Contributo alla teoria degli operatori lineari

Alcuni dei risultati qui contenuti trovansi riassunti nella Nota postuma:S. Pincherle,Sulla permutabilità negli operatori lineari, ? Bollettino dell'Un. Mat. It. ?, t. 15 (1936), pp. 153–161; va inoltre avvertito che — colla scomparsa del compianto Maestro — l'ultimo capitolo della presente Memoria è rimasto incompleto, ciò che però non nuoce all'organicità del lavoro.     

Reactivity of lithium 2,3-dihydro-1-benzothiophene-1-oxide toward aldehydes and imines and DFT calculations

The sulfinyl carbanion derived from 2,3-dihydro-1-benzothiophene-1-oxide and its lithium salt has been investigated by DFT calculations. The lithium carbanion was treated with aldehydes and imines to give chiral hydroxy and amino derivatives, with high stereoselectivity at the carbon α to the sulfoxide group (trans diastereoisomers), but with low diastereoselectivity at the hydroxyl or amine group. DFT calculations were used to rationalize the different stereochemical behavior of cyclic and acyclic lithiated sulfoxides in the reaction with aldehydes and azomethines.     

New insights into the seleniranium ion promoted cyclization of prenyl and propenylbenzene aryl ethers

The chromane core is widely represented in nature being part of a wide array of secondary metabolites of plant, fungal, and bacterial origin. In this paper an improved method for the chemical synthesis of differently substituted chromanes is described. Substituted 2H-1-benzopyrans have been synthesized in good to excellent yields (52–81%) by treatment of 3,3-dimethylallyl and propenylbenzene ethers of differently substituted phenols with phenylselenyl chloride.     

Allenyl esters as quenching agents for ruthenium olefin metathesis catalysts

In the attempt to synthesize substituted allenyl esters through a metathesis coupling of unsubstituted allenyl esters and alkenes using a variety of ruthenium catalysts, it was discovered that allenyl esters themselves cleanly arrested the activity of the catalysts. Further studies suggests possible utility of allene esters as general quenching agents for metathesis reactions. To explore this idea, several representative olefin metathesis reactions, including ring closing, were successfully terminated by the addition of simple allenyl esters for more convenient purification.     

Ytterbium triflate catalyzed synthesis of chlorinated lactones

The direct synthesis of chlorolactones from differently substituted alkenoic acids, using either sodium hypochlorite or chloramine T as the source of electrophilic chlorine and ytterbium triflate hydrate as the Lewis acid is described. In both cases the reactions proceeded in good yields affording selectively five- or six-membered chlorolactones.     

Novel deletion of the E3A ubiquitin protein ligase gene detected by multiplex ligation-dependent probe amplification in a patient with Angelman syndrome

Angelman syndrome (AS) is a severe neurobehavioural disorder caused by failure of expression of the maternal copy of the imprinted domain located on 15q11-q13. There are different mechanisms leading to AS: maternal microdeletion, uniparental disomy, defects in a putative imprinting centre, mutations of the E3 ubiquitin protein ligase (UBE3A) gene. However, some of suspected cases of AS are still scored negative to all the latter mutations. Recently, it has been shown that a proportion of negative cases bear large deletions overlapping one or more exons of the UBE3A gene. These deletions are difficult to detect by conventional gene-scanning methods due to the masking effect by the non-deleted allele. In this study, we have used for the first time multiplex ligation-dependent probe amplification (MLPA) and comparative multiplex dosage analysis (CMDA) to search for large deletions affecting the UBE3A gene. Using this approach, we identified a novel causative deletion involving exon 8 in an affected sibling. Based on our results, we propose the use of MLPA as a fast, accurate and inexpensive test to detect large deletions in the UBE3A gene in a small but significant percentage of AS patients.     

Coupling capillary electrochromatography with mass spectrometry by using a liquid-junction nano-spray interface

Capillary electrochromatography (CEC) was coupled with mass spectrometry (MS) for the separation of some selected pesticides and drug enantiomers. CEC separations were carried out in fused silica capillaries packed with either 5 μm RP₁₈ silica or 5 μm silica modified vancomycin particles. The capillary column was connected with the MS utilizing a laboratory-made liquid-junction interface equipped with a 50 μm I.D. capillary-tip positioned at a few mm from the orifice of the MS. The CEC–MS set-up was operated without external pressure assistance during the electrochromatographic run commonly used to avoid bubble formation. However a hydrostatic pressure of a few kPa was applied only to the liquid-junction interface to optimize the ion-spray due to the low I.D. of the capillary-tip. In order to optimize the CEC–MS method, several experimental parameters were studied, namely the inlet pressure, the hydrostatic pressure into the liquid-junction interface, the type of sheath-liquid and the mobile phase. The application of an inlet pressure influenced only analyte retention times that were shortened by increasing the pressure. On the contrary the hydrostatic pressure applied to the interface increased the flow rate into the tip also increasing the ion-signal recorded in the mass spectrometry. The ion-signal raised almost linearly by increasing the outlet pressure till 3.5 kPa and then decreased. The separation of the selected pesticides was not influenced at all changing the hydrostatic pressure on the interface. Some basic enantiomeric compounds of pharmaceutical interest were successfully separated by CEC achieving good resolution. They were detected by MS with limit of detection in a range of 0.24–0.60 μg/mL.     

Iron–cobalt nanocrystalline alloy supported on a cubic mesostructured silica matrix: FeCo/SBA-16 porous nanocomposites

A series of novel nanocomposites constituted of FeCo nanoparticles dispersed in an ordered cubic Im3m mesoporous silica matrix (SBA-16) have been successfully synthesized using the wet impregnation method. SBA-16, prepared using the non-ionic Pluronic 127 triblock copolymer as a structure-directing agent, is an excellent support for catalytic nanoparticles because of its peculiar three-dimensional cage-like structure, high surface area, thick walls, and high thermal stability. Low-angle X-ray diffraction, N₂ physisorption, and transmission electron microscopy analyses show that after metal loading, calcination at 500 °C, and reduction in H₂ flux at 800 °C, the nanocomposites retain the well-ordered structure of the matrix with cubic symmetry of pores. FeCo alloy nanoparticles with spherical shape and narrow size distribution (4–8 nm) are homogeneoulsy distributed throughout the matrix and they seem in a large extent to be allocated inside the pores.     

Perturbed asymptotically linear problems

The aim of this paper is to investigate the existence of solutions of the semilinear elliptic problem $$\left\{\begin{array}{ll} -\Delta u\ =\ p(x, u) + \varepsilon g(x, u)\quad {\rm in}\,\, \Omega, \\ u=0 \quad\quad\quad\quad\quad\quad\quad\quad\quad\,\,\,\,\,\,{\rm on}\,\, \partial\Omega, \end{array} \right. \quad\quad\quad(0.1) $$ where Ω is an open bounded domain of ${\mathbb{R}^N}$ , ${\varepsilon\in\mathbb{R}, p}$ is subcritical and asymptotically linear at infinity, and g is just a continuous function. Even when this problem has not a variational structure on ${H^1_0(\Omega)}$ , suitable procedures and estimates allow us to prove that the number of distinct critical levels of the functional associated to the unperturbed problem is “stable” under small perturbations, in particular obtaining multiplicity results if p is odd, both in the non-resonant and in the resonant case.