Nilpotent Gelfand pairs and spherical transforms of Schwartz functions I: rank-one actions on the centre

The spectrum of a Gelfand pair of the form ${(K\ltimes N,K)}$ , where N is a nilpotent group, can be embedded in a Euclidean space ${{\mathbb R}^d}$ . The identification of the spherical transforms of K-invariant Schwartz functions on N with the restrictions to the spectrum of Schwartz functions on ${{\mathbb R}^d}$ has been proved already when N is a Heisenberg group and in the case where N?=?N _3,2 is the free two-step nilpotent Lie group with three generators, with K?=?SO₃ (Astengo et?al. in J Funct Anal 251:772–791, 2007; Astengo et?al. in J Funct Anal 256:1565–1587, 2009; Fischer and Ricci in Ann Inst Fourier Gren 59:2143–2168, 2009). We prove that the same identification holds for all pairs in which the K-orbits in the centre of N are spheres. In the appendix, we produce bases of K-invariant polynomials on the Lie algebra ${{\mathfrak n}}$ of N for all Gelfand pairs ${(K\ltimes N,K)}$ in Vinberg’s list (Vinberg in Trans Moscow Math Soc 64:47–80, 2003; Yakimova in Transform Groups 11:305–335, 2006).     

Semi-rigid analogues of the calcium antagonist verapamil: A molecular modelling study

Summary In this work the rigid-analogue approach has been used to obtain information on the active conformation(s) of the calcium antagonist verapamil. A series of semi-rigid analogues of verapamil were synthesized and their biological activities evaluated on guinea-pig heart and aorta. These molecules were analysed by means of molecular modelling techniques.On the basis of the pharmacological profile and conformational analysis of these compounds, two different models for negative inotropic and negative chronotropic activity are proposed. The two actions seem to be due to conformations of the molecules which differ in the orientation of their phenylethylamino groups.     

Sulla risolubilita' degli operatori differenziali invarianti sul gruppo di Heisenberg

In questa nota si considera il problema della risolubilità per operatori del secondo ordine, invarianti a sinistra e omogenei, sul gruppo di HeisenbergH _n. Si presenta un approccio al problema basato sul prolungamento analitico dei coefficienti degli operatori, a partire dai risultati noti per il sub-Laplaciano. I dettagli sono contenuti in due articoli degli autori, in collaborazione con F. De Mari [DPR] e D. Müller [MPR]. Conferenza tenuta da F. Ricci il 25 ottobre 1995     

Femtosecond dynamics of Co thin films on Si support

The ultrafast electron and spin dynamics of Co films was investigated using a femto-second pump-probe technique. The samples were magnetically characterized by means of magnetooptical Kerr effect and non-optical magnetometers, i.e. superconductive quantum interference device and alternating gradient field magnetometer. Time evolution of both, Kerr rotation and ellipticity, was measured at different points of the static hysteresis cycle. This allowed separating magnetic and non-magnetic contributions to the signal. The sample magnetization was found to drop within 200 fs, following the pulse cross-correlation trace, while the magnetization recovery time was found to last few picoseconds.     

X-ray single-crystal structure and magnetic properties of Fe[CH(3)PO(3))] x H(2)O: a layered weak ferromagnet

The crystal and molecular structure of the layered weak-ferromagnet Fe[CH(3)PO(3)] x H(2)O has been solved by X-ray single-crystal diffraction techniques. Crystal data for Fe[CH(3)PO(3)] x H(2)O are the following: orthorhombic space group Pna2(1); a =17.538(2), b = 4.814(1), c = 5.719(1) A. The structure is lamellar, and it consists of alternating organic and inorganic layers along the a direction of the unit cell. The inorganic layers are made of Fe(II) ions octahedrally coordinated by five phosphonate oxygen atoms and one from oxygen of the water molecule. Each phosphonate group coordinates four metal ions, through chelation and bridging, making in this way a cross-linked Fe-O network. The resultant layers are then separated by bilayers of the methyl groups, with van der Waals contacts between them. The compound is air stable, and it dehydrates under inert atmosphere at temperatures above 120 degrees C. The oxidation state of the metal ion is +2, and the electronic configuration is d(6)( )()high spin (S = 2), as determined from dc magnetic susceptibility measurements from 150 K to ambient temperature. Below 100 K, the magnetic moment of Fe[CH(3)PO(3)] x H(2)O rises rapidly to a maximum at T(max) approximately equal to 24 K, and then it decreases again. The onset of peak at T = 25 K is associated with the 3D antiferromagnetic long-range ordering, T(N). The observed critical temperature, T(N), is like all the other previously reported Fe(II) phosphonates, and it appears to be nearly independent of the interlayer spacing in this family of hybrid organic-inorganic layered compounds. Below T(N), the compound behaves as a "weak ferromagnet", and represents the third kind of magnetic materials with a spontaneous magnetization below a finite critical temperature, ferromagnets and ferrimagnets being the other two types.     

The interaction of 4′, 6-diamidino-2-phenylindole (DAPI) with pepsin

We recently found that the fluorescent dye DAPI, well-known for its use with nucleic acids, is also able to interact with proteins as well as ordered phospholipids assemblies. The interaction of DAPI with pepsin under different conditions of pH and ionic strength was studied with fluorescence and circular dichroism techniques. From a comparison of the results obtained, the interaction appears to be rather tight and specific, dependent on both electrostatic and hydrophobic forces, and able to probe the tridimensional conformation of the protein.     

Ultrafast temporal evolution of interatomic Coulombic decay in NeKr dimers

We investigate interatomic Coulombic decay in NeKr dimers after neon inner-valence photoionization [Ne⁺(2s⁻¹)] using a synchrotron light source. We measure with high energy resolution the two singly charged ions of the Coulomb-exploding dimer dication and the photoelectron in coincidence. By carefully tracing the post-collision interaction between the photoelectron and the emitted ICD electron we are able to probe the temporal evolution of the state as it decays. Although the ionizing light pulses are 80 picoseconds long, we determine the lifetime of the intermediate dimer cation state and visualize the contraction of the nuclear structure on the femtosecond time scale.

We investigate the time-resolved dynamics of interatomic Coulombic decay in NeKr dimers after neon inner-valence photoionization using a synchrotron light source.