Un teorema di Radon-Nikodym per funzioni d’insieme subadditive

Riassunto In questo articolo si danno delle condizioni necessarie e sufficienti affinchè per una fissata coppia di funzioni d’insieme ν, μ crescenti esista una funzionef tale che ν=∫fdμ. Si ottiene cosi una proposizione comprendente il teorema di R-N. classico e dei teoremi di R-N., presentati da altri autori, riguardanti le funzioni d’insieme finitamente additive e le funzioni d’insieme subadditive e continue per successioni crescenti.

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Résumé Soient ν, μ:A→[0,+∞) deux fonctions d’ensemble croissantes sur une σ-algèbre d’ensemblesA⊂T(X), telles que pour chaqueA∈A avec ν(A)=μ(A)=0 on a l’égalité μ(A)=μ(A∪S) ∀S∈A (c’est le cas des fonctions sousadditives!). Dans cet article on démontre qu’il existe une fonctionf A-measurable telle que ν=∫fdμ si et seulement si pour chaquer∈(0, + ∞) il y a un ensembleA _r∈A qui vérifie les trois conditions suivantes: (1) ,B∈A avecB⊂A; (2) A (3) limν(A _r)=0. On déduit ainsi une proposition qui a été donnée parI. Forana: ?Si ν, μ sont simplement additives, il existe une fonctionf telle que ν=∫fdμ si et seulement si ν≪μ et la fonction d’ensemble additive a une decomposition de Hahn pour chaquer∈(0, + ∞), c’est-á-dire il y aA _r∈A tel que ?.

     

Temporal evolution of DMS and DMSP in Antarctic Coastal Sea water

The temporal evolution of concentrations of dimethylsulphide (DMS), its precursor dimethylsulphoniopropionate (DMSP) and chlorophyll a is surveyed weekly in the water column and in a landfast ice core at a coastal station of Gerlache Inlet (Terra Nova Bay, Antarctica) from 27 November 2000 to 14 February 2001. The DMS and DMSP profile concentrations in the water column are similar and show a clear temporal trend, with minimum values (<0.7?nM) at all depths occurring on 27 November 2000 and maximum values (4.8 × 10²?nM for DMS and 1.8 × 10²?nM for DMSP) in surface water on 27 December 2000 for DMS and on 19 December 2000 for DMSP. When the sea-ice cover is present, the temporal evolution of DMSP closely follows that of chlorophyll a in the water column, supporting the idea that DMSP, and therefore DMS, has a phytoplanktonic origin. However, when the ice cover breaks up during the late austral summer, a second phytoplankton bloom occurs, while the DMSP concentration in the sea-water column remains very low. In the ice core, the results show higher concentrations of DMSP than those of the underlying sea water, highlighting the important role of sea ice in the sulphur cycle of the Antarctic ecosystem.     

Kerr metric,geodesic motion,and Flyby Anomaly in fourth-order Conformal Gravity

In this paper we analyze the Kerr geometry in the context of Conformal Gravity, an alternative theory of gravitation, which is a direct extension of General Relativity (GR). Following previous studies in the literature, we introduce an explicit expression of the Kerr metric in Conformal Gravity, which naturally reduces to the standard GR Kerr geometry in the absence of Conformal Gravity effects. As in the standard case, we show that the Hamilton–Jacobi equation governing geodesic motion in a space-time based on this geometry is indeed separable and that a fourth constant of motion—similar to Carter’s constant—can also be introduced in Conformal Gravity. Consequently, we derive the fundamental equations of geodesic motion and show that the problem of solving these equations can be reduced to one of quadratures. In particular, we study the resulting time-like geodesics in Conformal Gravity Kerr geometry by numerically integrating the equations of motion for Earth flyby trajectories of spacecraft. We then compare our results with the existing data of the Flyby Anomaly in order to ascertain whether Conformal Gravity corrections are possibly the origin of this gravitational anomaly. Although Conformal Gravity slightly affects the trajectories of geodesic motion around a rotating spherical object, we show that these corrections are minimal and are not expected to be the origin of the Flyby Anomaly, unless conformal parameters are drastically different from current estimates. Therefore, our results confirm previous analyses, showing that modifications due to Conformal Gravity are not likely to be detected at the Solar System level, but might affect gravity at the galactic or cosmological scale.     

Binding of Androgen- and Estrogen-Like Flavonoids to Their Cognate (Non)Nuclear Receptors: A Comparison by Computational Prediction

Flavonoids are plant bioactives that are recognized as hormone-like polyphenols because of their similarity to the endogenous sex steroids 17β-estradiol and testosterone, and to their estrogen- and androgen-like activity. Most efforts to verify flavonoid binding to nuclear receptors (NRs) and explain their action have been focused on ERα, while less attention has been paid to other nuclear and non-nuclear membrane androgen and estrogen receptors. Here, we investigate six flavonoids (apigenin, genistein, luteolin, naringenin, quercetin, and resveratrol) that are widely present in fruits and vegetables, and often used as replacement therapy in menopause. We performed comparative computational docking simulations to predict their capability of binding nuclear receptors ERα, ERβ, ERRβ, ERRγ, androgen receptor (AR), and its variant AR^T877A and membrane receptors for androgens, i.e., ZIP9, GPRC6A, OXER1, TRPM8, and estrogens, i.e., G Protein-Coupled Estrogen Receptor (GPER). In agreement with data reported in literature, our results suggest that these flavonoids show a relevant degree of complementarity with both estrogen and androgen NR binding sites, likely triggering genomic-mediated effects. It is noteworthy that reliable protein–ligand complexes and estimated interaction energies were also obtained for some suggested estrogen and androgen membrane receptors, indicating that flavonoids could also exert non-genomic actions. Further investigations are needed to clarify flavonoid multiple genomic and non-genomic effects. Caution in their administration could be necessary, until the safe assumption of these natural molecules that are largely present in food is assured.     

Electrolytic Oxidation of Thiocyanate and Selenocyanate Salts and the Photoelectrochemical Effect.

New photosensitive materials can be obtained by electrochemical oxidation of thiocyanate and selenocyanate salts. Using (K,Na)SCN eutectic melt, the formation of an electrodic deposit, with photoelectrochemical properties, has already been reported by us. To improve the photoelectrochemical characteristics of the deposit, futher investigations were carried out in the following sistems: selenocyanate ammoniate, KSCH-Acetamide eutectic mixture and KSCN ethylene carbonate solution:. Attempts to obtain a massive deposit in the ammoniate solution were unsuccessful due to ammonia oxidation. Measurements performed on the other KSCN systems show that temperature is a parameter of remarkable importance. In fact, lowering the temperature one obtains a decrease on formation of parathiocyanogen on behalf of the polytrithiocyanogen, the species that gives rise to the photoeffect.