The fundamental theorem of algebra: A most elementary proof

This paper shows an elementary and direct proof of the Fundamental Theorem of Algebra, via Bolzano-Weierstrass Theorem on Minima and the Binomial Formula, that avoids: any root extraction other than the one used to define the modulus function over the complex plane, trigonometry, differentiation, integration, series, arguments by induction and arguments using epsilon's and delta's.Comment: 5 page

The Initial Mass Function of the Orion Nebula Cluster across the H-burning limit

We present a new census of the Orion Nebula Cluster (ONC) over a large field of view (>30'x30'), significantly increasing the known population of stellar and substellar cluster members with precisely determined properties. We develop and exploit a technique to determine stellar effective temperatures from optical colors, nearly doubling the previously available number of objects with effective temperature determinations in this benchmark cluster. Our technique utilizes colors from deep photometry in the I-band and in two medium-band filters at lambda~753 and 770nm, which accurately measure the depth of a molecular feature present in the spectra of cool stars. From these colors we can derive effective temperatures with a precision corresponding to better than one-half spectral subtype, and importantly this precision is independent of the extinction to the individual stars. Also, because this technique utilizes only photometry redward of 750nm, the results are only mildly sensitive to optical veiling produced by accretion. Completing our census with previously available data, we place some 1750 sources in the Hertzsprung-Russel diagram and assign masses and ages down to 0.02 solar masses. At faint luminosities, we detect a large population of background sources which is easily separated in our photometry from the bona fide cluster members. The resulting initial mass function of the cluster has good completeness well into the substellar mass range, and we find that it declines steeply with decreasing mass. This suggests a deficiency of newly formed brown dwarfs in the cluster compared to the Galactic disk population.Comment: 16 pages, 18 figures. Accepted for publication in The Astrophysical Journa

Information Needs of Refugees: A Case Study of a Refugee Group Learning English in a Further Education College

A great deal has been discussed among librarians and teaching staff concerning the needs of a group of refugees/immigrants to acquire information skills in a further education college where this group takes ESOL classes. There is not doubt from both parties that the acquisition of these skills is crucial for their integration into society. Nevertheless, the cause of the argument is about how these skills should be delivered and by whom. Traditionally, teachers have taken these groups once a week to the Learning Centre (LC) and deliver a class as part of the curriculum. However, no special treatment has been offered to these groups from librarians. During the last year, this situation has raised concern among librarians, as this may not be the most beneficial way for these students to acquire such skills. It has been observed that most students would go to the LC during that class but would not go back again until the following class. It has been noticed by library staff that these students would approach librarians only if asked to do so by the teacher. Many of them would only go to the library during this lesson to borrow or return books and not at any other time. This situation has led to a debate between the ESOL tutors and the library staff. While the first argue that students benefit more if they have an information skills session with the teacher, librarians disagree by arguing that if the students have this sessions on their own and with the help of the librarians, they are more likely to use the library for their independent study, and therefore, to become independent learners. As a result, a new programme has been launched on a trial basis in which ESOL teachers and library staff will work closely. The workshop will take place in a classroom and will be delivered by the teacher. Then students will be sent in small groups to the LC to complete a part of the research booklet designed for this purpose. Once in the library, they are the responsibility of the librarians

HST measures of Mass Accretion Rates in the Orion Nebula Cluster

The present observational understanding of the evolution of the mass accretion rates (Macc) in pre-main sequence stars is limited by the lack of accurate measurements of Macc over homogeneous and large statistical samples of young stars. Such observational effort is needed to properly constrain the theory of star formation and disk evolution. Based on HST/WFPC2 observations, we present a study of Macc for a sample of \sim 700 sources in the Orion Nebula Cluster, ranging from the Hydrogen-burning limit to M\ast \sim 2M\odot. We derive Macc from both the U-band excess and the H{\alpha} luminosity (LH{\alpha}), after determining empirically both the shape of the typical accretion spectrum across the Balmer jump and the relation between the accretion luminosity (Lacc) and LH{\alpha}, that is Lacc/L\odot = (1.31\pm0.03)\cdotLH{\alpha}/L\odot + (2.63\pm 0.13). Given our large statistical sample, we are able to accurately investigate relations between Macc and the parameters of the central star such as mass and age. We clearly find Macc to increase with stellar mass, and decrease over evolutionary time, but we also find strong evidence that the decay of Macc with stellar age occurs over longer timescales for more massive PMS stars. Our best fit relation between these parameters is given by: log(Macc/M\odot\cdotyr)=(-5.12 \pm 0.86) -(0.46 \pm 0.13) \cdot log(t/yr) -(5.75 \pm 1.47)\cdot log(M\ast/M\odot) + (1.17 \pm 0.23)\cdot log(t/yr) \cdot log(M\ast/M\odot). These results also suggest that the similarity solution model could be revised for sources with M\ast > 0.5M\odot. Finally, we do not find a clear trend indicating environmental effects on the accretion properties of the sources.Comment: 17 pages, 15 figures, accepted for publication in Ap