55 research outputs found
On computing joint invariants of vector fields
A constructive version of the Frobenius integrability theorem -- that can be
programmed effectively -- is given. This is used in computing invariants of
groups of low ranks and recover examples from a recent paper of Boyko, Patera
and Popoyvich \cite{BPP}
Spin coefficients for four-dimensional neutral metrics, and null geometry
Notation for spin coefficients for metrics of neutral signature in four
dimensions is introduced. The utility and interpretation of spin coefficients
is explored through themes in null geometry familiar from (complex) general
relativity. Four-dimensional Walker geometry is exploited to provide examples
and the generalization of the real neutral version of Pleba\~nski's (1975)
second heavenly equation to certain Walker geometries given in Law and
Matsushita [16] is extended further.Comment: 50 pages; minor typos corrected in v
On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines
We study transformations of coordinates on a Lorentzian Einstein manifold
with a parallel distribution of null lines and show that the general Walker
coordinates can be simplified. In these coordinates, the full Lorentzian
Einstein equation is reduced to equations on a family of Einstein Riemannian
metrics.Comment: Dedicated to Dmitri Vladimirovich Alekseevsky on his 70th birthda
Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)
The classifications of holonomy groups in Lorentzian and in Euclidean
signature are quite different. A group of interest in Lorentzian signature in n
dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2).
Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg,
and a single four-dimensional example with a non-zero cosmological constant was
exhibited by Ghanam and Thompson. Here we reduce the problem of finding the
general -dimensional Einstein metric of SIM(n-2) holonomy, with and without
a cosmological constant, to solving a set linear generalised Laplace and
Poisson equations on an (n-2)-dimensional Einstein base manifold. Explicit
examples may be constructed in terms of generalised harmonic functions. A
dimensional reduction of these multi-centre solutions gives new time-dependent
Kaluza-Klein black holes and monopoles, including time-dependent black holes in
a cosmological background whose spatial sections have non-vanishing curvature.Comment: Typos corrected; 29 page
Holonomy of Einstein Lorentzian manifolds
The classification of all possible holonomy algebras of Einstein and vacuum
Einstein Lorentzian manifolds is obtained. It is shown that each such algebra
appears as the holonomy algebra of an Einstein (resp., vacuum Einstein)
Lorentzian manifold, the direct constructions are given. Also the holonomy
algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The
classification of the holonomy algebras of Lorentzian manifolds is reviewed and
a complete description of the spaces of curvature tensors for these holonomies
is given.Comment: Dedicated to to Mark Volfovich Losik on his 75th birthday. This
version is an extended part of the previous version; another part of the
previous version is extended and submitted as arXiv:1001.444
Metrics With Vanishing Quantum Corrections
We investigate solutions of the classical Einstein or supergravity equations
that solve any set of quantum corrected Einstein equations in which the
Einstein tensor plus a multiple of the metric is equated to a symmetric
conserved tensor constructed from sums of terms the involving
contractions of the metric and powers of arbitrary covariant derivatives of the
curvature tensor. A classical solution, such as an Einstein metric, is called
{\it universal} if, when evaluated on that Einstein metric, is a
multiple of the metric. A Ricci flat classical solution is called {\it strongly
universal} if, when evaluated on that Ricci flat metric,
vanishes. It is well known that pp-waves in four spacetime dimensions are
strongly universal. We focus attention on a natural generalisation; Einstein
metrics with holonomy in which all scalar invariants are zero
or constant. In four dimensions we demonstrate that the generalised
Ghanam-Thompson metric is weakly universal and that the Goldberg-Kerr metric is
strongly universal; indeed, we show that universality extends to all
4-dimensional Einstein metrics. We also discuss generalizations
to higher dimensions.Comment: 23 page
A spinor approach to Walker geometry
A four-dimensional Walker geometry is a four-dimensional manifold M with a
neutral metric g and a parallel distribution of totally null two-planes. This
distribution has a natural characterization as a projective spinor field
subject to a certain constraint. Spinors therefore provide a natural tool for
studying Walker geometry, which we exploit to draw together several themes in
recent explicit studies of Walker geometry and in other work of Dunajski (2002)
and Plebanski (1975) in which Walker geometry is implicit. In addition to
studying local Walker geometry, we address a global question raised by the use
of spinors.Comment: 41 pages. Typos which persisted into published version corrected,
notably at (2.15
Efficacy and Safety of Artemether in the Treatment of Chronic Fascioliasis in Egypt: Exploratory Phase-2 Trials
Fasciola hepatica and F. gigantica are two liver flukes that parasitize herbivorous large size mammals (e.g., sheep and cattle), as well as humans. A single drug is available to treat infections with Fasciola flukes, namely, triclabendazole. Recently, laboratory studies and clinical trials in sheep and humans suffering from acute fascioliasis have shown that artesunate and artemether (drugs that are widely used against malaria) also show activity against fascioliasis. Hence, we were motivated to assess the efficacy and safety of oral artemether in patients with chronic Fasciola infections. The study was carried out in Egypt and artemether administered according to two different malaria treatment regimens. Cure rates observed with 6×80 mg and 3×200 mg artemether were 35% and 6%, respectively. In addition, high efficacy was observed when triclabendazole, the current drug of choice against human fascioliasis, was administered to patients remaining Fasciola positive following artemether treatment. Concluding, monotherapy with artemether does not represent an alternative to triclabendazole against fascioliasis, but its role in combination chemotherapy regimen remains to be investigated
Retroviral matrix and lipids, the intimate interaction
Retroviruses are enveloped viruses that assemble on the inner leaflet of cellular membranes. Improving biophysical techniques has recently unveiled many molecular aspects of the interaction between the retroviral structural protein Gag and the cellular membrane lipids. This interaction is driven by the N-terminal matrix domain of the protein, which probably undergoes important structural modifications during this process, and could induce membrane lipid distribution changes as well. This review aims at describing the molecular events occurring during MA-membrane interaction, and pointing out their consequences in terms of viral assembly. The striking conservation of the matrix membrane binding mode among retroviruses indicates that this particular step is most probably a relevant target for antiviral research
- …