Local boundedness of minimizers in a limit case

We prove the local boundedness of minimizers of a functional with anisotropic polynomial growth. The result here obtained is optimal if compared with previously know counterexamples. This work has been performed as a part of a National Research Project, supported by MPI (40%, 1987).     

On a class of quasilinear hyperbolic reducible systems allowing for special wave interactions

Summary A class of quasilinear hyperbolic reducible systems, which involve two first order homogeneous equations in one space dimension and time, is characterized by requiring the associated hodograph system to reduce to a particular canonical form allowing explicit integration. Furthermore for the mathematical models so determined, it is shown that any two pulses travelling in opposite directions interact on colliding but emerge with unaffected profiles from the interaction region. Such a kind of situation, though in a different physical context, is similar to that occurring in nonlinear dispersive media when two solitons collide but emerge unaltered from the interaction. Finally, the governing system of isentropic fluid-dynamics is considered. In this case it is determined a set of multiparameter pressure-density laws which allow for the soliton-like interactions studied herein.

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Riassunto In questo lavoro si caratterizza una classe di sistemi quasilineari del primo ordine iperbolici e riducibili che consentono un'esplicita integrazione dell'associato sistema odografo. Si dimonstra poi che i modelli matematici così determinati sono atti a descrivere interazioni di tipo solitonico tra onde semplici che viaggiano in direzione opposta. Infine nel caso del sistema della fluidodinamica isentropica, si caratterizzano delle forme funzionali per il legame pressione-densità che sono compatibili con le particolari interazioni tra onde semplici del tipo su menzionato.

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This work was supported by the C.N.R. through the G.N.F.M.     

Asymmetric triazines—XIII Reaction of phosphorus pentachloride with 4-nitrosopyrazoles

The reaction of phosphorus pentachloride with some 3:5-disubstituted-4-nitrosopyrazoles (dimethyl, diphenyl, methyl phenyl and phenyl carbomethoxy) has been investigated. Formation of a new class of compounds, 1-chloro-4-cyano-2:3-diazabuta-1:3-dienes, is described. By treatment with ammonia and subsequent alkali-induced cyclisation these substances are converted into 5-amino-as-triazines and reactions of the latter have been investigated.     

Organocatalytic stereoselective epoxidation of trisubstituted acrylonitriles

The first diastereospecific and enantioselective epoxidation of trans-2-aroyl-3-arylacrylonitriles by means of the commercially available diaryl L-prolinol/tert-butyl hydroperoxide system has been developed. These diversely functionalized epoxides were obtained in excellent yield (up to 99%), complete diastereoselectivity for the trans-isomer, and good enantioselectivity (up to 84% ee). Highly enantioenriched epoxides can be easily obtained after a single crystallization (ee > 90%).     

Noncovalent organocatalytic synthesis of enantioenriched terminal aziridines with a quaternary stereogenic center

A high-yielding and enantioselective access to novel N-Boc terminal aziridines, bearing a quaternary stereogenic center, has been developed via an aza-Michael initiated ring-closure (aza-MIRC) reaction of α-acyl acrylates with an N-tosyloxy tert-butyl carbamate catalyzed by a chiral amino thiourea. The feasibility of the aziridine regioselective ring-opening to valuable α,α-disubstituted α-amino acid esters has been demonstrated.     

Minimality via Second Variation for a Nonlocal Isoperimetric Problem

We discuss the local minimality of certain configurations for a nonlocal isoperimetric problem used to model microphase separation in diblock copolymer melts. We show that critical configurations with positive second variation are local minimizers of the nonlocal area functional and, in fact, satisfy a quantitative isoperimetric inequality with respect to sets that are L ¹-close. The link with local minimizers for the diffuse-interface Ohta-Kawasaki energy is also discussed. As a byproduct of the quantitative estimate, we get new results concerning periodic local minimizers of the area functional and a proof, via second variation, of the sharp quantitative isoperimetric inequality in the standard Euclidean case. As a further application, we address the global and local minimality of certain lamellar configurations.     

Analysis of models for the Ziegler-Natta stereospecific polymerization on the basis of non-bonded interactions at the catalytic site—I. The Cossee model

The model proposed by Cossee for Ziegler-Natta polymerization of propene is re-examined by computing the non-bonded energies for all sets of possible internal coordinates of the atoms at the catalytic site. For catalytic sites in the bulk of (110) surfaces of TiCl₃-α, it is possible to explain the regiospecificity of the reaction but, at variance with Cossee, we see no evidence that the surface conditions the methyl group of the olefin to protrude out of the crystal. The stereospecificity may arise however from the fixed, chiral orientation of the first carbon—carbon chain bond, due to interactions with the surface. Further computations seem to indicate that the polymerization could occur with much less steric hindrances on edges or reliefs of the surfaces, the relative positions of olefin and chain being exchanged in respect to the Cossee model.     

A remark on the <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">1</Emphasis></Superscript>-lower semicontinuity for integral functionals in BV

We study the L ¹ -lower semicontinuity in BV of an integral functional of the type . Our assumptions on f extend previous results recently obtained by Gori, Maggi and Marcellini in the case where the above functional is restricted to W ^1,1 .     

Amorphous carbon and carbonaceous materials in space I.—Laboratory measurements

Summary We present here the most recent measurements (UV and Raman spectroscopy) carried out on carbonaceous materials candidates as cosmic dust. To speed up publication, the proofs were not sent to the authors and were supervised by the scientific Committee.