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 $\left\{ {b_i ,a_i } \right\}$ .     

Anisotropic ferromagnetism induced in rutile single crystals by Co implantation

The magnetic and electrical properties of Co-implanted single crystalline TiO₂ rutile are presented. For fluences of the order of 10¹⁷ cm^-2 and implantation energy of 150 keV the maximum atomic concentration of cobalt is 13 at% at a depth of 65 nm from the surface. The as implanted single crystals exhibit superparamagnetic behaviour attributed to the formation of nanosized cobalt clusters. After annealing at 1073 K an anisotropic ferromagnetic behaviour emerges with the easy magnetization axis lying in the (001) plane of rutile. The ferromagnetic behaviour is associated with oriented cobalt aggregates. Electrical conductivity of the implanted samples annealed in vacuum also exhibits anisotropic behaviour at low temperatures, but no magnetoresistive effects were detected.     

Nonlocal properties of entangled two-photon generalized binomial states in two separate cavities

Entangled two-photon generalized binomial states of the electromagnetic field in two separate cavities are considered. The nonlocal properties of this entangled field state are analyzed by studying the electric field correlations between the two cavities. A Bell’s inequality violation is obtained using an appropriate dichotomic cavity operator that is, in principle, measurable. The text was submitted by the authors in English.     

A multivariate extension of Sarhan and Balakrishnan’s bivariate distribution and its ageing and dependence properties

A new class of bivariate distributions (NBD) was recently introduced by Sarhan and Balakrishnan [A.M. Sarhan, N. Balakrishnan, A new class of bivariate distributions and its mixture, J. Multivariate Anal. 98 (2007) 1508-1527]. In this note, we give the joint survival function of a multivariate extension of the NBD, which is not an absolutely continuous multivariate distribution, and its marginal and extreme order statistics distributions are also derived. The multivariate ageing and dependence properties of the proposed n-dimensional distribution are also discussed, and then we analyze the stochastic ageing of its marginals and its minimum and maximum order statistics.     

Determination of the Chemical Structure of Poly-β (-)-pinene by NMR Spectroscopy

This paper is dedicated to the memory of our friend and colleague Annalaura Segre.

The chemical structure of a series of β (-)-pinene polymers (PBP) obtained by radiation-induced polymerization, free radical initiation, cationic polymerization over a Friedel-Craft catalyst and by coordinative polymerization over a Ziegler-Natta catalyst has been fully elucidated by ¹H and ¹³C-NMR spectroscopy. 2D NMR techniques have been applied in order to assign all the NMR resonances to the structures of the PBP investigated. The NMR spectra show that the most regular PBP structure is obtained by radiation-induced polymerization followed by the free radical initiated polymerization. The most defective structure has been observed in the case of PBP prepared by cationic mechanism over a Friedel-Crafts catalyst. The discussion accounts for different types of defects and cross-links present in the PBPs investigated whose fundamental structure is based on the p-menthene repeating unit.

NMR self-diffusion measurements have been performed to evaluate the molecular weight of all the PBP investigated. The highest molecular weight (2600 Dalton) was found in the case of PBP prepared by Ziegler-Natta catalyst, while the lowest molecular weight was found in the case of PBP prepared by radiation-induced polymerization (about 1000 Dalton).     

Electrolytic Oxidation of Thiocyanate and Selenocyanate Salts and the Photoelectrochemical Effect.

New photosensitive materials can be obtained by electrochemical oxidation of thiocyanate and selenocyanate salts. Using (K,Na)SCN eutectic melt, the formation of an electrodic deposit, with photoelectrochemical properties, has already been reported by us. To improve the photoelectrochemical characteristics of the deposit, futher investigations were carried out in the following sistems: selenocyanate ammoniate, KSCH-Acetamide eutectic mixture and KSCN ethylene carbonate solution:. Attempts to obtain a massive deposit in the ammoniate solution were unsuccessful due to ammonia oxidation. Measurements performed on the other KSCN systems show that temperature is a parameter of remarkable importance. In fact, lowering the temperature one obtains a decrease on formation of parathiocyanogen on behalf of the polytrithiocyanogen, the species that gives rise to the photoeffect.