Global Action-Angle Variables for Non-Commutative Integrable Systems

In this paper we analyze the obstructions to the existence of global action-angle variables for regular non-commutative integrable systems (NCI systems) on Poisson manifolds. In contrast with local action-angle variables, which exist as soon as the fibers of the momentum map of such an integrable system are compact, global action-angle variables rarely exist. This fact was first observed and analyzed by Duistermaat in the case of Liouville integrable systems on symplectic manifolds and later by Dazord-Delzant in the case of non-commutative integrable systems on symplectic manifolds. In our more general case where phase space is an arbitrary Poisson manifold, there are more obstructions, as we will show both abstractly and on concrete examples. Our approach makes use of a few new features which we introduce: the action bundle and the action lattice bundle of the NCI system (these bundles are canonically defined) and three foliations (the action, angle and transverse foliation), whose existence is also subject to obstructions, often of a cohomological nature

Tetrahydrofuran (co)polymers as potential materials for vascular prostheses

Polyethers were studied as potential materials for vascular prostheses. By crosslinking poly(tetramethylene oxide) (PTMO) with poly(ethylene oxide) (PEO), hydrophilic networks were obtained containing PTMO as well as PEO. Attempts were made to reduce the crystallinity and melting point of PTMO because of the required elastomeric behaviour at body temperature. Compared to non-crosslinked PTMO, crosslinking in the melt resulted in a decrease in the melting point from 43·7 to 38·7°C and a decrease of the crystallinity from 46 to 28%. By copolymerizing tetrahydrofuran with oxetane or dimethyloxetane, melting points below 38°C were obtained, together with crystallinities lower than 20%

In vivo testing of crosslinked polyethers. II. Weight loss, IR analysis, and swelling behavior after implantation

As reported in Part I (In vivo testing of crosslinked polyethers. I. Tissue reactions and biodegradation, J. Biomed. Mater. Res., this issue, pp. 307-320), microscopical evaluation after implantation of crosslinked (co)polyethers in rats showed differences in the rate of biodegradation, depending on the presence of tertiary hydrogen atoms in the main chain and the hydrophilicity of the polyether system. In this article (Part II) the biostability will be discussed in terms of weight loss, the swelling behavior, and changes in the chemical structure of the crosslinked polyethers after implantation. The biostability increased in the order poly(POx) < poly(THF-co-OX) < poly(THF) for the relatively hydrophobic polyethers. This confirmed our hypothesis that the absence of tertiary hydrogen atoms would improve the biostability. On the other hand, signs of biodegradation were observed for all polyether system studied. Infrared surface analysis showed that biodegradation was triggered by oxidative attack on the polymeric chain, leading to the formation of carboxylic ester and acid groups. It also was found that in the THF-based (co)polyethers, α-methylene groups were more sensitive than β-methylene groups. For a hydrophilic poly(THF)/PEO blend, an increase in surface PEO content was found, which might be due to preferential degradation of the PEO domains

Metastable amorphous phases in tellurium-base alloys

An amorphous structure has been reported in a gold-silicon alloy (2) obtained by rapid cooling through the solidification range.(3) This amorphous alloy, however, was not stable at room temperature. Crystallization into one or several metastable phases took place within twenty-four hours, and a detailed study of the structure could not easily be carried out

Optical characterization and selective addressing of the resonant modes of a micropillar cavity with a white light beam

We have performed white-light reflectivity measurements on GaAs/AlAs micropillar cavities with diameters ranging from 1 {\mu}m up to 20 {\mu}m. We are able to resolve the spatial field distribution of each cavity mode in real space by scanning a small-sized beam across the top facet of each micropillar. We spectrally resolve distinct transverse optical cavity modes in reflectivity. Using this procedure we can selectively address a single mode in the multimode micropillar cavity. Calculations for the coupling efficiency of a small-diameter beam to each mode are in very good agreement with our reflectivity measurements.Comment: 7 pages, 8 figure

Whole genome sequencing-based mapping and candidate identification of mutations from fixed zebrafish tissue

As forward genetic screens in zebrafish become more common, the number of mutants that cannot be identified by gross morphology or through transgenic approaches, such as many nervous system defects, has also increased. Screening for these difficult-to-visualize phenotypes demands techniques such as whole-mount in situ hybridization (WISH) or antibody staining, which require tissue fixation. To date, fixed tissue has not been amenable for generating libraries for whole genome sequencing (WGS). Here, we describe a method for using genomic DNA from fixed tissue and a bioinformatics suite for WGS-based mapping of zebrafish mutants. We tested our protocol using two known zebrafish mutant alleles, gpr126st49 and egr2bfh227, both of which cause myelin defects. As further proof of concept we mapped a novel mutation, stl64, identified in a zebrafish WISH screen for myelination defects. We linked stl64 to chromosome 1 and identified a candidate nonsense mutation in the F-box and WD repeat domain containing 7 (fbxw7) gene. Importantly, stl64 mutants phenocopy previously described fbxw7vu56 mutants, and knockdown of fbxw7 in wild-type animals produced similar defects, demonstrating that stl64 disrupts fbxw7. Together, these data show that our mapping protocol can map and identify causative lesions in mutant screens that require tissue fixation for phenotypic analysis

The Magellanic Puzzle: origin of the periphery

In this paper, we analyse the metallicity structure of the Magellanic Clouds using parameters derived from the Gaia DR3 low-resolution XP spectra, astrometry and photometry. We find that the qualitative behavior of the radial metallicity gradients in the LMC and SMC are quite similar, with both of them having a metallicity plateau at intermediate radii and a second at larger radii. The LMC has a first metallicity plateau at [Fe/H]$\approx$-0.8 for 3$-$7\degr, while the SMC has one at [Fe/H]$\approx$-1.1 at 3$-$5\degr. The outer LMC periphery has a fairly constant metallicity of [Fe/H]$\approx$-1.0 (10$-$18\degr), while the outer SMC periphery has a value of [Fe/H]$\approx$-1.3 (6$-$10\degr). The sharp drop in metallicity in the LMC at $\sim$8\dgr and the marked difference in age distributions in these two regions suggests that there were two important evolutionary phases in the LMC. In addition, we find that the Magellanic periphery substructures, likely Magellanic debris, are mostly dominated by LMC material stripped off in old interactions with the SMC. This presents a new picture in contrast with the popular belief that the debris around the Clouds had been mostly stripped off from the SMC due to having a lower mass. We perform a detailed analysis for each known substructure and identify its potential origin based on metallicities and motions with respect to each galaxy.Comment: 11 pages, 7 figures. Submitted to MNRAS. Comments welcome