Polygons in billiard orbits

We study the geometry of billiard orbits on rectangular billiards. A truncated billiard orbit induces a partition of the rectangle into polygons. We prove that thirteen is a sharp upper bound for the number of different areas of these polygons.Comment: 14 page

The effect of distant large scale structure on weak lensing mass estimates

We quantify the uncertainty in weak lensing mass estimates of clusters of galaxies, caused by distant (uncorrelated) large scale structure along the line of sight. We find that the effect is fairly small for deep observations (20<R<26) of massive clusters (sigma=1000 km/s) at intermediate redshifts, where the bulk of the sources are at high redshifts compared to the cluster redshift. If the lensing signal is measured out to 1.5 h_{50}^{-1} Mpc the typical 1sigma relative uncertainty in the mass is about 6%. However, in other situations the induced uncertainty can be larger. For instance, in the case of nearby clusters, such as the Coma cluster, background structures introduce a considerable uncertainty in the mass, limiting the maximum achievable S/N-ratio to \sim 7, even for deep observations. The noise in the cluster mass estimate caused by the large scale structure increases with increasing aperture size, which will also complicate attempts to constrain cluster mass profiles at large distances from the cluster centre. However, the distant large scale structure studied here can be considered an additional (statistical) source of error, and by averaging the results of several clusters the noise is decreased.Comment: accepted for publication in Astronomy and Astrophysics 11 pages, 9 figure

A Preliminary Report on Investigations into (Bon nyid) 'Od gsal and Zhi khro bar do in Earlier Zhang zhung sNyan rgyud and sNyan rgyud Literature

Revue d’Etudes Tibétaines Number 17, October 200

Effect of “overlapping” voltage contacts in planar hall transducers

A mathematical model is derived to compute the output of a planar Hall tranducer (PHT) with overlapping voltage contacts at arbitrary positions and of arbitrary sizes. The model is based on the finite difference representation of the integral equation J…n ds = 0. In order to verify the model, the output of five PHTs with varying overlap sizes is measured in homogeneous and inhomogeneous fields. The computed results prove to be in good agreement with the experimental ones. The model is used to predict the effect of overlapping contacts on the output and resolution for several transducer configurations. The results are given in a number of diagrams. It is shown that a PHT with lower contacts (at the medium side) can be advantageous with respect to a biased (barber-pole) magnetoresistive (MR) head having the same size

Metacognition and transfer within a course or instructional design rules and metacognition

A metacognitive strategy for doing research, included transfer, was taught in a course of nine afternoons. The success of this course raised some questions. How do the students learn? How does metacognition play a role? The course was designed in accordance with several instructional principles. The course was divided into three domains in which the strategy was introduced, practised, and applied respectively. Literature research revealed four possible metacognitive variants that correlate so it was supposed that implementing them all helped to reach the objectives of the course. The relation of the metacognitive variants with the instructional principles is described. To study learning the students were divided into three groups (weak, moderate, good) by their marks for other courses. The performance of the groups in each domain was monitored by their marks, scoring of metacognitive skills, questionnaires, observations, and time keeping. The moderate students scored as high as the good ones for the strategy in the last domain, a unique result. The metacognitive development of the other metacognitive skills was not linear. The conclusions are that the success of this course can be explained by a system of double sequencing and an interaction of all metacognitive variants, and that instructional design rules for metacognitive and cognitive objectives are differen

Structure of, access to, and uncertainty in reasoning and their dependence on content

It is known that content has an effect on reasoning. In this paper the influence of the content on the structure of reasoning, the access to it, and the ability to handle uncertainty was studied. The participants were presented with reasoning tasks about the weather and about the oscilloscope in which uncertain premises were introduced. Correct reasoning procedures were identified including correct reasoning with wrong answers. In correct reasoning procedures about the weather, three different structures of reasoning were identified. The participants were mostly able to reason with uncertain components. In reasoning about the oscilloscope, less correct reasoning procedures were found. No empirical and theoretical structures were used. The hidden structure differed here from the one in the weather case because the participants were not able to handle all uncertain components in otherwise correct reasoning. The implications of this unique finding for the acquisition of reasoning skills are discusse