Monodromy and K-theory of Schubert curves via generalized jeu de taquin

We establish a combinatorial connection between the real geometry and the K-theory of complex Schubert curves \(S(\lambda _\bullet )\), which are one-dimensional Schubert problems defined with respect to flags osculating the rational normal curve. In Levinson (One-dimensional Schubert problems with respect to osculating flags, 2016, doi: 10.4153/CJM-2015-061-1), it was shown that the real geometry of these curves is described by the orbits of a map \(\omega \) on skew tableaux, defined as the commutator of jeu de taquin rectification and promotion. In particular, the real locus of the Schubert curve is naturally a covering space of \({\mathbb {RP}}^1\), with \(\omega \) as the monodromy operator. We provide a fast, local algorithm for computing \(\omega \) without rectifying the skew tableau and show that certain steps in our algorithm are in bijective correspondence with Pechenik and Yong’s genomic tableaux (Pechenik and Yong in Genomic tableaux, 2016. arXiv:1603.08490), which enumerate the K-theoretic Littlewood–Richardson coefficient associated to the Schubert curve. We then give purely combinatorial proofs of several numerical results involving the K-theory and real geometry of \(S(\lambda _\bullet )\).     

Molybdenum site structure of Escherichia coli YedY, a novel bacterial oxidoreductase

We report a structural characterization using X-ray absorption spectroscopy of the molybdenum site of Escherichia coli YedY, a novel oxidoreductase related to be the sulfite oxidase family of molybdenum enzymes. We find that the enzyme can exist in Mo(V) and Mo(IV) oxidation states but cannot be readily oxidized to the Mo(VI) form. Mo(V) YedY has molybdenum coordination similar to that of sulfite oxidase, with one Mo═O at 1.71 ?, three Mo-S at 2.39 ?, and one Mo-OH at 2.09 ?, which elongates to 2.20 ? upon reduction to Mo(IV), indicating Mo-OH(2) coordination. The Mo(V) enzyme also possesses a long Mo-O coordination at 2.64 ?, which may be due to oxygen coordination by Asn-45 O(δ), with Mo-O(δ) approximately trans to the Mo═O group. A comparison with sulfite oxidase indicates that YedY possesses a much more uniform Mo-S coordination, with a maximum permitted deviation of less than 0.05 ?. Our results indicate that the YedY active site shows considerable similarity to but also important differences from that of reduced forms of sulfite oxidase.     

High-throughput age synchronisation of Caenorhabditis elegans

We present a passive microfluidic strategy for sorting adult C. elegans nematodes on the basis of age and size. The separation mechanism takes advantage of phenotypic differences between 'adult' and 'juvenile' organisms and their behaviour in microfluidic architectures. In brief, the microfluidic device allows worms to sort themselves in a passive manner.     

Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set

We construct multidimensional Schrödinger operators with a spectrum that has no gaps at high energies and that is nowhere dense at low energies. This gives the first example for which this widely expected topological structure of the spectrum in the class of uniformly recurrent Schrödinger operators, namely the coexistence of a half-line and a Cantor-type structure, can be confirmed. Our construction uses Schrödinger operators with separable potentials that decompose into one-dimensional potentials generated by the Fibonacci sequence and relies on the study of such operators via the trace map and the Fricke-Vogt invariant. To show that the spectrum contains a half-line, we prove an abstract Bethe–Sommerfeld criterion for sums of Cantor sets which may be of independent interest.     

Observation of transcrystalline growth of PLA crystals on sisal fibre bundles and the effect of crystal structure on interfacial shear strength

Hot-stage microscopy was used to characterise crystal growth at the interface between sisal fibre bundles and a polylactic acid (PLA) matrix in order to better understand the mechanical properties of sisal fibre–PLA composites. Cooling rates and crystallisation temperatures and times were varied to influence crystalline morphology at the interface. Single sisal fibre bundles were evaluated in their as received state or treated with 6 wt.% caustic soda solution for 48?h at room temperature. A microbond shear test was used to characterise the shear strength of the interface as a function of fibre surface treatment. These tests were performed on sisal fibre bundles carefully embedded in flat films of PLA supported on card mounts. Fibre bundles in a PLA matrix were cooled from 180?°C at rates from 2 to 9?°C/min and then crystallised isothermally. For as received fibre bundles uneven growth of PLA spherulites occurred at all cooling rates and crystallisation temperatures. For caustic soda treated fibres, uneven spherulitic growth was observed at crystallisation temperatures at and above 125?°C. In contrast, transcrystalline growth was observed for samples cooled to 120?°C at cooling rates from 2 to 6?°C/min and then allowed to crystallise. The microbond shear strengths of untreated and caustic soda treated fibre bundles were evaluated using Weibull statistics and the caustic soda treated fibres exhibited higher interfacial shear strengths in comparison to untreated fibres, reflecting the development of a transcrystalline layer at the fibre to matrix interface.     

Influence of nanofillers on the thermal and mechanical behavior of DGEBA-based adhesives for bonded-in timber connections

Results of an experimental investigation into the thermal behavior and mechanical properties of a room-temperature-cured epoxy adhesive (diglycidyl ether of bisphenol A, DGEBA) cross-linked with polyetheramines and filled with different fillers, namely nanosilica, liquid rubber (CTBN), and clay, are reported. The nanosilica and liquid rubber increased the flexural strength and elastic modulus of the adhesive systems; the addition of clay particles raised the elastic modulus significantly, but embrittled the adhesive. Establishing a correct cure time is very important for bonded-in timber structures, as it will affect the bond strength. A study on the effect of cure time on the flexural strength was carried out, from which it follows that the adhesives should be cured for at least 20 days at room temperature. The damping characteristics and the glass-transition temperature of the adhesives were determined by using a dynamic mechanical thermal analysis. The results showed that the filled adhesives had a higher storage modulus, which was in agreement with the elastic moduli determined from static bending tests. The introduction of the fillers increased its glass-transition temperature considerably. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 599–614, September–October, 2006.     

Development of electrochemical oxygen meter for liquid sodium

The development of an electrochemical oxygen meter for liquid sodium is briefly accounted. The current design, based on a solid electrolyte crucible machined out of a sintered pellet is described along with some technological details. Present experience with testing in sodium loops and post-exposure analysis has shown that the chosen assembly is capable of achieving approximately the Nernst voltage. The service period was limited mainly by corrosion and by some incompatibilities in reference electrode compartment materials.