9,836 research outputs found
A Hamiltonian functional for the linearized Einstein vacuum field equations
By considering the Einstein vacuum field equations linearized about the
Minkowski metric, the evolution equations for the gauge-invariant quantities
characterizing the gravitational field are written in a Hamiltonian form by
using a conserved functional as Hamiltonian; this Hamiltonian is not the analog
of the energy of the field. A Poisson bracket between functionals of the field,
compatible with the constraints satisfied by the field variables, is obtained.
The generator of spatial translations associated with such bracket is also
obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie
Local continuity laws on the phase space of Einstein equations with sources
Local continuity equations involving background fields and variantions of the
fields, are obtained for a restricted class of solutions of the
Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the
concept of the adjoint of a differential operator. Such covariant conservation
laws are generated by means of decoupled equations and their adjoints in such a
way that the corresponding covariantly conserved currents possess some
gauge-invariant properties and are expressed in terms of Debye potentials.
These continuity laws lead to both a covariant description of bilinear forms on
the phase space and the existence of conserved quantities. Differences and
similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page
Indices y referencia en Peirce.
Sin resume
Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty
We analyze the quantum dynamics of the non-relativistic two-dimensional
isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken
as toy model to analyze some of the various quantum theories that can be built
from the application of Dirac's quantization rule to the various symplectic
structures recently reported for this classical system. It is pointed out that
that these quantum theories are inequivalent in the sense that the mean values
for the operators (observables) associated with the same physical classical
observable do not agree with each other. The inequivalence does not arise from
ambiguities in the ordering of operators but from the fact of having several
symplectic structures defined with respect to the same set of coordinates. It
is also shown that the uncertainty relations between the fundamental
observables depend on the particular quantum theory chosen. It is important to
emphasize that these (somehow paradoxical) results emerge from the combination
of two paradigms: Dirac's quantization rule and the usual Copenhagen
interpretation of quantum mechanics.Comment: 8 pages, LaTex file, no figures. Accepted for publication in Phys.
Rev.
Contextualizing The Higher Education In A Post-Pandemic Era: A Trisectoral Perception
The sudden shift towards remote learning two years ago to curb the spread of the pandemic caught
educational institutions off-guard. It specifically proved to be a struggle in the Philippine context
because as noted by Mineo (2020), not all learners were prepared for the shift in learning modalities.
However, even with the current easing of restrictions nationwide, the Commission on Education
chair Prospero de Vera III implied that as far as the higher education is concerned, flexible learning is
now here to stay. As such, this study aimed to explore the perceptions of students, faculty members,
and university administrators on hybrid flexible (HyFlex) instruction. The study utilized a mixed
method research design. To interpret the results, frequency distributions and mean values were
presented. Findings revealed that. While the students moderately agree that like the flexibility that
hybrid flexible courses may offer, they were still undecided whether they can study at home as much
as I can when attending face-to-face classes. On the other hand, faculty members and the university
administrators mostly have positive perspectives on hybrid flexible (HyFlex) learning design which
may be related to the fact that most of them already participated in trainings related to the designing
and implementation of a hybrid flexible classroom. Accordingly, the following recommendations
were formulated: for the students to continuously participate and engage in research studies that
aims to devise teaching and learning continuity plan in the context of post-pandemic education; for
faculty members to regularly attend capacity-building trainings; for the university administration in
general to consider the hybrid flexible learning design as an option since both the students and
faculty members were found to have positive perceptions on it; lastly, for future researchers to assess
other organizational considerations related to the implementation of HyFlex courses
Charged particle dynamics in the presence of non-Gaussian L\'evy electrostatic fluctuations
Full orbit dynamics of charged particles in a -dimensional helical
magnetic field in the presence of -stable L\'evy electrostatic
fluctuations and linear friction modeling collisional Coulomb drag is studied
via Monte Carlo numerical simulations. The L\'evy fluctuations are introduced
to model the effect of non-local transport due to fractional diffusion in
velocity space resulting from intermittent electrostatic turbulence. The
probability distribution functions of energy, particle displacements, and
Larmor radii are computed and showed to exhibit a transition from exponential
decay, in the case of Gaussian fluctuations, to power law decay in the case of
L\'evy fluctuations. The absolute value of the power law decay exponents are
linearly proportional to the L\'evy index . The observed anomalous
non-Gaussian statistics of the particles' Larmor radii (resulting from outlier
transport events) indicate that, when electrostatic turbulent fluctuations
exhibit non-Gaussian L\'evy statistics, gyro-averaging and guiding centre
approximations might face limitations and full particle orbit effects should be
taken into account.Comment: 5 pages, 5 figures. Accepted as a letter in Physics of Plasma
A Study of the N-D-K Scalability Problem in Large-Scale Image Classification
Image classification is a extensively studied problem that lies at the heart of computer vision. However, the challenge remains to develop a system that can identify and classify thousands of objects like the human visual system. The accumulation of massive image data sets has permitted the study of this problem at a big-data scale. However current algorithms have been shown to fall short of being practical and accurate at scale. To further understand how these algorithms scale, we developed a library of functions to explore the scalability of the support vector machine (SVM) linear classification algorithm when applied to problems of image classification. Our study provides valuable insights into not only how the SVM algorithm scales up and where it falls short, but also into how to create smarter and more efficient image classifiers that are fine- tuned for the large scale image classification challenge
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