Generation of Analytic Semigroups by Elliptic Operators with Dirichlet Boundary Conditions in a Cylindrical Domain

We consider an elliptic operator of second order with Dirichlet boundary conditions in a cylindrical domain. We show that a suitable interpretation of this operator in a certain space of continuous functions vanishing on the boundary is the infinitesimal generator of an analytic semigroup in the space of continuous functions. We prove several inclusions of the domain of the infinitesimal generator and of the real interpolation spaces between this domain and the basic space of continuous functions.     

Diffraction and localization in low-dimensional photonic bandgaps

We show that, in low-dimensional photonic bandgaps, wave diffraction resulting from localization in the translational-invariant directions is strongly influenced by the photonic band structure of the periodic crystal, leading to new kinds of wave localization. In particular, for a periodic layered structure we show that, close to a bandgap edge, diffraction is enhanced, with a transition from a parabolic diffraction curve-typical of isotropic media and supporting Gaussian beams-to hyperbolic or elliptic diffraction curves. In the last two cases localization in the form of stationary X-shaped or sinc-shaped waves is possible.     

Entangled imaging and wave-particle duality: from the microscopic to the macroscopic realm

We formulate a theory for entangled imaging, which includes also the case of a large number of photons in the two entangled beams. We show that the results for imaging and for the wave-particle duality features, which have been demonstrated in the microscopic case, persist in the macroscopic domain. We show that the quantum character of the imaging phenomena is guaranteed by the simultaneous spatial entanglement in the near and in the far field.     

Solid-phase synthesis and characterization of a novel fullerene-peptide derived from histone H3

A peptide analogue from a histone H3 protein containing the L-fulleropyrrolidino-glutamic acid has been prepared by a solid-phase approach and has been fully characterized. By molecular modelling it was verified that this peptide derivative is able to retain a binding capacity to the MHC (major histocompatibility complex) molecule similar to that of the cognate epitope.     

Paramagnetic defect centers at the MgO surface. An alternative model to oxygen vacancies

On the basis of embedded cluster calculations, we propose a new model for the structure of paramagnetic color centers at the MgO surface usually denoted as F(S)(H)(+) (an electron trapped near an adsorbed proton). These centers are produced by exposing the surface of polycrystalline MgO to H(2) followed by UV irradiation. We demonstrate that properties of H atom absorbed at surface sites such as step edges (MgO(step)) and reverse corner sites (MgO(RC)), formed at the intersection of two step edges, are compatible with a number of features observed for F(S)(H)(+). Our calculations suggest that (i) H(2) dissociates at the reverse corner site heterolytically and that there is no barrier for this exothermic reaction; (ii) the calculated vibrations of the resulting MgO(RC)(H(+))(H(-)) complex are fully consistent with the measured ones; (iii) desorption of a neutral H atom from the diamagnetic precursor requires UV light and leads to the formation of stable neutral paramagnetic centers at the surface, MgO(step)(H(+))(e(-))(trapped) and MgO(RC)(H(+))(e(-))(trapped). The computed isotropic hyperfine coupling constants and optical transitions of these centers are in broad agreement with the existing experimental data. We argue that these centers, which do not belong to the class of "oxygen vacancies", are two of the many possible forms of the F(S)(H)(+) defect center.     

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

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.     

Combinatorial analysis of Tetris-like games

We study some combinatorial properties of Tetris-like games by using Schützenberger methodology and probability generating functions. We prove that every Tetris-like game is equivalent to a finite state automaton and propose a straight foward algorithm to transform a Tetris-like game into its corresponding automaton. In this way, we can study the average number of pieces inserted during a game and the average score as a function of the player's ability and the pieces extrusion.