extinction than the starlight, and we confirm the correlations between stellar and nebular velocity dispersions and between emission-line luminosity and velocity dispersions, although with substantial scatter. Nuclear luminosities correlate with stellar velocity dispersions, but Seyferts with conspicuous star-forming activity deviate systematically towards higher luminosities. Removing the contribution of young stars to the optical continuum produces a tighter and steeper relation,   L ∝σ⁴_★  , consistent with the Faber–Jackson law.
Emission-line ratios indicative of the gas excitation such as [O  iii ]/Hβ and [O  iii ]/[O  ii ] are statistically smaller for Seyferts with significant star formation, implying that ionization by massive stars is responsible for a substantial and sometimes even a dominant fraction of the Hβ and [O  ii ] fluxes. We use our models to constrain the maximum fraction of the ionizing power that can be generated by a hidden active galactic nucleus (AGN). We correlate this fraction with classical indicators of AGN photoionization (i.e. X-ray luminosity and nebular excitation), but find no significant correlations. Thus, while there is a strong contribution of starbursts to the excitation of the nuclear nebular emission in low-luminosity Seyferts, the contribution of the hidden AGN remains elusive even in hard X-rays.     

Catchment scale hydrology of an irrigated cropping system under soil conservation practices

Soil erosion by water is a pressing environmental problem caused and suffered by agriculture in Mediterranean environments. Soil conservation practices can contribute to alleviating this problem. The aim of this study is to gain more profound knowledge of the effects of conservation practices on soil losses by linking crop management and soil status to runoff and sediment losses measured at the outlet of a catchment during seven years. The catchment has 27.42 ha and is located in a commercial farm in southern Spain, where a package of soil conservation practices is an essential component of the farming system. The catchment is devoted to irrigated annual crops with maize–cotton–wheat as the primary rotation. Mean annual rainfall‐induced runoff coefficient was 0.14 and mean annual soil loss was 2.4 Mg ha^?1 y^?1. Irrigation contributed to 40% of the crop water supply, but the amount of runoff and sediment yield that it generated was negligible. A Principal Components Analysis showed that total soil loss is determined by the magnitude of the event (rainfall and runoff depths, duration) and by factors related to the aggressiveness of the events (rainfall intensity and preceding soil moisture). A third component showed the importance of crop coverage to reduce sediment losses. Cover crops grown during autumn and early winter and crop residues protecting the soil surface enhanced soil conservation notably. The role of irrigation to facilitate growing cover crops in Mediterranean environments is discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Stoichiometry among bioactive trace metals in seawater on the Bering Sea shelf

The distribution of Al, Mn, Fe, Co, Ni, Cu, Zn, Cd, and Pb in seawater was investigated on the Bering Sea shelf (56–64°N, 165–169°W) in September 2000. The unfiltered and filtered seawater samples were used for determination of total dissolvable (TD) and dissolved (D) metals (M), respectively. The TD-M concentrations were generally higher than in the Pacific Ocean. TD-Cd was highest in deep water of the outer shelf domain and dominated by dissolved species. The other TD-M were highest at stations close to the Yukon River delta and had higher fractions of labile particulate (LP) species that were obtained as the difference between TD-M and D-M. Dissolved Al, Ni, and Cu were characterized by input from the Yukon River. Dissolved Mn and Co showed maximums on the bottom of the coastal domain, suggesting influence of sedimentary Mn reduction. The correlations of D-Zn, D-Cd, and macronutrients indicated their distributions were largely controlled through uptake by microorganisms and remineralization from settling particles. All these three processes (river input, sedimentary reduction, and biogeochemical cycle) had an influence on the distribution of D-Fe. D-Pb was fairly uniformly distributed in the study area. The stoichiometry of D-M in the Bering Sea shelf showed enrichment of Co and Pb and depletion of Ni, Cu, Zn, and Cd compared with that in the North Pacific. The LP-M/LP-Al ratio revealed significant enrichment of the other eight metals relative to their crustal abundance, suggesting importance of formation of Fe–Mn oxides and adsorption of trace metals on the oxides.     

On the motion of three rigid bodies: Central configurations

In the present paper, the motion of three rigid bodies is considered. With a set of new variables, and the 10 first integrals of the motion, the problem is reduced to a system of order 25 and one quadrature. The plane motions are characterized, and finally, an equation for the existence of central configurations (in particular, Lagrangian and Eulerian solutions) has been found. Besides, the case of three axisymmetric ellipsoids is studied.     

Areas of fuzzy geographical entities

Fuzzy Geographical Entities (FGEs) refer in this paper to geographical entities with fuzzy spatial extent. The use of FGEs in geographical information systems requires the existence of operators capable of processing them. In this paper, our contribution to that field focuses on the computation of areas. Two methods are considered, one crisp due to Rosenfeld (1984 Rosenfeld, A. 1984. The diameter of a fuzzy set. Fuzzy Sets and Systems, 13: 241–246. [Crossref], [Web of Science ®] , [Google Scholar]), which has limited applicability, and the other fuzzy, which is a new approach. The new fuzzy area operator gives more information about the possible values of the area and enables the fuzziness in the spatial extent of the entity to be propagated to the area. Crisp and fuzzy areas have different meanings, and the use of one or the other depends not only on the purpose of the computation but also on the semantics of the membership functions. When the FGEs are represented by normal fuzzy sets, the fuzzy area operator generates fuzzy numbers, and therefore arithmetic operations can be performed with them using fuzzy arithmetic. However, we show that care must be taken with the use of the fuzzy arithmetic operators because, in some situations, the usual operators should not be applied. Properties of the Rosenfeld and fuzzy area operators are analysed, establishing a parallel with properties of the areas of crisp sets.