A parametric study of the lensing properties of dodecagonal photonic quasicrystals

We present a study of the lensing properties of two-dimensional (2-D) photonic quasicrystal (PQC) slabs made of dielectric cylinders arranged according to a 12-fold-symmetric square-triangle aperiodic tiling. Our full-wave numerical analysis confirms the results recently emerged in the technical literature and, in particular, the possibility of achieving focusing effects within several frequency regions. However, contrary to the original interpretation, such focusing effects turn out to be critically associated to local symmetry points in the PQC slab, and strongly dependent on its thickness and termination. Nevertheless, our study reveals the presence of some peculiar properties, like the ability to focus the light even for slabs with a reduced lateral width, or beaming effects, which render PQC slabs potentially interesting and worth of deeper investigation.     

Reduction of conformational mobility and aggregation in W60G β2‐microglobulin: assessment by 15N NMR relaxation

The amyloid pathology associated with long‐term haemodialysis is due to the deposition of β₂‐microglobulin, the non‐polymorphic light chain of class I major histocompatibility complex, that accumulates at bone joints into amyloid fibrils. Several lines of evidence show the relevance of the tryptophan residue at position 60 for the fibrillogenic transition of the protein. A comparative ¹⁵N NMR relaxation analysis is presented for wild‐type human β₂‐microglobulin and W60G β₂‐microglobulin, i.e. the mutant with a glycyne replacing the natural tryptophan residue at position 60. The experimental data, collected at 11.4 T and 310 K, were analyzed by means of the reduced spectral density approach. Molecular dynamics (MD) simulations and corresponding thermodynamic integration, together with hydrodynamic calculations were performed to support data interpretation. The analysis results for the mutant protein are consistent with a reduced aggregation with respect to the wild‐type counterpart, as a consequence of an increased conformational rigidity probed by either NMR relaxation and MD simulations. Although dynamics in solution is other than fibrillar competence, the assessed properties of the mutant protein can be related with its reduced ability of forming fibrils when seeded in 20% trifluoroethanol. Copyright © 2013 John Wiley & Sons, Ltd.     

Positive solutions of multi-point boundary value problems at resonance

We establish new results on the existence of positive solutions for some multi-point boundary value problems at resonance. Our results are based on a recent Leggett–Williams norm-type theorem due to O’Regan and Zima. We also derive a new result for a three-point problem, previously studied by several authors.     

Multiple nonnegative solutions of systems with coupled nonlinear boundary conditions

Using the theory of fixed point index, we discuss the existence and multiplicity of nonnegative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a variety of situations. We illustrate in an example that all the constants that occur in our theory can be computed. Copyright © 2013 John Wiley & Sons, Ltd.     

Refining Castelnuovo-Halphen bounds

Fix integers r,d,s,π with r≥4, d?s, r?1≤s≤2r?4, and π≥0. Refining classical results for the genus of a projective curve, we exhibit a sharp upper bound for the arithmetic genus p _a (C) of an integral projective curve C?? ^r of degree d, assuming that C is not contained in any surface of degree <s, and not contained in any surface of degree s with sectional genus >π. Next we discuss other types of bound for p _a (C), involving conditions on the entire Hilbert polynomial of the integral surfaces on which C may lie.     

Synthesis of 4-N-alkyl and ribose-modified AICAR analogues on solid support

Herein, we report the solid-phase synthesis of several 5-aminoimidazole-4-(N-alkyl)carboxamide-1-ribosides (4-N-alkyl AICARs) and the corresponding 2′,3′-secoriboside derivatives. The method uses the N-1-dinitrophenyl-inosine 5′-bonded to a solid support. This inosine derivative has the C-2 of the purine base strongly activated towards the attack of N-nucleophiles thus allowing the preparation of several N-1 alkylated inosine supports from which a small library of 4-N-alkyl AICAR derivatives has been synthesized. A set of new 4-N-alkyl AICA-2′,3′-secoriboside derivatives have also been obtained in high yields by solid-phase cleavage of the 2′,3′-ribose bond.     

New derivatives of pyrimidine nucleosides: Synthesis,physico-chemical properties and biological activity

The paper reports the synthesis and physico-chemical data of eight new pyrimidine nucleosides C-4 substituted and two imidazo[1,2-c]pyrimidine nucleosides as well as preliminary results of their biological effects on neuroblastoma cells in culture.     

Magnetic susceptibility of the singlet ground-state system (LaPr)Sn3

Recent experimental work on La_1-xPr_xSn₃ alloys shows anomalous low-temperature properties which have been tentatively ascribed to Kondo and crystalline-electric-field effects. In order to examine in this paper the soundness of this hypothesis we calculate the magnetic susceptibility of La_1-xPr_xSn₃ compounds, taking consistently into account crystal-field and Kondo effects. Our theoretical results are in good agreement with the experimental data, giving strong support to the interpretation of La_1-xPr_xSn₃ as the first-observed singlet ground-state system in which the Kondo effect arises from excited crystal-field levels.     

An algorithm producing a standard spine of a 3-manifold presented by surgery along a link

We provide a simple algorithm which produces a (branched) standard spine of a 3-manifold presented by surgery along a framed link inS ³, giving an explicit upper bound on the complexity of the spine in terms of the complexity of a diagram of the link. As a corollary, we get an easy constructive proof of Casler’s result on the existence of a standard spine for a closed 3-manifold. We also describe an o-graph which represents the spine.     

Mass spectrometry of heterocyclic compounds. X—The unusual cleavage of the alkyl–oxygen bond of 3-carboxyesters of 2-phenyl-4-pyridones

The dominant and unusual electron impact-induced losses of CH₃? and C₂H₅? from molecular ions of 3-carbomethoxy and 3-carbethoxy derivatives of 2-phenyl-4-pyridones are explained by invoking the participation of the phenyl group.