Su un caso di non esistenza e su uno di esistenza e unicità della soluzione di un problema della magnetoidrodinamica stazionaria

Riassunto In questa nota si affrontano alcune questioni di esistenza e unicità della soluzione classica del problema del moto stazionario di un fluido omogeneo, incomprimibile, perfetto, elettricamente condutore attorno ad un ostacolo dielettrico e scarico in un punto del quale è situato un dipolo magnetico. Precisamente, si dimostra dapprima che, nel caso in cui il fluido abbia conduttività finita, il problema suddetto non ammette soluzione se al campo cinetico e al campo magnetico sono imposte condizioni all'infinito alquanto restrittive. Si dimostra poi che opportune ipotesi all'infinito assicurano l'esistenza e l'unicità della soluzione del medesimo problema nel caso in cui il fluido sia un conduttore perfetto.

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Summary This paper deals with some questions of classical solution existence and uniqueness for the problem of the steady flow of an homogeneous, incompressible, perfect, electrically conducting fluid past a dielectric and discharged obstacle in which a magnetic dipole is situated. More precisely, in the first place the non-existence of solutions of the above mentioned problem is proved for fluids of finite conductivity, if rather restrictive conditions are placed on behavior of the kinetic and magnetic fields at infinity. In the next place an existence and uniqueness theorem is established for perfectly conducting fluids.

     

Sulla influenza della polarizzazione delle radio-onde nei fenomeni di interazione ionosferica

Riassunto Si studia l'influenza della polarizzazione delle radio-onde su alcuni fenomeni non lineari nella ionosfera tramite una nuova e più completa relazione funzionale fra i vettori densità di corrente e campo elettrico. Tale studio riguarda la comparsa di onde di banda laterale e la loro dipendenza dalle direzioni di polarizzazione delle onde interagenti.

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Summary The influence of radio wave polarization on some nonlinear phenomena in the inosphere is studied through a new and more complete functional relation between current density and electric field vectors. This study is concerned with the occurrence of ?sideband? waves and their dependence on the polarization directions of interacting waves.

     

A new chiral lanthanide NMR probe for the determination of the enantiomeric purity of alpha-hydroxy acids and the absolute configuration of alpha-amino acids in water

A water-soluble, enantiopure lanthanide complex, SSS-[Ln x L3], has been assessed as an effective chiral derivatizing agent for the determination of the enantiomeric purity of alpha-hydroxy acids in aqueous solution. The complex displays superior chemical shift non-equivalence (DeltaDeltadelta approximately 2-11 ppm) for the diastereomeric resonances of interest compared to lanthanide shift reagents reported in the literature (DeltaDeltadelta <0.1 ppm, typically). 1H NMR studies have also revealed that SSS-[Ln x L3] can be used to determine the absolute configuration of alpha-amino acids at physiological pH, in water. The ability of SSS-[Ln x L3] to signal anion binding and, in particular, to distinguish between diastereomers through optical techniques such as lanthanide luminescence and circular dichroism has also been assessed.     

Hill Four-Body Problem with Oblate Bodies: An Application to the Sun–Jupiter–Hektor–Skamandrios System

We consider a restricted four-body problem, with a precise hierarchy between the bodies: two larger bodies and a smaller one, all three of oblate shape, and a fourth, infinitesimal body, in the neighborhood of the smaller of the three bodies. The three heavy bodies are assumed to move in a plane under their mutual gravity, and the fourth body to move in the three-dimensional space under the gravitational influence of the three heavy bodies, but without affecting them. We first find that the triangular central configuration of the three heavy oblate bodies is a scalene triangle (rather than an equilateral triangle as in the point mass case). Then, assuming that these three bodies are in such a central configuration, we perform a Hill approximation of the equations of motion describing the dynamics of the infinitesimal body in a neighborhood of the smaller body. Through the use of Hill’s variables and a limiting procedure, this approximation amounts to sending the two larger bodies to infinity. Finally, for the Hill approximation, we find the equilibrium points for the motion of the infinitesimal body and determine their stability. As a motivating example, we identify the three heavy bodies with the Sun, Jupiter, and the Jupiter’s Trojan asteroid Hektor, which are assumed to move in a triangular central configuration. Then, we consider the dynamics of Hektor’s moonlet Skamandrios.

     

The high-resolution infrared spectrum of Si2H6: rotation–torsion analysis of the ν5 and ν7 fundamentals,and torsional splittings in the degenerate vibrational states

The infrared active ν₇ and ν₅ fundamentals of disilane, coupled by an x,y Coriolis interaction, have been analysed on a Fourier transform spectrum between 2120 and 2225?cm^?1, at the Doppler limited spectral resolution. A Fermi resonance with 2ν ₂?+?ν₉ affects the Δ K?=?1 side of ν₇, and both ν₇ and ν₅ show the effects of several additional localized perturbations. Line splittings in the ν₅ transitions are not observed, showing that the torsional splitting in the ν₅ excited state and in the vibrational ground state are almost equal. The intrinsic torsional splitting of ν₇ is found to be smaller than in the ground vibrational state by 0.0085?cm^?1. This splitting value and those found for the other two infrared active degenerate fundamentals, ν₈ and ν₉, follow the trend expected from our theoretical predictions. Exploratory numerical calculations show that the decrease of the torsional splittings, observed in the fundamental degenerate vibrational states of disilane, can actually be accounted for by the head–tail and torsional Coriolis coupling of all the degenerate vibrational fundamentals, in several torsional states.