3,485 research outputs found
Fermi-Frenet coordinates for space-like curves
We generalize Fermi coordinates, which correspond to an adapted set of
coordinates describing the vicinity of an observer's worldline, to the
worldsheet of an arbitrary spatial curve in a static spacetime. The spatial
coordinate axes are fixed using a covariant Frenet triad so that the metric can
be expressed using the curvature and torsion of the spatial curve. As an
application of Fermi-Frenet coordinates, we show that they allow covariant
inertial forces to be expressed in a simple and physically intuitive way.Comment: 7 page
On the embedding of spacetime in five-dimensional Weyl spaces
We revisit Weyl geometry in the context of recent higher-dimensional theories
of spacetime. After introducing the Weyl theory in a modern geometrical
language we present some results that represent extensions of Riemannian
theorems. We consider the theory of local embeddings and submanifolds in the
context of Weyl geometries and show how a Riemannian spacetime may be locally
and isometrically embedded in a Weyl bulk. We discuss the problem of classical
confinement and the stability of motion of particles and photons in the
neighbourhood of branes for the case when the Weyl bulk has the geometry of a
warped product space. We show how the confinement and stability properties of
geodesics near the brane may be affected by the Weyl field. We construct a
classical analogue of quantum confinement inspired in theoretical-field models
by considering a Weyl scalar field which depends only on the extra coordinate.Comment: 16 pages, new title and references adde
Riemannian Geometry of Noncommutative Surfaces
A Riemannian geometry of noncommutative n-dimensional surfaces is developed
as a first step towards the construction of a consistent noncommutative
gravitational theory. Historically, as well, Riemannian geometry was recognized
to be the underlying structure of Einstein's theory of general relativity and
led to further developments of the latter. The notions of metric and
connections on such noncommutative surfaces are introduced and it is shown that
the connections are metric-compatible, giving rise to the corresponding Riemann
curvature. The latter also satisfies the noncommutative analogue of the first
and second Bianchi identities. As examples, noncommutative analogues of the
sphere, torus and hyperboloid are studied in detail. The problem of covariance
under appropriately defined general coordinate transformations is also
discussed and commented on as compared with other treatments.Comment: 28 pages, some clarifications, examples and references added, version
to appear in J. Math. Phy
Soliton surfaces associated with symmetries of ODEs written in Lax representation
The main aim of this paper is to discuss recent results on the adaptation of
the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras,
which was originally derived for PDEs [Grundland, Post 2011], to the case of
integrable ODEs admitting Lax representations. We give explicit forms of the
\g-valued immersion functions based on conformal symmetries involving the
spectral parameter, a gauge transformation of the wave function and generalized
symmetries of the linear spectral problem. The procedure is applied to a
symmetry reduction of the static -field equations leading to the
Jacobian elliptic equation. As examples, we obtain diverse types of surfaces
for different choices of Jacobian elliptic functions for a range of values of
parameters.Comment: 14 Pages, 2 figures Conference Proceedings for QST7 Pragu
Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice
We investigate the phase diagram of a discrete version of the Maier-Saupe
model with the inclusion of additional degrees of freedom to mimic a
distribution of rodlike and disklike molecules. Solutions of this problem on a
Bethe lattice come from the analysis of the fixed points of a set of nonlinear
recursion relations. Besides the fixed points associated with isotropic and
uniaxial nematic structures, there is also a fixed point associated with a
biaxial nematic structure. Due to the existence of large overlaps of the
stability regions, we resorted to a scheme to calculate the free energy of
these structures deep in the interior of a large Cayley tree. Both
thermodynamic and dynamic-stability analyses rule out the presence of a biaxial
phase, in qualitative agreement with previous mean-field results
From Golden Spirals to Constant Slope Surfaces
In this paper, we find all constant slope surfaces in the Euclidean 3-space,
namely those surfaces for which the position vector of a point of the surface
makes constant angle with the normal at the surface in that point. These
surfaces could be thought as the bi-dimensional analogue of the generalized
helices. Some pictures are drawn by using the parametric equations we found.Comment: 11 pages, 8 figure
Improving the quality of Portuguese SMEs through competence evaluation
UIDB/04647/2020 UIDP/04647/2020Problem and goal. Since we are going through a key moment in terms of technological advances and their effect on the labour field, the investigation of the on-the-job training processes gains a predominant role. Moreover, the need to research an approach that promotes a balance between the four spheres of development of learning – economic, sustain-able, community and personal – is emerging. This study was conceived as a result of this ur-gency, aiming to respond to the following problem: to what extent does a training model, based on the VPL (Validation of Prior Learning) approach and supported by principles of the educational sciences, can contribute to individual empowerment and, consequently, to an improvement in the organizational quality of Portuguese SMEs (Small and Medium-sized Enterprises)? Methodology. The division of the research into two parts – Study 1 and Study 2 – al-lowed the collection and analysis of structural data (Study 1) that served as a basis for the defi- nition of a dynamic strategy (Study 2). Although undertaken at different times, they have thus proved to be complementary. In fact, the design of the training model was based, firstly, on the results obtained through exploratory interviews with key informants and, secondly, on the data obtained throughout the training process that involved ninety-two employees from ten Portuguese SMEs from diverse categories and sectors. Results. The training model, which emerged from the interaction between the theoreti-cal reflection and the practical context, comprises five components: distance learning, recog-nition of skills, language skills, intercultural skills and an individual action plan. Conclusion. This study, being an important contribution to the topic of on-the-job training in Portuguese SMEs, at the same time opens the way for the continuation of the research.publishersversionpublishe
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