Revisiting the radio interferometer measurement equation. I. A full-sky Jones formalism

Since its formulation by Hamaker et al., the radio interferometer measurement equation (RIME) has provided a rigorous mathematical basis for the development of novel calibration methods and techniques, including various approaches to the problem of direction-dependent effects (DDEs). This series of papers aims to place recent developments in the treatment of DDEs into one RIME-based mathematical framework, and to demonstrate the ease with which the various effects can be described and understood. It also aims to show the benefits of a RIME-based approach to calibration. Paper I re-derives the RIME from first principles, extends the formalism to the full-sky case, and incorporates DDEs. Paper II then uses the formalism to describe self-calibration, both with a full RIME, and with the approximate equations of older software packages, and shows how this is affected by DDEs. It also gives an overview of real-life DDEs and proposed methods of dealing with them. Applying this to WSRT data (Paper III) results in a noise-limited image of the field around 3C 147 with a very high dynamic range (1.6 million), and none of the off-axis artifacts that plague regular selfcal. The resulting differential gain solutions contain significant information on DDEs, and can be used for iterative improvements of sky models. Perhaps most importantly, sources as faint as 2 mJy have been shown to yield meaningful differential gain solutions, and thus can be used as potential calibration beacons in other DDE-related schemes.Comment: 12 pages, no figures, published in A&

Fixed-point-free involutions and Schur P-positivity

The orbits of the symplectic group acting on the type A flag variety are indexed by the fixed-point-free involutions in a finite symmetric group. The cohomology classes of the closures of these orbits have polynomial representatives $\hat{\mathfrak{S}}^{\tt{FPF}}_z$ akin to Schubert polynomials. We show that the fixed-point-free involution Stanley symmetric functions $\hat{F}^{\tt{FPF}}_z$, which are stable limits of the polynomials $\hat{\mathfrak{S}}^{\tt{FPF}}_z$, are Schur $P$-positive. To do so, we construct an analogue of the Lascoux-Sch\"utzenberger tree, an algebraic recurrence that computes Schubert polynomials. As a byproduct of our proof, we obtain a Pfaffian formula of geometric interest for $\hat{\mathfrak{S}}^{\tt{FPF}}_z$ when $z$ is a fixed-point-free version of a Grassmannian permutation. We also classify the fixed-point-free involution Stanley symmetric functions that are single Schur $P$-functions, and show that the decomposition of $\hat{F}^{\tt{FPF}}_z$ into Schur $P$-functions is unitriangular with respect to dominance order on strict partitions. These results and proofs mirror previous work by the authors related to the orthogonal group action on the type A flag variety.Comment: 34 pages, 1 figure. This article was formerly the second half of arXiv:1701.02824; v2: revised introduction, expanded proofs and examples, added index of notation, minor correction

Manned Mars mission cost estimate

The potential costs of several options of a manned Mars mission are examined. A cost estimating methodology based primarily on existing Marshall Space Flight Center (MSFC) parametric cost models is summarized. These models include the MSFC Space Station Cost Model and the MSFC Launch Vehicle Cost Model as well as other modes and techniques. The ground rules and assumptions of the cost estimating methodology are discussed and cost estimates presented for six potential mission options which were studied. The estimated manned Mars mission costs are compared to the cost of the somewhat analogous Apollo Program cost after normalizing the Apollo cost to the environment and ground rules of the manned Mars missions. It is concluded that a manned Mars mission, as currently defined, could be accomplished for under $30 billion in 1985 dollars excluding launch vehicle development and mission operations

PSRCHIVE and PSRFITS: Definition of the Stokes Parameters and Instrumental Basis Conventions

This paper defines the mathematical convention adopted to describe an electromagnetic wave and its polarisation state, as implemented in the PSRCHIVE software and represented in the PSRFITS definition. Contrast is made between the convention that has been widely accepted by pulsar astronomers and the IAU/IEEE definitions of the Stokes parameters. The former is adopted as the PSR/IEEE convention, and a set of useful parameters are presented for describing the differences between the PSR/IEEE standard and the conventions (either implicit or explicit) that form part of the design of observatory instrumentation. To aid in the empirical determination of instrumental convention parameters, well-calibrated average polarisation profiles of PSR J0304+1932 and PSR J0742-2822 are presented at radio wavelengths of approximately 10, 20, and 40 cm.Comment: 7 pages, 2 figures, to be published in PAS

Cathodoluminescence of powder layers of nanometer-sized Y2O3:Eu and micrometer-sized ZnO:Zn phosphor particles

Copyright @ The Electrochemical Society, Inc. 2013. All rights reserved. Except as provided under U.S. copyright law, this work may not be reproduced, resold, distributed, or modified without the express permission of The Electrochemical Society (ECS). The archival version of this work was published in The ECS Journal of Solid State Science and Technology, 2(9), R201 - R207, 2013.We present a simple method to measure the cathodoluminescence of charging and non-charging phosphor powder layers at low primary electron beam energy. The method is based on comparing a non-charging surface of a conducting material such as copper or indium tin oxide with charging surfaces of non-conducting phosphors. The phosphors that were investigated were ZnO:Zn, which is slightly conductive and supposed not to charge upon electron bombardment, and Y2O3:Eu, which charges at sufficiently high current density. It was found that the luminous efficacies of ZnO:Zn and Y2O3:Eu at 5 keV primary beam energy were 23 and 16 lm/w respectively, larger than reported in the literature. This is partly explained by calculating the efficacy from the summation of the luminances measured in the reflected and transmitted mode. This method also minimizes the inaccuracy introduced by the effect of the coating weight. The ratio between luminances measured in reflection and transmission is described in terms of a one-dimensional light scattering theory

Coxeter-Knuth graphs and a signed Little map for type B reduced words

We define an analog of David Little's algorithm for reduced words in type B, and investigate its main properties. In particular, we show that our algorithm preserves the recording tableau of Kra\'{s}kiewicz insertion, and that it provides a bijective realization of the Type B transition equations in Schubert calculus. Many other aspects of type A theory carry over to this new setting. Our primary tool is a shifted version of the dual equivalence graphs defined by Assaf and further developed by Roberts. We provide an axiomatic characterization of shifted dual equivalence graphs, and use them to prove a structure theorem for the graph of Type B Coxeter-Knuth relations.Comment: 41 pages, 10 figures, many improvements from version 1, substantively the same as the version in Electronic Journal of Combinatorics, Vol 21, Issue

Factors affecting sorghum protein digestibility

In the semi-arid tropics worldwide, sorghum (Sorghum bicolor (L.) Moench) is cultivated by farmers on a subsistence level and consumed as food by humans. A nutritional limitation to its use is the poor digestibility of sorghum protein when wet cooked. The factors affecting wet cooked sorghum protein digestibility may be categorised into two main groups: exogenous factors (grain organisational structure, polyphenols, phytic acid, starch and non-starch polysaccharides) and endogenous factors (disulphide and non-disulphide crosslinking, kafirin hydrophobicity and changes in protein secondary structure). All these factors have been shown to influence sorghum protein digestibility. More than one factor may be at play at any time depending on the nature or the state in which the sorghum grain is; that is whether whole grain, endosperm, protein body preparation, high-tannin or condensed-tannin-free. It is proposed that protein crosslinking may be the greatest factor that influences sorghum protein digestibility. This may be between ?- and ß-kafirin proteins at the protein body periphery, which may impede digestion of the centrally located major storage protein, a-kafirin, or between ?- or ß-kafirin and a-kafiri

ATMOSPHERE ENTRY SIMULATOR AND ITS APPLICATION TO THE DETERMINATION OF ABLATIVE PROPERTIES OF MATERIALS FOR BALLISTIC MISSILES

Ames atmosphere entry simulator and its use in determining characteristics of ethyl cellulose as ablative heat shield for ballistic missile