Sulla K-variazione Essenziale di Una Funzione reale

In this paper we consider a definition of essentialK-variation for real functions which gives information on the absolute integrability of its approximate derivate on a measurable set.     

Primitive rispetto all’ oscillazione

We study the real valued functions having a primitive with respect to the oscillation or a primitive with respect to the oscillation up to anegligible set.

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Supported by MURST of Italy.     

Isochronous systems and their quantization

We review recent results about classical isochronous systems characterized by the presence of an open (hence fully dimensional) region in their phase space in which all their solutions are completely periodic (i.e., periodic in all degrees of freedom) with the same fixed period (independent of the initial data provided they are inside the isochronicity region). We report a technique for generating such systems, whose wide applicability justifies the statement that isochronous systems are not rare. We also present an analogous technique applicable to a vast class of Hamiltonian systems and generating isochronous Hamiltonian systems. We also report some results concerning the quantized versions of such systems.     

Global weak solutions to the Nordström-Vlasov system

The Nordström-Vlasov system is a Lorentz invariant model for a self-gravitating collisionless gas. We establish suitable a priori bounds on the solutions of this system, which together with energy estimates and the smoothing effect of “momentum averaging” yield the existence of global weak solutions to the corresponding initial value problem. In the process we improve the continuation criterion for classical solutions which was derived recently. The weak solutions are shown to preserve mass.     

Shape recognition of alkylammonium ions by 1,3-bridged calix[5]arene crown-6 ethers: endo- vs exo-cavity complexation

A series of tri-O-substituted 1,3-bridged calix[5]arene crown-6 ethers bearing alkyl, arylalkyl, alkoxyalkyl, and alkoxycarbonylmethyl residues at the lower rim and either (t)()Bu or H substituents at the upper rim have been synthesized. (1)H NMR studies have shown that p-tert-butylcalix[5]crowns, irrespective of the size and nature of their lower rim pendant groups, adopt preorganized conelike conformations, whereas p-H-calix[5]crowns with bulky substituents preferentially exist in solution as partial cone conformers (C(1) symmetry). Calix[5]crown derivatives behave as mono- or ditopic receptors for isomeric butylammonium ions, forming endo-cavity (inside the calixarene cup) and/or exo-cavity (at the crown ether moiety) 1:1 complexes according to the shape of the guest. These two binding modes can be clearly distinguished and monitored by (1)H NMR titration experiments.     

The Lax representation for an integrable class of relativistic dynamical systems

We exhibit the Lax pair for the class of relativistic dynamical systems recently introduced by Ruijsenaars and Schneider, whose equations of motion read, whereB is an arbitrary constant and the Weierstrass elliptic function.For the 3 academic years 1983–1986     

X-ray and mössbauer studies of tricyclohexyltin(IV) halides. The crystal structures of (cyclo-C6H11)3SnX (X = F,Br and I)

The structures of tricyclohexyltin fluoride (I), bromide (II) and iodide (III) have been determined by X-ray analysis. Compound I crystallizes in the space group P2₁/m with a = 10.422(6), b = 17.238(9), c = 5.769(3) Å, β = 104.6(1)° and Z = 2. Compounds II and III crystallize in the space group Pcmn with a = 10.427(6), b = 16.914(9), c = 11.366(6) Å, Z = 4; and a = 10.400(6), b = 16.900(10), c = 11.400(4) Å, Z = 4, respectively. All three structures consist of discrete tetrahedral (cyclo-C₆H₁₁)₃SnX units.The temperature dependence of the Mössbauer resonance areas has been examined in order to obtain information about the relationship between chemical structure and lattice dynamics.     

Iron-Iridium Mixed-Metal Carbonyl Clusters: A Mössbauer Study of the Structure and of the Adsorption of [Fe2Ir2(CO)12]2− on MgO

¹⁹³Ir and ⁵⁷Fe Mössbauer spectroscopy was used to investigate the structure of the [Fe₂Ir₂(CO)₁₂]^2- cluster compound and the adsorption of this cluster on hydrated MgO. Supported samples were prepared by impregnation of the magnesia with solutions of [Et₄N]₂[Fe₂Ir₂(CO)₁₂] in acetone. The Mössbauer and FT-IR spectra of the MgO-supported cluster confirm that the bimetallic carbonyl is molecularly physisorbed onto MgO without undergoing any transformation or decomposition. The easy solvent extraction of the intact cluster from the oxide surface excludes ion pairing between the cluster anion and the Mg²⁺ surface sites. Mössbauer spectra are in agreement with the refined structure of the molecular cluster and the temperature dependence of the ⁵⁷Fe Mössbauer spectra above 80 K is consistent with the low degree of interaction of the cluster with the support. This technique, therefore, appears to be promising in order to infer structural information when X-ray determination fails.     

Syntheses and crystal structures of dinuclear complexes containing d-block and f-block luminophores. Sensitization of NIR luminescence from Yb(III), Nd(III), and Er(III) centers by energy transfer from Re(I)- and Pt(II)-bipyrimidine metal centers

Mononuclear complexes [Re(bpym)(CO)(3)Cl] and [Pt(bpym)(CC-C(6)H(4)CF(3))(2)] (bpym = 2,2'-bipyrimidine), in which one of the bipyrimidine sites is vacant, have been used as "complex ligands" to prepare heterodinuclear d-f complexes in which a lanthanide tris(1,3-diketonate) unit is attached to the secondary bipyrimidine site to evaluate the ability of d-block chromophores to act as antennae for causing sensitized near-infrared (NIR) luminescence from adjacent lanthanide(III) centers. The two sets of complexes so prepared are [Re(CO)(3)Cl(mu-bpym)Ln(fod)(3)] (abbreviated as Re-Ln; where Ln = Yb, Nd, Er) and [(F(3)C-C(6)H(4)-CC)(2)Pt(mu-bpym)Ln(hfac)(3)] (abbreviated as Pt-Ln; where Ln = Nd, Gd). Members of both series have been structurally characterized; the metal-metal separation across the bipyrimidine bridge is approximately 6.3 A in each case. In these complexes, the (3)MLCT (MLCT = metal to ligand charge-transfer) luminescences of the mononuclear [Re(bpym)(CO)(3)Cl] and [Pt(bpym)(CC-C(6)H(4)CF(3))(2)] complexes are quenched by energy transfer to those lanthanides (Ln = Yb, Nd, Er) that have low-lying f-f states capable of NIR luminescence; as a result, sensitized NIR luminescence is seen from the lanthanide center following excitation of the d-block unit. In the solid state, quenching of the luminescence from the d-block chromophore is complete, indicating efficient d --> f energy transfer, as a result of the short metal-metal separation across the bipyrimidine bridge. In a CH(2)Cl(2) solution, partial dissociation of the dinuclear complexes into the mononuclear units occurs, with the result that some (3)MLCT luminescence is observed from mononuclear [Re(bpym)(CO)(3)Cl] or [Pt(bpym)(CC-C(6)H(4)CF(3))(2)] present in the equilibrium mixture. Solution UV-vis and luminescence titrations, carried out by the addition of portions of Ln(fod)(3)(H(2)O)(2) or Ln(hfac)(3)(H(2)O)(2) to the d-block complex ligands, indicate that binding of the lanthanide tris(1,3-diketonate) unit at the secondary bipyrimidine site to give the d-f dinuclear complexes occurs with an association constant of ca. 10(5) M(-)(1).