Time-average measurement of velocity, density, temperature, and turbulence velocity fluctuations using Rayleigh and Mie scattering

Measurement of time-averaged velocity, density, temperature, and turbulence velocity fluctuations in sparsely seeded gas flows using a non-intrusive, point-wise technique based on Rayleigh and Mie scattering is discussed. A Fabry-Perot interferometer (FPI) is used to spectrally resolve laser light scattered by molecules and particulates in gas flows. The spectral content of the scattered light provides information about velocity, density, and temperature of the gas. A CCD camera is used to record images of the fringes formed by scattered light passing through the interferometer. Models of the spectral components are used in a least squares fitting routine to estimate the parameters from fringe images. Flow measurements are presented for subsonic and supersonic jet flows. The application range for this technique is mostly for high velocity situations (>25 m/s). Velocity, density, temperature, and turbulence velocity fluctuations were determined with accuracies within 5 m/s, 4%, 2%, and 5 m/s, respectively.     

Biocompatible copper(I) catalysts for in vivo imaging of glycans

The Cu(I)-catalyzed azide-alkyne cycloaddition (CuAAC) is the standard method for bioorthogonal conjugation. However, current Cu(I) catalyst formulations are toxic, hindering their use in living systems. Here we report that BTTES, a tris(triazolylmethyl)amine-based ligand for Cu(I), promotes the cycloaddition reaction rapidly in living systems without apparent toxicity. This catalyst allows, for the first time, noninvasive imaging of fucosylated glycans during zebrafish early embryogenesis. We microinjected embryos with alkyne-bearing GDP-fucose at the one-cell stage and detected the metabolically incorporated unnatural sugars using the biocompatible click chemistry. Labeled glycans could be imaged in the enveloping layer of zebrafish embryos between blastula and early larval stages. This new method paves the way for rapid, noninvasive imaging of biomolecules in living organisms.     

Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides

We report the first demonstration of cw wavelength conversion from the telecommunications band to the mid-IR (MIR) region via four-wave mixing in silicon nanowaveguides. We measure a parametric bandwidth of 748 nm by converting a 1636 nm signal to produce a 2384 nm idler and show continuously tunable wavelength conversion from 1792 to 2116 nm. This report indicates that the advantages of silicon photonics may be leveraged to create devices for a large range of MIR applications that require cw operation.     

Adjusting for confounding by cluster using generalized linear mixed models

We show how to use generalized linear mixed models to adjust for confounding by cluster of the effect of a within-cluster covariate. We derive estimators for both a cluster-specific causal effect and a population-averaged causal effect.     

Assessing the Productivity of the Direct Conversion of Methane-to-Methanol over Copper-Exchanged Zeolite Omega (MAZ) via Oxygen Looping

The methane-to-methanol (MtM) conversion via the oxygen looping approach using copper-exchanged zeolites has been extensively studied over the last decade. While a lot of research has focussed on maximizing yield and selectivity, little has been directed toward productivity—a metric far more meaningful for evaluating industrial potential. Using copper-exchanged zeolite omega (Cu-omega), a material highly active and selective for the MtM conversion using the isothermal oxygen looping approach, we show that this material exhibits unprecedented potential for industrial valorization. In doing so, we also present a novel methodology combining operando XAS and mass spectrometry for the screening of materials for the MtM conversion in oxygen looping mode.     

On Genericity and Ershov's Hierarchy

It is natural to wish to study miniaturisations of Cohen forcing suitable to sets of low arithmetic complexity. We consider extensions of the work of Schaeffer [9] and Jockusch and Posner [6] by looking at genericity notions within the Δ₂ sets. Different equivalent characterisations of 1‐genericity suggest different ways in which the definition might be generalised. There are two natural ways of casting the notion of 1‐genericity: in terms of sets of strings and in terms of density functions, as we will see here. While these definitions coincide at the first level of the difference hierarchy, they turn out to differ at other levels. Furthermore, these differences remain when the remainder of the Δ⁰₂ sets are considered. While the string characterization of 1‐genericity collapses at the second level of the difference hierarchy to 2‐genericity, the density function definition gives a very interesting hierarchy at level w and above. Both of these results point towards the deep similarities exhibited by the n‐c.e. degrees for n ≥ 2.     

The Emergence of Mathematical Modeling Competencies: An Investigation of Prospective Secondary Mathematics Teachers

A study with prospective teachers without prior mathematical modeling experience sheds light on how their newly developed conceptual understanding of modeling manifested itself in their work on the final task of a modeling module within a pedagogy course in secondary mathematics curriculum and assessment. The main purpose of the module was to provide opportunity for the prospective teachers to experience the Common Core Mathematical Practice Model with Mathematics and begin to develop competency in modeling. Their work and reflections displayed a range of proficiency in several competencies associated with the modeling process. Examples of their work illustrating these ranges are provided. The prospective teachers expressed both struggle and rewards during the process, and reflected on challenges for teaching modeling. The results suggest that infusing modules in existing courses can be an effective way to elevate prospective teachers from unfamiliarity with modeling to noticeable levels of proficiency in various modeling sub-competencies.     

Non-symmetric Cauchy kernels for the classical groups

We give non-symmetric versions of the Cauchy kernel and Littlewood's kernels, corresponding to the types A, B, C and D, of the classical groups. Defining two families of key polynomials (one of them being the Demazure characters), we show that these new kernels are diagonal in the basis of key polynomials. We define scalar products such that the two families of key polynomials are adjoint to each other.