A proof of van Aubel's theorem using orthogonal vectors

We show how two linearly independent vectors can be used to construct two orthogonal vectors of equal magnitude in a simple way. The proof that the constructed vectors are orthogonal and of equal magnitude is a good exercise for students studying properties of scalar and vector triple products. We then show how this result can be used to prove van Aubel's theorem that relates the two line segments joining the centres of squares on opposite sides of a plane quadrilateral.

Prevalence and nonrandom distribution of exonic mutations in interferon regulatory factor 6 in 307 families with Van der Woude syndrome and 37 families with popliteal pterygium syndrome

Purpose: Interferon regulatory factor 6 encodes a member of the IRF family of transcription factors. Mutations in interferon regulatory factor 6 cause Van der Woude and popliteal pterygium syndrome, two related orofacial clefting disorders. Here, we compared and contrasted the frequency and distribution of exonic Mutations in interferon regulatory factor 6 between two large geographically distinct collections of families with Van der Woude and between one collection of families with popliteal pterygium syndrome. Methods: We performed direct sequence analysis of interferon regulatory factor 6 exons oil samples from three collections, two with Van der Woude and one with popliteal pterygium syndrome. Results: We identified mutations in interferon regulatory factor 6 exons in 68% of families in both Van der Woude collections and in 97% of families with popliteal pterygium syndrome. In sum, 106 novel disease-causing variants were found. The distribution of mutations in the interferon regulatory factor 6 exons in each collection was not random; exons 3, 4, 7, and 9 accounted for 80%. In the Van der Woude collections, the mutations were evenly divided between protein truncation and missense, whereas most mutations identified in the popliteal pterygium syndrome collection were missense. Further, the missense mutations associated with popliteal pterygium syndrome were localized significantly to exon 4, at residues that are predicted to bind directly to DNA. Conclusion: The nonrandom distribution of mutations in the interferon regulatory factor 6 exons suggests a two-tier approach for efficient mutation screens for interferon regulatory factor 6. The type and distribution of mutations are consistent with the hypothesis that Van der Woude is caused by haploinsufficiency of interferon regulatory factor 6. Oil the other hand, the distribution of popliteal pterygium syndrome-associated mutations suggests a different, though not mutually exclusive, effect oil interferon regulatory factor 6 function. Genet Med 2009:11(4):241-247.

Advanced functionality for radio analysis in the Offline software framework of the Pierre Auger Observatory

The advent of the Auger Engineering Radio Array (AERA) necessitates the development of a powerful framework for the analysis of radio measurements of cosmic ray air showers. As AERA performs ""radio-hybrid"" measurements of air shower radio emission in coincidence with the surface particle detectors and fluorescence telescopes of the Pierre Auger Observatory, the radio analysis functionality had to be incorporated in the existing hybrid analysis solutions for fluorescence and surface detector data. This goal has been achieved in a natural way by extending the existing Auger Offline software framework with radio functionality. In this article, we lay out the design, highlights and features of the radio extension implemented in the Auger Offline framework. Its functionality has achieved a high degree of sophistication and offers advanced features such as vectorial reconstruction of the electric field, advanced signal processing algorithms, a transparent and efficient handling of FFTs, a very detailed simulation of detector effects, and the read-in of multiple data formats including data from various radio simulation codes. The source code of this radio functionality can be made available to interested parties on request. (C) 2011 Elsevier B.V. All rights reserved.

Trigger and aperture of the surface detector array of the Pierre Auger Observatory

The surface detector array of the Pierre Auger Observatory consists of 1600 water-Cherenkov detectors, for the study of extensive air showers (EAS) generated by ultra-high-energy cosmic rays. We describe the trigger hierarchy, from the identification of candidate showers at the level of a single detector, amongst a large background (mainly random single cosmic ray muons), up to the selection of real events and the rejection of random coincidences. Such trigger makes the surface detector array fully efficient for the detection of EAS with energy above 3 x 10(18) eV, for all zenith angles between 0 degrees and 60 degrees, independently of the position of the impact point and of the mass of the primary particle. In these range of energies and angles, the exposure of the surface array can be determined purely on the basis of the geometrical acceptance. (C) 2009 Elsevier B.V. All rights reserved.

Anisotropy and chemical composition of ultra-high energy cosmic rays using arrival directions measured by the Pierre Auger Observatory

The Pierre Auger Collaboration has reported. evidence for anisotropy in the distribution of arrival directions of the cosmic rays with energies E > E(th) = 5.5 x 10(19) eV. These show a correlation with the distribution of nearby extragalactic objects, including an apparent excess around the direction of Centaurus A. If the particles responsible for these excesses at E > E(th) are heavy nuclei with charge Z, the proton component of the sources should lead to excesses in the same regions at energies E/Z. We here report the lack of anisotropies in these directions at energies above E(th)/Z (for illustrative values of Z = 6, 13, 26). If the anisotropies above E(th) are due to nuclei with charge Z, and under reasonable assumptions about the acceleration process, these observations imply stringent constraints on the allowed proton fraction at the lower energies.

Search for first harmonic modulation in the right ascension distribution of cosmic rays detected at the Pierre Auger Observatory

We present the results of searches for dipolar-type anisotropies in different energy ranges above 2.5 x 10(17) eV with the surface detector array of the Pierre Auger Observatory, reporting on both the phase and the amplitude measurements of the first harmonic modulation in the right-ascension distribution. Upper limits on the amplitudes are obtained, which provide the most stringent bounds at present, being below 2% at 99% C.L. for EeV energies. We also compare our results to those of previous experiments as well as with some theoretical expectations. (C) 2011 Elsevier B.V. All rights reserved.

The Pierre Auger Observatory scaler mode for the study of solar activity modulation of galactic cosmic rays

Since data-taking began in January 2004, the Pierre Auger Observatory has been recording the count rates of low energy secondary cosmic ray particles for the self-calibration of the ground detectors of its surface detector array. After correcting for atmospheric effects, modulations of galactic cosmic rays due to solar activity and transient events are observed. Temporal variations related with the activity of the heliosphere can be determined with high accuracy due to the high total count rates. In this study, the available data are presented together with an analysis focused on the observation of Forbush decreases, where a strong correlation with neutron monitor data is found.

The exposure of the hybrid detector of the Pierre Auger Observatory

The Pierre Auger Observatory is a detector for ultra-high energy cosmic rays. It consists of a surface array to measure secondary particles at ground level and a fluorescence detector to measure the development of air showers in the atmosphere above the array. The ""hybrid"" detection mode combines the information from the two subsystems. We describe the determination of the hybrid exposure for events observed by the fluorescence telescopes in coincidence with at least one water-Cherenkov detector of the surface array. A detailed knowledge of the time dependence of the detection operations is crucial for an accurate evaluation of the exposure. We discuss the relevance of monitoring data collected during operations, such as the status of the fluorescence detector, background light and atmospheric conditions, that are used in both simulation and reconstruction. (C) 2010 Elsevier B.V. All rights reserved.

Update on the correlation of the highest energy cosmic rays with nearby extragalactic matter

Data collected by the Pierre Auger Observatory through 31 August 2007 showed evidence for anisotropy in the arrival directions of cosmic rays above the Greisen-Zatsepin-Kuz`min energy threshold, 6 x 10(19) eV. The anisotropy was measured by the fraction of arrival directions that are less than 3.1 degrees from the position of an active galactic nucleus within 75 Mpc (using the Veron-Cetty and Veron 12th catalog). An updated measurement of this fraction is reported here using the arrival directions of cosmic rays recorded above the same energy threshold through 31 December 2009. The number of arrival directions has increased from 27 to 69, allowing a more precise measurement. The correlating fraction is (38(-6)(+7))%, compared with 21% expected for isotropic cosmic rays. This is down from the early estimate of (69-(+11)(13))%. The enlarged set of arrival directions is examined also in relation to other populations of nearby extragalactic objects: galaxies in the 2 Microns All Sky Survey and active galactic nuclei detected in hard X-rays by the Swift Burst Alert Telescope. A celestial region around the position of the radiogalaxy Cen A has the largest excess of arrival directions relative to isotropic expectations. The 2-point autocorrelation function is shown for the enlarged set of arrival directions and compared to the isotropic expectation. (C) 2010 Elsevier B.V. All rights reserved.

Measurement of the energy spectrum of cosmic rays above 10(18) eV using the Pierre Auger Observatory

We report a measurement of the flux of cosmic rays with unprecedented precision and Statistics using the Pierre Auger Observatory Based on fluorescence observations in coincidence with at least one Surface detector we derive a spectrum for energies above 10(18) eV We also update the previously published energy spectrum obtained with the surface detector array The two spectra are combined addressing the systematic uncertainties and, in particular. the influence of the energy resolution on the spectral shape The spectrum can be described by a broken power law E(-gamma) with index gamma = 3 3 below the ankle which is measured at log(10)(E(ankle)/eV) = 18 6 Above the ankle the spectrum is described by a power law with index 2 6 followed by a flux suppression, above about log(10)(E/eV) = 19 5, detected with high statistical significance (C) 2010 Elsevier B V All rights reserved

A study of the effect of molecular and aerosol conditions in the atmosphere on air fluorescence measurements at the Pierre Auger Observatory

The air fluorescence detector of the Pierre Auger Observatory is designed to perforin calorimetric measurements of extensive air showers created by Cosmic rays of above 10(18) eV. To correct these measurements for the effects introduced by atmospheric fluctuations, the Observatory contains a group Of monitoring instruments to record atmospheric conditions across the detector site, ail area exceeding 3000 km(2). The atmospheric data are used extensively in the reconstruction of air showers, and are particularly important for the correct determination of shower energies and the depths of shower maxima. This paper contains a summary of the molecular and aerosol conditions measured at the Pierre Auger Observatory since the start of regular operations in 2004, and includes a discussion of the impact of these measurements oil air shower reconstructions. Between 10(18) and 10(20) eV, the systematic Uncertainties due to all atmospheric effects increase from 4% to 8% in measurements of shower energy, and 4 g cm(-2) to 8 g cm(-2) in measurements of the shower maximum. (C) 2010 Elsevier B.V. All rights reserved.

Döden i Falun 1750 till 1770 : Gruvhanteringen och miljön i ett jämförande perspektiv

Syftet med denna uppsats är att utröna om risken att avlida i förtid var större i Falun än på tre andra jämnstora orter i Mellansverige med i övrigt likartade miljömässiga förutsättningar, mellan åren 1750 till 1770. Det använda källmaterialet är Tabellverkets folkbokförings- och mortalitetstabeller för åren 1750 till 1770. Dödsfall i miljörelaterade sjukdomar för Falun har jämförts med orterna Mora, Gefle och Hedemora. Miljön i Falun skiljde sig från de andra orterna främst på grund av den massiva exponeringen av svaveldioxid och metallhaltiga partiklar, som förekom som ett resultat av gruvverksamheten och den efterföljande kopparframställningen. Gefle var en tätort med stadens problem medan Mora var ett agrart samhälle och Hedemora var både och. Resultatet visar, att risken att avlida i bröst- och lungrelaterade sjukdomar var signifikant högre i Falun än i Mora och Hedemora. Även i Gävle var risken mindre än i Falun, dock ej lika tydligt, vilket sannolikt är en följd av att Gävle var en tätort, som allmänt gav en högre dödlighet. Även den allmänna risken att avlida i förtid var högre i Falun än för de andra orterna. Undersökningen visar också på den risk, som fanns, att avlida i förtid, som de olika epidemierna gav upphov till och den stora inverkan det får. Medelåldern var högre i Falun än för de andra undersökta orterna men detta förklaras främst och rimligast av demografiska skillnader

Diagnostisering av elever i geometri : En studie med utgångspunkt i van Hieles teori

Detta är en studie som har sin utgångspunkt i Pierre M. van Hieles teori om lärande i geometri, som presenterades 1986 i boken Structure and Insight. Van Hiele har i boken vidareutvecklat sin och Dina van Hiele-Geldofs ursprungliga lärandeteori från 1955. Vår studie har som syfte att se om van Hieles teori går att tillämpa i en individuell, skriftlig diagnos för att nivåbestämma elever i årskurs 1 på gymnasiet.