Caratterizzazione delle tracce per spazi con peso

Sunto Si prova un teorema di tracce per spazi di funzioni, definite su R ₊ ⁿ , con norme del tipo . Entrata in Redazione il 23 luglio 1969. Lavoro eseguito nell'ambito dei gruppi di ricerca del Comitato Nazionale per la Matematica del C.N.R.     

A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions

Comparison results of Talenti type for elliptic problems with Dirichlet boundary conditions have been widely investigated in recent decades. In this paper, we deal with Robin boundary conditions. Surprisingly, contrary to the Dirichlet case, Robin boundary conditions make the comparison sensitive to the dimension, and while the planar case seems to be completely settled, in higher dimensions some open problems are yet unsolved. © 2023 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.     

An explicit computation of the Bergman kernel function

We give an explicit computation of the Bergman kernel function on the domain

7‐Chloro‐3,6‐di­methyl‐1H‐indene‐2‐carb­aldehyde

In the crystal structure of C₁₂H₁₁ClO, the (planar) mol­ecules give rise to a parallel packing. A model crystal obtained by semi‐empirical and packing‐energy calculations is consistent with the observed structure.     

Theoretical and spectroscopic study of the effect of ring substitution on the adsorption of anisole on platinum

The adsorption of anisole, 3,5-dimethylanisole, and 3,5-bis-(trifluoromethyl)-anisole on Pt(111) was studied theoretically and compared to the adsorption of benzene using relativistically corrected density functional theory. A cluster of 31 platinum atoms was used to simulate the surface. The three anisoles were found to be less strongly adsorbed than the parent molecule benzene, 3,5-bis-(trifluoromethyl)-anisole showing weakest adsorption, with an adsorption energy of only one-third that of benzene. The theoretical study was complemented by in situ ATR-IR spectroscopy of the adsorption of the anisole derivatives on a polycrystalline Pt film. The spectroscopic study indicated that the adsorption strength of the anisoles follows the same order as predicted by the calculations. In addition, catalytic hydrogenation tests showed that the propensity to aromatic ring hydrogenation can also be correlated to the mode and strength of adsorption of the anisoles. The degree of saturation followed the same order as the adsorption strength found by the calculations and indicated by spectroscopy. Although 3,5-dimethyl substitution on anisole resulted in only a partial loss of adsorption energy and reactivity toward ring hydrogenation as compared to anisole, the substitution by CF(3) groups led to a large loss of adsorption energy and complete loss of reactivity toward aromatic ring saturation. Along with the study of the substituent effect on the adsorption of aromatic molecules, the correlation between adsorption and propensity to saturation of aromatic substrates could be corroborated.     

Modulation versus Templating: Fine‐Tuning of Hierarchally Porous PCN‐250 Using Fatty Acids To Engineer Guest Adsorption

Modulation and templating are two synthetic techniques that have garnered significant attention over the last several years for the preparation of hierarchically porous metal–organic frameworks (HP‐MOFs). In this study, by using fatty acids with different lengths and concentrations as dual‐functional modulators/templates, we were able to obtain HP‐MOFs with tunable mesopores that exhibit different pore diameters and locations. We found that the length and concentration of the fatty acids can determine if micelle formation occurs, which in turn dictates the porosity of the resulting HP‐MOFs. The HP‐MOFs with different mesopores differed in their performance in gas uptake and dye adsorption, and the structure–performance relationships were ascribed to the pore diameters and locations. This approach could provide a potentially universal method to efficiently introduce hierarchal mesopores into existing microporous MOF adsorbents with tunable properties.     

Radical-based grafting of GMA on sutures of different nature

Irradiation of a number of different sutures largely employed in the clinical practice with either high energy electrons or with γ-rays followed by quenching with glycidyl methacrylate (GMA) conveniently led to derivatization through a radical-based process. The radicals involved were detected by means of ESR spectroscopy and were characterized on the basis of their ESR spectral parameters which were also found to be consistent with the hfs constants predicted by DFT calculations. Evidence of the GMA derivatization of the sutures was obtained via(13)C CP-MAS NMR spectroscopy, while its extent was evaluated gravimetrically.