Singular sets of planar hyperbolic billiards are regular

Many planar hyperbolic billiards are conjectured to be ergodic. This paper represents a first step towards the proof of this conjecture. The Hopf argument is a standard technique for proving the ergodicity of a smooth hyperbolic system. Under additional hypotheses, this technique also applies to certain hyperbolic systems with singularities, including hyperbolic billiards. The supplementary hypotheses concern the subset of the phase space where the system fails to be C ² differentiable. In this work, we give a detailed proof of one of these hypotheses for a large collection of planar hyperbolic billiards. Namely, we prove that the singular set and each of its iterations consist of a finite number of compact curves of class C ² with finitely many intersection points.     

Photosensitive, all-glass AgPO3/silicaphotonic bandgap fiber

Photonic bandgap (PBG) guidance is observed in a solid core photonic crystal fiber (PCF) consisting of silver metaphosphate (AgPO(3)) glass embedded into a silica cladding, realized by vacuum-assisted infiltration of the molten glass into the hollow channels of a commercial silica PCF. Morphologic analysis of the cladding microstructure by optical and scanning electron microscopy reveals the formation of highly homogeneous glass strands along the PCF length. The characteristic transmission spectrum of the fiber shows PBG guidance in the range between 350 and 1650 nm. The exposure of the cladding glass matrix, using 355 nm, 150 ps laser irradiation, allows photo-induced enhancement of the transmission-to-stop-band extinction ratio by ～60 dB/cm and bandwidth tuning. Numerical calculations of the transmission pattern of the fabricated AgPO(3)/silica bandgap fiber are in good agreement with experiments.     

FLAMEnGO: a fuzzy logic approach for methyl group assignment using NOESY and paramagnetic relaxation enhancement data

Building on a recent method by Matthews and co-workers [1], we developed a new and efficient algorithm to assign methyl resonances from sparse and ambiguous NMR data. The new algorithm (FLAMEnGO: Fuzzy Logic Assignment of MEthyl GrOups) uses Monte Carlo sampling in conjunction with fuzzy logic to obtain the assignment of methyl resonances at high fidelity. Furthermore, we demonstrate that the inclusion of paramagnetic relaxation enhancement (PRE) data in the assignment strategy increases the percentage of correct assignments with sparse NOE data. Using synthetic tests and experimental data we show that this new approach provides up to ～80% correct assignments with only 30% of methyl-methyl NOE data. In the experimental case of ubiquitin, PRE data from two spin labeled sites improve the percentage of assigned methyl groups up to ～91%. This new strategy promises to further expand methyl group NMR spectroscopy to very large macromolecular systems.     

Entry to nitrogen-containing heterocycles by based-promoted heterocyclization on allenylamides of l-α-aminoacids

Allenylamides of Boc-protected α-aminoacids easily gave in basic medium heterocyclic products arising from attack of the NH group on the inside C-C double bond of the 1,2-diene moiety, namely imidazolidinones, pyrazinones, and a pyrrole compound. The microwave-assisted heterocyclization occurred cleanly at C-β of the allenyl group with formation of pyrazin-2-ones having an endo- or exocyclic double bond.     

A Degenerate Birdcage with Integrated Tx/Rx Switches and Butler Matrix for the Human Limbs at 7 T

The theoretically known degeneracy condition of the band-pass birdcage coil has rarely been exploited in transmit coil designs. We have created an eight-channel degenerate birdcage for the human limbs at 7 T, with dedicated Tx/Rx switches and a Butler matrix. The coil can be split into two half cylinders, as required for its application to patients with limited mobility. The design of the coil, the Butler matrix, and Tx/Rx switches relied on a combination of analytical, circuital, and numerical simulations. The birdcage theory was extended to the degenerate case. The theoretical and practical aspects of the design and construction of the coil are presented. The performance of the coil was demonstrated by simulations, workbench, and scanner measurements. The fully assembled prototype presents good performance in terms of efficiency, B₁ homogeneity, and signal-to-noise ratio, despite the asymmetry introduced by the splittable design. The first in vivo images of the knee are also shown. A novel RF coil design consisting of an eight-channel splittable degenerate birdcage has been developed, and it is now available for 7 T MRI applications of the human lower limbs, including high-resolution imaging of the knee cartilages and of the patellar trabecular structure.     

High-order conservative finite difference GLM–MHD schemes for cell-centered MHD

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities.     

On the Traceability of the Hazelnut Production Chain by Means of Trace Elements

The production chain of hazelnuts has been studied by analyzing three sets of samples produced in purity from three different pools of hazelnuts of cultivar “Tonda Gentile Trilobata”, “Tonda Gentile Romana” and “Mortarella”, all cultivated in Italy. From each pool, five processed products were obtained: roasted hazelnuts, hazelnut paste, hazelnut cream, Gianduja paste and Gianduiotto paste. After pre-treatment by means of dry ashing, all samples from each cultivar, including raw hazelnuts, were then analyzed by means of Inductively Coupled Plasma–Optical Emission Spectroscopy (ICP-OES) and Inductively Coupled Plasma–Mass Spectrometry (ICP-MS). A good discrimination was obtained among the different chain stages according to the distribution of the trace elements, as expected. More interesting was the discrimination among the different cultivars: it was possible to distinguish the samples produced from the respective cultivar by means of specific chemical markers, particularly Mo and Ni.     

SRB Measures for Polygonal Billiards with Contracting Reflection Laws

We prove that polygonal billiards with contracting reflection laws exhibit hyperbolic attractors with countably many ergodic SRB measures. These measures are robust under small perturbations of the reflection law, and the tables for which they exist form a generic set in the space of all convex polygons. Specific polygonal tables are studied in detail.