On the Generation of Certain Bundles of the Projective Space

Extending a result of Manivel, we prove the following: THEOREM. Suppose $\sum\limits_i {b_i \geqslant } \sum\limits_i {a_i } + n$ and $$\sum\limits_i {b_i } [n + d_i d_i - 1] \geqslant \sum\limits_i {a_i } [n + l_i l_i - 1] + n.$$ Then the kernel E(d) of the general morphism: $$\mathop \oplus \limits_{i = 1}^v (Bi \otimes O_{P^n } (d_i )) \to \mathop \oplus \limits_{j = 1}^v (A_j \otimes O_{P^n } (l_i ))$$ (l ₁>...>l _s>d ₁>...>d _v) is a globally generated vector bundle, except for at most finitely many sets $\left\{ {b_i ,a_i } \right\}$ .     

Integral representation of linear functionals on spaces of unbounded functions

Let be a vector lattice of real functions on a set with , and let be a linear positive functional on . Conditions are given which imply the representation , , for some bounded charge . As an application, for any bounded charge on a field , the dual of is shown to be isometrically isomorphic to a suitable space of bounded charges on . In addition, it is proved that, under one more assumption on , is the integral with respect to a -additive bounded charge.

     

Noninvariant zeta-function regularization in quantum Liouville theory

We consider two possible zeta-function regularization schemes of quantum Liouville theory. One refers to the Laplace–Beltrami operator covariant under conformal transformations, the other to the naive noninvariant operator. The first produces an invariant regularization which however does not give rise to a theory invariant under the full conformal group. The other is equivalent to the regularization proposed by A.B. Zamolodchikov and Al.B. Zamolodchikov and gives rise to a theory invariant under the full conformal group.     

Inverse kinematics resonance scattering on thick target with EXCYT beams

The resonance scattering method in inverse kinematics on infinite target has been applied to two systems, ¹⁸O + α and ⁹Be + α, in order to test and to optimize an experimental apparatus in view of a set of resonance scattering experiments to be performed with ⁸Li and ⁹Li radioactive ion beams delivered by the facility EXCYT. The scattering excitation functions, deduced for the two systems, were compared with previous results reported in literature. Results show that reliable stopping power data are essential for the application of this technique.     

Thiolated poly(ε-caprolactone) macroligand with vacant coordination sites on gold substrate: Synthesis and surface characterization

Surface-confined telechelic poly(ε-caprolactone) macroligand with two distinct functional groups per polymeric chain has been synthesized and characterized. The molecular microstructure of the macroligand with regard to the properties of the end-capped functionalities and with those on surface substrate has been studied by solution and surface analytical methods (i.e., X-ray photoelectron spectroscopy (XPS), grazing angle reflectance-Fourier transform IR spectroscopy (GA-FTIR), water contact angle measurements, and atomic force microscopy (AFM)) to elucidate the structure and properties of such multifunctional polymer on gold (1 1 1) substrate.     

Enantiopure α-imino glyoxylate: a versatile substrate for the spontaneous asymmetric synthesis of unnatural hydroxyaryl glycinates

A novel synthesis of useful enantiomerically pure arylglycinates via spontaneous reaction between phenol or naphthol derivatives and enantiopure α-imino glyoxylate in the absence of an acid catalyst is reported. A library of enantiopure substituted phenol or naphthol glycinates was obtained in good yields and high diastereoselectivities. Diastereoisomerically pure aryl glycinates were obtained by direct flash chromatography separation of the crude reaction mixture. The free OH moiety of the phenols or naphthols contributed to the activation of the imino group to form an intermolecular hydrogen bond and promoted the reaction in the absence of an acid catalyst, as shown in the transition state reported. The diastereoselectivity is due to thermodynamic control in the addition step.     

Density and Volume Properties of Ethane-1,2-diol + 1,2-Dimethoxyethane + Water Ternary Mixtures from −10° to 80°

Thermodynamic interactions in the ethane-1,2-diol (1) + 1,2-dimethoxyethane(2) + water (3) ternary system have been investigated in terms of the excessmolar volume, derived from density measurements at 19 different temperaturesfrom –10;dg to 80;dgC. Fourteen three-component mixtures have been considered,covering the entire composition range. The excess molar volumes are discussedin terms of conformational changes induced in each component by the presenceof another one. The results obtained support the hypothesis of the absence of anythree-component complex adducts under all experimental conditions investigated.