Representations of celestial coordinates in FITS

In Paper I, Greisen & Calabretta (2002) describe a generalized method for assigning physical coordinates to FITS image pixels. This paper implements this method for all spherical map projections likely to be of interest in astronomy. The new methods encompass existing informal FITS spherical coordinate conventions and translations from them are described. Detailed examples of header interpretation and construction are given.Comment: Consequent to Paper I: "Representations of world coordinates in FITS". 45 pages, 38 figures, 13 tables, aa macros v5.2 (2002/Jun). Both papers submitted to Astronomy & Astrophysics (2002/07/19). Replaced to try to get figure and table placement right (no textual changes

The On The Fly Imaging Technique

The On-The-Fly (OTF) imaging technique enables single-dish radio telescopes to construct images of small areas of the sky with greater efficiency and accuracy. This paper describes the practical application of the OTF imaging technique. By way of example the implementation of the OTF imaging technique at the NRAO 12 Meter Telescope is described. Specific requirements for data sampling, image formation, and Doppler correction are discussed.Comment: 10 pages, 13 figures, accepted A&

Representations of world coordinates in FITS

The initial descriptions of the FITS format provided a simplified method for describing the physical coordinate values of the image pixels, but deliberately did not specify any of the detailed conventions required to convey the complexities of actual image coordinates. Building on conventions in wide use within astronomy, this paper proposes general extensions to the original methods for describing the world coordinates of FITS data. In subsequent papers, we apply these general conventions to the methods by which spherical coordinates may be projected onto a two-dimensional plane and to frequency/wavelength/velocity coordinates.Comment: 15 Pages, 1 figure, LaTex with Astronomy & Astrophysics macro package, submitted to A&A, related papers at http://www.aoc.nrao.edu/~egreise

Taking Language Out Of The Equation: The Assessment Of Basic Math Competence Without Language

Although numeracy, next to literacy, is an essential skill in many knowledge based societies of the 21st century, between 5 and 10 % of the population suffer from more or less severe mathematics learning disorders or dyscalculia. However, mathematical ability is not a pure construct. Instead, mathematical ability maintains a complex relationship with linguistic abilities. This relationship has significant implications for the assessment of a person’s mathematical ability in multilingual contexts. The hereby presented research project addresses the consequences of that relationship in the context of Luxembourg, a highly multilingual country at the center of Europe. The aim of the project was to tackle psychometric issues that arise when the test taker does not master the language of the test sufficiently and to offer an alternative solution to available assessment batteries based on verbal instructions and tasks. In the first study, we demonstrate the role of reading comprehension in the language of instruction on third grader’s performance in mathematics in Luxembourg and show that non-native speaker’s underachievement in mathematics can be largely or entirely explained by their lacking reading comprehension in the language of assessment. In the next study we report on the two first pilot studies with NUMTEST, an assessment battery that aims to measure children’s basic mathematical competence by replacing verbal instructions and task content with video instructions and animated tasks. The findings of these studies show that children’s basic mathematical competence can indeed be reliably assessed using this new paradigm. Opportunities and limitations of the paradigm are discussed. The third and final study of this project addresses the psychometric characteristics of this newly developed assessment battery. Its findings show that the NUMTEST battery provides for good reliability and concurrent validity all while being language neutral. In summary, the presented project provides for an encouraging proof of concept for the video instruction method while offering preliminary evidence for its validity as an early screener for math learning difficulties

Cosmic ray primary mass composition above the knee: deduction from lateral distribution of electrons

Influence of shower fluctuations on the shape of lateral distribution of electrons in EAS of fixed size measured by scintillation counters is analyzed in framework of scaling formalism. Correction factors for the mean square radius of electrons are calculated for the experimental conditions of KASCADE array. Possible improvement of the primary mass discrimination by analysis of lateral distribution of EAS electrons is discussed in detail.Comment: Proceedings of the XIV International Symposium on Very High Energy Cosmic Ray Interaction

The Negative Stigma Surrounding Mathematics

There is a negative stigma that surrounds mathematics in our education system. It is important to bring notice to this for the benefit of future students. There is a lot of research claiming that math is looked down on, but they do not answer why, or what we can do to fix it. Why is there a greater negative stigma around math and not other subjects? What roles to teachers, parents, and peers play in this stigma? In this article, I created a survey for people to answer questions regarding their opinion on math, who they believe typically does well in math, and what affect the people around them contribute to their view of math. As our world is growing technologically, we need teachers to showcase their passion for math to their students. Marissa Greisen is a high school student in the PSU High School Senior Inquiry Program, University Studies Program, Portland State University

The Greisen Equation Explained and Improved

Analytic description of the evolution of cosmic ray showers is dominated by the Greisen equation nearly five decades old. We present an alternative approach with several advantages. Among the new features are a prediction of the differential distribution, replacing Greisen's form which fails to be positive definite. Explicit comparison with Monte Carlo simulations shows excellent agreement after a few radiation lengths of development. We find a clear connection between Monte Carlo adjustment of Greisen's form and underlying physics, and present a concise derivation with all steps explicit. We also reconstruct the steps needed to reproduce Greisen's approximate formula, which appears not to have been published previously.Comment: 8 pages, 7 figures, revised version, accepted for publication in Phys. Rev.

Power Laws and the Cosmic Ray Energy Spectrum

Two separate statistical tests are applied to the AGASA and preliminary Auger Cosmic Ray Energy spectra in an attempt to find deviation from a pure power-law. The first test is constructed from the probability distribution for the maximum event of a sample drawn from a power-law. The second employs the TP-statistic, a function defined to deviate from zero when the sample deviates from the power-law form, regardless of the value of the power index. The AGASA data show no significant deviation from a power-law when subjected to both tests. Applying these tests to the Auger spectrum suggests deviation from a power-law. However, potentially large systematics on the relative energy scale prevent us from drawing definite conclusions at this time.Comment: 21 pages, 18 figures, submitted to Astro. Part. Phy

Radio Emission from Cosmic Ray Air Showers: Coherent Geosynchrotron Radiation

Cosmic ray air showers have been known for over 30 years to emit pulsed radio emission in the frequency range from a few to a few hundred MHz, an effect that offers great opportunities for the study of extensive air showers with upcoming fully digital "software radio telescopes" such as LOFAR and the enhancement of particle detector arrays such as KASCADE Grande or the Pierre Auger Observatory. However, there are still a lot of open questions regarding the strength of the emission as well as the underlying emission mechanism. Accompanying the development of a LOFAR prototype station dedicated to the observation of radio emission from extensive air showers, LOPES, we therefore take a new approach to modeling the emission process, interpreting it as "coherent geosynchrotron emission" from electron-positron pairs gyrating in the earth's magnetic field. We develop our model in a step-by-step procedure incorporating increasingly realistic shower geometries in order to disentangle the coherence effects arising from the different scales present in the air shower structure and assess their influence on the spectrum and radial dependence of the emitted radiation. We infer that the air shower "pancake" thickness directly limits the frequency range of the emitted radiation, while the radial dependence of the emission is mainly governed by the intrinsic beaming cone of the synchrotron radiation and the superposition of the emission over the air shower evolution as a whole. Our model succeeds in reproducing the qualitative trends in the emission spectrum and radial dependence that were observed in the past, and is consistent with the absolute level of the emission within the relatively large systematic errors in the experimental data.Comment: 17 pages, 18 figures, accepted for publication by Astronomy & Astrophysic