5,082 research outputs found
Improving QED-Tutrix by Automating the Generation of Proofs
The idea of assisting teachers with technological tools is not new.
Mathematics in general, and geometry in particular, provide interesting
challenges when developing educative softwares, both in the education and
computer science aspects. QED-Tutrix is an intelligent tutor for geometry
offering an interface to help high school students in the resolution of
demonstration problems. It focuses on specific goals: 1) to allow the student
to freely explore the problem and its figure, 2) to accept proofs elements in
any order, 3) to handle a variety of proofs, which can be customized by the
teacher, and 4) to be able to help the student at any step of the resolution of
the problem, if the need arises. The software is also independent from the
intervention of the teacher. QED-Tutrix offers an interesting approach to
geometry education, but is currently crippled by the lengthiness of the process
of implementing new problems, a task that must still be done manually.
Therefore, one of the main focuses of the QED-Tutrix' research team is to ease
the implementation of new problems, by automating the tedious step of finding
all possible proofs for a given problem. This automation must follow
fundamental constraints in order to create problems compatible with QED-Tutrix:
1) readability of the proofs, 2) accessibility at a high school level, and 3)
possibility for the teacher to modify the parameters defining the
"acceptability" of a proof. We present in this paper the result of our
preliminary exploration of possible avenues for this task. Automated theorem
proving in geometry is a widely studied subject, and various provers exist.
However, our constraints are quite specific and some adaptation would be
required to use an existing prover. We have therefore implemented a prototype
of automated prover to suit our needs. The future goal is to compare
performances and usability in our specific use-case between the existing
provers and our implementation.Comment: In Proceedings ThEdu'17, arXiv:1803.0072
The perils of thresholding
The thresholding of time series of activity or intensity is frequently used
to define and differentiate events. This is either implicit, for example due to
resolution limits, or explicit, in order to filter certain small scale physics
from the supposed true asymptotic events. Thresholding the birth-death process,
however, introduces a scaling region into the event size distribution, which is
characterised by an exponent that is unrelated to the actual asymptote and is
rather an artefact of thresholding. As a result, numerical fits of simulation
data produce a range of exponents, with the true asymptote visible only in the
tail of the distribution. This tail is increasingly difficult to sample as the
threshold is increased. In the present case, the exponents and the spurious
nature of the scaling region can be determined analytically, thus demonstrating
the way in which thresholding conceals the true asymptote. The analysis also
suggests a procedure for detecting the influence of the threshold by means of a
data collapse involving the threshold-imposed scale.Comment: 16 pages, 10 figure
Scalar field induced oscillations of neutron stars and gravitational collapse
We study the interaction of massless scalar fields with self-gravitating
neutron stars by means of fully dynamic numerical simulations of the
Einstein-Klein-Gordon perfect fluid system. Our investigation is restricted to
spherical symmetry and the neutron stars are approximated by relativistic
polytropes. Studying the nonlinear dynamics of isolated neutron stars is very
effectively performed within the characteristic formulation of general
relativity, in which the spacetime is foliated by a family of outgoing light
cones. We are able to compactify the entire spacetime on a computational grid
and simultaneously impose natural radiative boundary conditions and extract
accurate radiative signals. We study the transfer of energy from the scalar
field to the fluid star. We find, in particular, that depending on the
compactness of the neutron star model, the scalar wave forces the neutron star
either to oscillate in its radial modes of pulsation or to undergo
gravitational collapse to a black hole on a dynamical timescale. The radiative
signal, read off at future null infinity, shows quasi-normal oscillations
before the setting of a late time power-law tail.Comment: 12 pages, 13 figures, submitted to Phys. Rev.
The sustainability behaviour of small firms in tourism: the role of self-efficacy and contextual constraints
This article presents a grounded theory to explain why some small businesses in tourism adopt sustainable business practices while others do not, even when they share environmental and wider sustainability concerns. It does so based on research undertaken among business owners in Crete. The paper starts by considering studies on sustainability awareness, knowledge and the mechanisms for accepting responsibility. Secondly, it summarises the influence of task difficulty and effort on sustainability self-efficacy. Thirdly, it focuses on social comparisons and vicarious experiences, as a way of learning what is important. Finally, it examines powerlessness due to perceived situational constraints. In so doing, the study finds that self-efficacy helps to explain sustainable attitude formation and the attitude-behaviour gap; it partly shifts the locus of responsibility for an inability to act sustainably away from the individual and towards their context. The paper contributes to the theoretical literature on small businesses and sustainability, and leads to new avenues for policy interventions
Seqüència d'ensenyament-aprenentatge per a l'estudi de la interacció llum-matèria a secundària
Aquest article descriu una seqüència d'ensenyament-aprenentatge per a l'estudi de la in-teracció de la llum infraroja (IR) amb la matèria utilitzant diferents eines TIC. Es tracta d'una sessió contextualitzada al voltant de l'efecte d'hivernacle, plantejada per explorar els fonaments de la interacció entre la matèria i la radiació electromagnètica, que permet també introduir diversos conceptes relacionats amb l'espectroscòpia IR
Numerical 3+1 general relativistic magnetohydrodynamics: a local characteristic approach
We present a general procedure to solve numerically the general relativistic
magnetohydrodynamics (GRMHD) equations within the framework of the 3+1
formalism. The work reported here extends our previous investigation in general
relativistic hydrodynamics (Banyuls et al. 1997) where magnetic fields were not
considered. The GRMHD equations are written in conservative form to exploit
their hyperbolic character in the solution procedure. All theoretical
ingredients necessary to build up high-resolution shock-capturing schemes based
on the solution of local Riemann problems (i.e. Godunov-type schemes) are
described. In particular, we use a renormalized set of regular eigenvectors of
the flux Jacobians of the relativistic magnetohydrodynamics equations. In
addition, the paper describes a procedure based on the equivalence principle of
general relativity that allows the use of Riemann solvers designed for special
relativistic magnetohydrodynamics in GRMHD. Our formulation and numerical
methodology are assessed by performing various test simulations recently
considered by different authors. These include magnetized shock tubes,
spherical accretion onto a Schwarzschild black hole, equatorial accretion onto
a Kerr black hole, and magnetized thick accretion disks around a black hole
prone to the magnetorotational instability.Comment: 18 pages, 8 figures, submitted to Ap
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