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.     

Quantification methods of amorphous/crystalline fractions in high-energy ball milled pharmaceutical products

In this work, thermoanalytical, diffractometry, and microscopy measurements have been performed in order to characterize the effect of high energy milling on a drug active in the migraine prophylaxis and smoke cessation. We can assert that the mechanical treatment induces only a partial amorphisation of the solid phase, in particular it reduces the crystal order by producing lattice defects which propagate from the surface to the bulk crystal. For this reason, the DSC is able to detect the presence of ordered solid, while the powder X-ray diffractometry, because of its low penetration depth, does not reach the crystalline core of the particles.     

Global stability of a class of discontinuous dual billiards

An infinite-parameter family of discontinuous area-preserving maps is studied, using geometrical methods. Necessary and sufficient conditions are determined for the existence of some bounding invariant sets, which guarantee global stability. It is shown that under some additional constraints, all orbits become periodic, most of them Lyapounov stable, and with a maximal period in any bounded domain of phase space. This yields a class of maps acting on a discrete phase space.