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     

Pressure-temperature phase diagrams of smectogenic 4'-alkyl-4-cyanobiphenyls (9CB, 10CB, 11CB and 12CB)

The pressure-temperature ( p - T ) phase diagrams for four smectogenic members of the 4'-alkyl-4-cyanobiphenyl homologous series ( n CB, n =9, 10, 11 and 12) over the temperature range 320-410 K and pressure range 0.1-300 MPa (3 kbar) were constructed using DTA. At 1 atm 9CB exhibits nematic and smectic A d phases, while the other members show only the smectic A d phase. However, at elevated pressures the clearing line splits in the case of 10CB and 11CB which indicates the induction of a nematic phase. It was found that the triple point, where the isotropic, nematic and smectic phases coexist, is strongly shifted to higher pressures with increasing chain length. This was interpreted as being caused by a loss of the rod-like shape of the molecules containing longer alkyl tails which explore a range of conformations. The slope of the clearing line, d T /d p , depends strongly on the length of the alkyl chain for the n CB series, but does not show a step-wise change between the nematogenic and smectogenic members.     

An interior estimate for a nonlinear parabolic equation

In this paper the derivatives of the solution of an initial boundary value problem for a nonlinear uniformly parabolic equation in the interior with the total variation of the boundary data and the L^∞-norm of the initial condition are estimated.     

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.     

Bounds for non‐periodic mixtures of infinitely many materials

We prove bounds on the homogenized coefficients for general non‐periodic mixtures of an arbitrary number of isotropic materials, in the heat conduction framework. The component materials and their proportions are given through the Young measure associated to the sequence of coefficient functions. Upper and lower bounds inequalities are deduced in terms of algebraic relations between this Young measure and the eigenvalues of the H‐limit matrix. The proofs employ arguments of compensated compactness and fine properties of Young measures. When restricted to the periodic case, we recover known bounds. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

Enzymatic synthesis of 3-hydroxybutyramides and their conversion to optically active 1,3-aminoalcohols

3-Hydroxybutyramides are obtained in high optical yield from ethyl (±)-3-hydroxybutyrate and aliphatic amines when the reaction is catalyzed by Candida antartica lipase. The chemical reduction of these 3-hydroxybutyramides yields the corresponding 1,3 -aminoalcohols.     

Equisingularity classes of birational projections of normal singularities to a plane

Given a birational normal extension O of a two-dimensional local regular ring (R,m), we describe all the equisingularity types of the complete m-primary ideals J in R whose blowing-up X=BlJ(R) has some point Q whose local ring OX,Q is analytically isomorphic to O.     

57Fe Mössbauer Spectroscopy Study of LaFe1−x Co x O3 (x=0 and 0.5) Formed by Mechanical Milling

Hyperfine Interactions - Perovskite-related phases of the type LaFe1?x Co x O3 (x=0 and 0.5) have been synthesised by milling techniques. The materials are of smaller particle size and more...