Generalized Mukai conjecture for special Fano varieties

Let X be a Fano variety of dimension n, pseudoindex i _X and Picard number ρ_X. A generalization of a conjecture of Mukai says that ρ_X(i _X −1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i _X ≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρ_X> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.     

A new microwave dielectric method for studying photoinitiated chain radical polymerization processes

Measurements of both real and imaginary parts of the dielectric constant at a fixed microwave frequency have been performed on n-butyl acrylate/poly(n-butyl acrylate) mixtures. The dielectric constant of the mixtures has been compared with that of neat n-butyl acrylate during UV photoinitiated polymerization. The values of the imaginary part of the dielectric constant thus obtained have allowed determination of the instantaneous monomer concentration and verified the kinetic equation for the photoinitiated polymerization process. The limits of validity of the method as well as its capability of providing detailed kinetic information are also discussed.     

Superenergy of Gravitational Waves in the Exact Theory

Gravitational waves and radiation in the exact theory are studied in a unique framework. The observer's point of view is introduced. Some results by Lichnerowicz are generalized and interpreted in terms of reference frames. This allows us to recognize the role played by the gravitational force field in the exact generalization of Bel's superenergy flux theorem. It is also possible to recover the usual concept of wave as energy transmission, by means of a suitable superenergy scalar.     

FT–IR microspectroscopy study of blends of ester functionalized ethylene–propylene copolymer with (vinylidene fluoride-hexafluoropropene) elastomer

An ethylene—propylene (EPR) copolymer functionalized with (1,2-dicarboethoxy)ethyl groups has been blended with a vinylidene fluoride—hexafluropropene elastomer (NML). The existence of intermolecular interactions involving mainly the carbonyl groups of the side chains of the functionalized copolymer and the methylene hydrogens of the fluoroelastomer through hydrogen bonding was shown by means of FT—IR spectroscopy. The structure and composition of some microdomains in the mixture was examined by means of FT—IR microspectroscopy.     

On a path-independent integral approach to fast tearing of elastomers

Summary The feasibility of a path-independent integral approach to fracture mechanics of elastomers and the objectivity of the pertinent crack stability criterion are discussed with reference to tearing with negligible mechanical dissipations.

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Sommario In questo articolo si discutono le possibilità offerte dall'impiego dell'integrale J e del relativo criterio di stabilità della cricca nello studio della frattura veloce di materiali elastomerici.

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List of symbols and abbreviations F Deformation gradient. - Feled Finite Element for Large Elastic Deformations. - T Strain energy release per unit crack growth (termedG in fracture mechanics of metals). - T _l First Piola-Kirchhoff stress tensor. - u Displacement vector. - W Stored energy function per unit of volume in the undeformed configuration. - x Spatial co-ordinates. - X Material co-ordinates.     

Synthesis and catalytic activity of a fluorous-tagged TEMPO radical

A fluorous-tagged TEMPO radical has been prepared and its catalytic activity in the chemoselective oxidation of alcohols to carbonyl compounds has been investigated. The new fluorous radical proved to be an efficient, selective and easily recoverable catalyst, which can be conveniently used in standard organic solvents and then isolated and recycled by fluorous liquid-liquid extraction.     

Total synthesis of (±)-cyclooroidin

The first total synthesis of (±)-cyclooroidin, a member of the pyrrole-imidazole alkaloid family recently isolated from the sponge Agelas oroides in optically pure form, is described. The synthesis was achieved in nine linear steps, with an overall yield of 10%. Key step was a Wolff bromoketone synthesis performed on the intermediate longamide B.     

A highly stable short alpha-helix constrained by a main-chain hydrogen-bond surrogate

Herein we describe a strategy for the preparation of artificial alpha-helices involving replacement of one of the main-chain hydrogen bonds with a covalent linkage. To mimic the C=O...H-N hydrogen bond as closely as possible, we envisioned a covalent bond of the type C=X-Y-N, where X and Y are two carbon atoms connected through an olefin metathesis reaction. Our results demonstrate that the replacement of a hydrogen bond between the i and i + 4 residues at the N-terminus of a short peptide with a carbon-carbon bond results in a highly stable constrained alpha-helix at physiological conditions as indicated by CD and NMR spectroscopies. The advantage of this strategy is that it allows access to short alpha-helices with strict preservation of molecular recognition surfaces required for biomolecular interactions.     

Optically active hydrocarbon polymers with aromatic side chains. II. Poly-(S)-p-sec-butylstyrene

The synthesis of optically active p-sec-butylstyrene (I) has been carried out starting with (S)-2-phenylbutane (II) having optical purity 88–91%. The optical purity of I thus obtained was found to be 73–75%. The polymerization of I with stereospecific coordinated anionic catalysts gave amorphous polymers, as in the case of many other p-substituted styrene derivatives. The fractions obtained from these polymers have very similar rotatory power at 589 nm which is practically equal to that of polymer of I obtained by nonstereospecific radical initiator and of low molecular weight structural models. Accordingly the ¹L_b electronic transition of the aromatic chromophore shows a very low rotatory strength in all samples examined. This result is related to the lack in solution of conformations with a predominant single chirality of the main chain of the macromolecules derived from I.