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.     

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.     

The behaviour of alkylcobalt carbonyls under “oxo” conditions

Both normal and secondary alkylcobalt carbonyls are shown not to undergo isomerization under catalytic “oxo” conditions, and the relevance of this obervation for the mechanism of the “oxo” reaction is discussed.     

Thermodynamic properties of organic compounds in aqueous solution. II. Apparent molal heat capacities of piperidines,morpholines, and piperazines

Apparent molal heat capacities of some piperidine, morpholine, and piperazine derivatives in aqueous solution have been determined by adiabatic calorimetry in the temperature range 20–55°C and in the molality range 0.2–1m. Comparison of experimental values with those calculated through group contributions, found for monofunctional compounds, indicates strong interactions between the hydrophilic centers. An interpretation is given of the possible mechanism of this interaction. Also, values of ΔC _p for the addition reaction of proton to nitrogen centers of mono- and bifunctional organic compounds are examined.     

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.     

Hydroformylation and hydrocarbethoxylation of 1,2-dicarbethoxy-1,2,3,6-tetrahydropyridazine and 1,2-dicarbethoxy-1,2,3,4-tetrahydropyridazine

The unsaturated compounds 1,2-dicarbethoxy-1,2,3,6-tetrahydropyridazine 1 and 1,2-dicarbethoxy-1,2,3,4-tetrahydropyridazine 2 have been hydroformylated and hydrocarbethoxylated in the presence of some well known cobalt, rhodium, palladium and platinum catalysts. The hydroformylation reaction can be tuned by a suitable choice of the catalyst precursor and reaction conditions, thus allowing the synthesis with high selectivity of one of the two possible isomeric aldehydes. The carbonylation reaction is less synthetically useful, since it shows low activity and unsatisfactory chemo- and regio-selectivity. However, the ester 1,2,4-tricarbethoxyhexahydropyridazine 10 can be prepared in good yield from olefin 1 by using the complex [PdCl₂(PPh₃)₂] as the catalyst precursor.     

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.     

Asymmetric synthesis by chiral ruthenium complexes : VI. Enantiomer-discrimination in the hydrogen transfer from racemic alcohols to prochiral ketones in the presence of H4Ru4(CO)8[(−)-diop]2

Hydrogen transfer from racemic alcohols to prochiral ketones in the presence of H₄Ru₄(CO)₈[(?)-DIOP]₂ has been examined. The enantiomer-discrimination is influenced by the structure of the reactants, temperature and the excess of phosphine present.     

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.