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.     

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.     

Markovian approximation in foreign exchange markets

In this paper, using the exit-time statistic, we study the structure of the price variations for the high-frequency data set of the bid–ask Deutschemark/US dollar exchange rate quotes registered by the inter-bank Reuters network over the period October 1, 1992 to September 30, 1993. Having rejected random-walk models for the returns, we propose a Markovian model which reproduce the available information of the financial series. Besides the usual correlation analysis we have verified the validity of this model by means of other tools all inspired by information theory. These techniques are not only severe tests of the approximation but also evidence of some aspects of the data series which have a clear financial relevance.     

State-specific reactions and autoionization dynamics of Ar produced by synchrotron radiation

The long-lived excited states of doubly charged rare gases can markedly affect their reactivity. In this paper we demonstrate the presence of strong state-specific effects in the charge exchange of Ar²⁺ (³P, ¹D and ¹S) with several neutral targets (He, Ne, Kr, Xe, D₂, and CH₄). State sensitive measurements have been performed by producing the different Ar²⁺ electronic states via tunable synchrotron radiation (Elettra-Trieste, Italy and SuperACO-Orsay, France). From the product ion yield data of charge transfer, state-selected total cross-sections have been deduced. Using the state-specific reactivity of Ar²⁺ towards different neutral targets, it has been possible to extract the photon-energy-dependent production branching of the three doubly charged states and to investigate the autoionization dynamics of neutral or singly charged Ar in the vicinity of the double ionization threshold.     

Yield criteria for quasibrittle and frictional materials: A generalization to surfaces with corners

Convexity of a yield function (or phase-transformation function) and its relations to convexity of the corresponding yield surface (or phase-transformation surface) is essential to the invention, definition and comparison with experiments of new yield (or phase-transformation) criteria. This issue was previously addressed only under the hypothesis of smoothness of the surface, but yield surfaces with corners (for instance, the Hill, Tresca or Coulomb–Mohr yield criteria) are known to be of fundamental importance in plasticity theory. The generalization of a proposition relating convexity of the function and the corresponding surface to nonsmooth yield and phase-transformation surfaces is provided in this paper, together with the (necessary to the proof) extension of a theorem on nonsmooth elastic potential functions. While the former of these generalizations is crucial for yield and phase-transformation functions, the latter may find applications for potential energy functions describing phase-transforming materials, or materials with discontinuous locking in tension, or contact of a body with a discrete elastic/frictional support.