Characterization theorems for the projective space and vector bundle adjunction

 We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector bundle adjunction. We use methods and techniques of the so called Mori theory, in particular the study of rational curves on projective manifolds. Received: 16 May 2002 / Revised version: 18 November 2002 Published online: 3 March 2003 Mathematics Subject Classification (2000): 14E30, 14J40, 14J45     

Positive value of information in games

We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experiments à la Blackwell. AMS 2000 Subject Classification:Primary 91A35.The work of Bruno Bassan and Marco Scarsini was partially supported by MIUR-COFIN. The authors express their thanks to Sylvain Sorin for enlightening comments.     

The LEM exponential integrator for advection–diffusion–reaction equations

We implement a second-order exponential integrator for semidiscretized advection–diffusion–reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by finite differences or finite elements, show that the Leja–Euler–Midpoint (LEM) exponential integrator can be up to 5 times faster than a classical second-order implicit solver.     

Synthesis and cationic photopolymerization of new fluorinated,polyfunctional propenyl ether oligomers

New fluorinated, polyfunctional propenyl ether functionalized resins were synthesized, and their behavior in cationic photopolymerization was investigated. The photopolymerization proceeded efficiently with a high double‐bond conversion (>90%), giving rise to UV‐cured coatings characterized by low glass‐transition temperatures (?33 °C ≤ glass‐transition temperature ≤ ?15 °C) and hydrophobic surface properties. A fluorinated additive was also employed as a reactive additive in the cationic photopolymerization of trimethylolpropane tripropenyl ether, increasing the double‐bond conversion, polymer network flexibility, thermal stability, and surface hydrophobicity. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6943–6951, 2006     

Willmore submanifolds of the Möbius space and a Bernstein-type theorem

We study Willmore immersed submanifoldsf: M ^m →S ⁿ into then-Möbius space, withm≥2, as critical points of a conformally invariant functionalW. We compute the Euler-Lagrange equation and relate this functional with another one applied to the conformal Gauss map of immersions intoS ⁿ . We solve a Bernestein-type problem for compact Willmore hypersurfaces ofS ⁿ , namely, if ?a ∈? ⁿ⁺² such that <γf, a > ≠ 0 onM, whereγ _f is the hyperbolic conformal Gauss map and <, > is the Lorentz inner product of? ⁿ⁺², and iff satisfies an additional condition, thenf(M) is an (n?1)-sphere.     

Proton-proton correlations at small relative momentum in neon-nucleus collisions at E/A=400 and 800 MeV

Proton-proton small angle correlations have been measured in neon-nucleus collisions, using the 4 pi detector Diogene, at 400 and 800 MeV per nucleon incident energies. Values of the size of the emitting region are obtained by comparison with the Koonin formula, taking into account the biases of the apparatus. The dependence of the density on target mass and incident energy is also analysed.     

Determination of the substituent effect on the O-H bond dissociation enthalpies of phenolic antioxidants by the EPR radical equilibration technique

The bond dissociation enthalpies (BDE) of several phenols containing electron-withdrawing substituents in the para position have been determined by means of the EPR radical equilibration technique. It has been found that CN, NO(2), CHO, COOR, and COOH induce an increase of the BDE value of the O-H bond, thus producing a worsening of the antioxidant activity of phenols, while Cl, Ph, and CH[double bond]CHPh show an opposite effect. The contributions of these substituents for the calculation of the BDE values in polysubstituted phenols by using the group additivity rule have also been derived. It is shown that this rule provides quite reliable predictions of bond strengths, so that the method can be conveniently used to estimate new data on substituted phenols.     

The replacement of five-membered N-donor heterocycles from aminotrichlorogold(III) complexes. A comparison with pyridines

The kinetics of the process AuCl₃(nu) + Cl⁻→ AuCl ₄ ⁻ + nu (nu = one of a number of five-membered N-donor heterocycles covering a wide range of basicity, namely: oxazole, 2,4,5-trimethyloxazole, thiazole, 5-methylthiazole, 4-methylthiazole, 4,5-dimethylthiazole, 2,4-dimethylthiazole, 2,4,5-trimethylthiazole, imidazole and 2-methylimidazole) have been studied in methanol at 25 °C. The reactions follow the usual two-term rate law, rate = (k ₁ + k ₂[Cl⁻])[complex], observed in a square-planar substitution associative-mechanism. The second-order rate constants, k ₂, indicate that the discriminating ability of Au^(III) in these complexes is good and markedly influenced by the nature of the leaving group. A linear-free-energy relationship, logk ₂ = 0.53pK _a + constant, is observed between the rate constant and the basicity of the leaving group for its replacement by chloride. The results are compared with data from the literature regarding a series of complexes of the type AuCl₃(py) (py = one of a number of pyridines) reacting with the Cl⁻ anion under the same experimental conditions. The reactivity depends not only upon ligand basicity but also upon the nature of the ligand in the order: pyridines> five-membered heterocycles. Steric factor due to the presence of a single methyl group ortho to the sp² nitrogen atom in the ring has no influence on the rate of substitution while, surprisingly, when there are two ortho methyl groups a remarkable steric retardation effect is observable. The results are discussed in terms of reaction-profile in the associative-substitution reaction and bonding interactions in the ground and transition states.