Observations of the gas stream in the mass transfer binary HR 2142 prime 1

The mass transfer binary system HR 2142 was observed at selected phases with the high resolution spectrograph on IUE. The observations were scheduled throughout the interval 0.91 phi 0.00 in order to allow viewing of the light of the primary star through the gas stream as it presents different orientations to the line of sight. Numerous UV lines formed in the gas stream were identified. The strengths and velocity variations displayed by these lines are compared with those observed in the ground based spectral region. As part of a preliminary analysis of the IUE data, column densities and velocities from Si III (4), Si IV (1), and Ti III (1) are used to deduce electron densities in the gas stream as well as its thickness. Possible evidence for stratification in the gas stream is presented

Isotopic Equivalence from Bezier Curve Subdivision

We prove that the control polygon of a Bezier curve B becomes homeomorphic and ambient isotopic to B via subdivision, and we provide closed-form formulas to compute the number of iterations to ensure these topological characteristics. We first show that the exterior angles of control polygons converge exponentially to zero under subdivision.Comment: arXiv admin note: substantial text overlap with arXiv:1211.035

Reid on knowledge and justification in Physical Education

[FIRST PARAGRAPHS] To my knowledge, very little has been written on the educational justification of PE activities for the last decade. Since PE now does have a place on the National Curriculum, albeit arguably a minor one, the justification issue does seem to have been put on the back burner by the profession. In a recent and welcome addition to the literature, Reid revisits the debate, outlining two ‘conventional assumptions’ made by what he calls the ‘new orthodoxy’ in PE: 1. The ‘early Hirstian’ account3, which sees knowledge as propositional, and education as academic. When applied to PE, this suggests: 2. The distinction between practical performance and the ‘theory’ related to it - i.e. the propositional knowledge of Human Movement Science (HMS). The paper is a critique of these two assumptions, and a defence of the claim that PE ‘can indeed satisfy the knowledge requirements of education; but ... without making claims to academic significance’ (p95)

Projection operator formalism and entropy

The entropy definition is deduced by means of (re)deriving the generalized non-linear Langevin equation using Zwanzig projector operator formalism. It is shown to be necessarily related to an invariant measure which, in classical mechanics, can always be taken to be the Liouville measure. It is not true that one is free to choose a ``relevant'' probability density independently as is done in other flavors of projection operator formalism. This observation induces an entropy expression which is valid also outside the thermodynamic limit and in far from equilibrium situations. The Zwanzig projection operator formalism therefore gives a deductive derivation of non-equilibrium, and equilibrium, thermodynamics. The entropy definition found is closely related to the (generalized) microcanonical Boltzmann-Planck definition but with some subtle differences. No ``shell thickness'' arguments are needed, nor desirable, for a rigorous definition. The entropy expression depends on the choice of macroscopic variables and does not exactly transform as a scalar quantity. The relation with expressions used in the GENERIC formalism are discussed