The Apollo Auxiliary Power Supply System, Project Apollo

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Global Classical Solutions of the Boltzmann Equation with Long-Range Interactions and Soft Potentials

In this work we prove global stability for the Boltzmann equation (1872) with the physical collision kernels derived by Maxwell in 1866 for the full range of inverse power intermolecular potentials, $r^{-(p-1)}$ with $p>2$. This completes the work which we began in (arXiv:0912.0888v1). We more generally cover collision kernels with parameters $s\in (0,1)$ and $\gamma$ satisfying $\gamma > -(n-2)-2s$ in arbitrary dimensions $\mathbb{T}^n \times \mathbb{R}^n$ with $n\ge 2$. Moreover, we prove rapid convergence as predicted by the Boltzmann H-Theorem. When $\gamma + 2s \ge 0$, we have exponential time decay to the Maxwellian equilibrium states. When $\gamma + 2s < 0$, our solutions decay polynomially fast in time with any rate. These results are constructive. Additionally, we prove sharp constructive upper and lower bounds for the linearized collision operator in terms of a geometric fractional Sobolev norm; we thus observe that a spectral gap exists only when $\gamma + 2s \ge 0$, as conjectured in Mouhot-Strain (2007).Comment: This file has not changed, but this work has been combined with (arXiv:0912.0888v1), simplified and extended into a new preprint, please see the updated version: arXiv:1011.5441v

Fuse and switch functions combined within a single housing

Fuswitch provides both switch and fuse functions within a single housing. A mercury capillary is used to alternately vaporize and condense the mercury within a reservoir. The housing is impervious to mercury and the fuse portion of the device operates on the principle of the self-healing mercury fuse

Speciation without chromatography: Part I. Determination of tributyltin in aqueous samples by chloride generation, headspace solid-phase microextraction and inductively coupled plasma time of flight mass spectrometry

An analytical procedure was developed for the determination of tributyltin in aqueous samples. The relatively high volatility of the organometal halide species confers suitability for their headspace sampling from the vapour phase above natural waters or leached solid samples. Tributyltin was collected from the sample headspace above various chloride-containing matrices, including HCl, sodium chloride solution and sea-water, by passive sampling using a polydimethylsiloxane/divinylbenzene (PDMS/DVB)-coated solid-phase microextraction (SPME) fiber. Inductively coupled plasma time-of-flight mass spectrometry (ICP-TOFMS) was used for detection following thermal desorption of analytes from the fiber. A detection limit of 5.8 pg ml–1(as tin) was realized in aqueous samples. Method validation was achieved using NRCC PACS-2 (Sediment) certified reference material, for which reasonable agreement between certified and measured values for tributyltin content was obtained

Mental health and emotional well-being of students in further education - a scoping study

This study aimed to explore how FE colleges in England are engaging with and addressing the mental health needs of their young students (aged 16-19), both in terms of promoting positive mental health and emotional well-being and in responding to identified mental health problems

Interactive Communication with Unknown Noise Rate

Alice and Bob want to run a protocol over a noisy channel, where a certain number of bits are flipped adversarially. Several results take a protocol requiring $L$ bits of noise-free communication and make it robust over such a channel. In a recent breakthrough result, Haeupler described an algorithm that sends a number of bits that is conjectured to be near optimal in such a model. However, his algorithm critically requires $a \ priori$ knowledge of the number of bits that will be flipped by the adversary. We describe an algorithm requiring no such knowledge. If an adversary flips $T$ bits, our algorithm sends $L + O\left(\sqrt{L(T+1)\log L} + T\right)$ bits in expectation and succeeds with high probability in $L$. It does so without any $a \ priori$ knowledge of $T$. Assuming a conjectured lower bound by Haeupler, our result is optimal up to logarithmic factors. Our algorithm critically relies on the assumption of a private channel. We show that privacy is necessary when the amount of noise is unknown.Comment: Made substantial improvements to the algorithm and analysis. Previous version had a subtle error involving the adversary's ability to attack fingerprint

Diagnosis and management of hyponatraemia: AGREEing the guidelines

Hyponatraemia is a common electrolyte disorder associated with significant complications and controversies regarding its optimal management. Clinical practice guidelines and consensus statements have attempted to provide clinicians with evidence-based diagnostic and treatment strategies for hyponatraemia. Recently published guidance documents differ in their methods employed to review the quality of available evidence. Nagler et al. used the Appraisal of Guideline for Research and Evaluation (AGREE II) instrument in a systematic review of guidelines and consensus statements for the diagnosis and management of hyponatraemia. Nagler and colleagues highlighted the variability in methodological rigour applied to guideline development and inconsistencies between publications in relation to management of hyponatraemia (including the recommended rate of correction of a low serum sodium concentration). These differences could cause confusion for practising physicians managing patients with hyponatraemia. Please see related article: http://www.biomedcentral.com/1741-7015/12/231

Classification of Minimal Separating Sets in Low Genus Surfaces

Consider a surface $S$ and let $M\subset S$. If $S\setminus M$ is not connected, then we say $M$ \emph{separates} $S$, and we refer to $M$ as a \emph{separating set} of $S$. If $M$ separates $S$, and no proper subset of $M$ separates $S$, then we say $M$ is a \emph{minimal separating set} of $S$. In this paper we use methods of computational combinatorial topology to classify the minimal separating sets of the orientable surfaces of genus $g=2$ and $g=3$. The classification for genus 0 and 1 was done in earlier work, using methods of algebraic topology.Comment: 24 pages, 5 figures, 2 tables (11 pages

Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism

In a previous publication, two of us derived a relation between the scattering amplitude of three identical bosons, $\mathcal M_3$, and a real function referred to as the {divergence-free} K matrix and denoted $\mathcal K_{\text{df},3}$. The result arose in the context of a relation between finite-volume energies and $\mathcal K_{\text{df},3}$, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between $\mathcal K_{\text{df},3}$ and $\mathcal M_3$. We show that, for any real choice of $\mathcal K_{\text{df},3}$, $\mathcal M_3$ satisfies the three-particle unitarity constraint to all orders. Given that $\mathcal K_{\text{df},3}$ is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).Comment: 19 pages, 4 figures, JLAB-THY-19-2945, CERN-TH-2019-07