730 research outputs found
Superposition Formulas for Darboux Integrable Exterior Differential Systems
In this paper we present a far-reaching generalization of E. Vessiot's
analysis of the Darboux integrable partial differential equations in one
dependent and two independent variables. Our approach provides new insights
into this classical method, uncovers the fundamental geometric invariants of
Darboux integrable systems, and provides for systematic, algorithmic
integration of such systems. This work is formulated within the general
framework of Pfaffian exterior differential systems and, as such, has
applications well beyond those currently found in the literature. In
particular, our integration method is applicable to systems of hyperbolic PDE
such as the Toda lattice equations, 2 dimensional wave maps and systems of
overdetermined PDE.Comment: 80 page report. Updated version with some new sections, and major
improvements to other
Cosmology, cohomology, and compactification
Ashtekar and Samuel have shown that Bianchi cosmological models with compact
spatial sections must be of Bianchi class A. Motivated by general results on
the symmetry reduction of variational principles, we show how to extend the
Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as
defined, e.g., by Singer and Thurston. In particular, it is shown that any
m-dimensional homogeneous space G/K admitting a G-invariant volume form will
allow a compact discrete quotient only if the Lie algebra cohomology of G
relative to K is non-vanishing at degree m.Comment: 6 pages, LaTe
Gravitational Waves: Just Plane Symmetry
We present some remarkable properties of the symmetry group for gravitational
plane waves. Our main observation is that metrics with plane wave symmetry
satisfy every system of generally covariant vacuum field equations except the
Einstein equations. The proof uses the homothety admitted by metrics with plane
wave symmetry and the scaling behavior of generally covariant field equations.
We also discuss a mini-superspace description of spacetimes with plane wave
symmetry.Comment: 10 pages, TeX, uses IOP style file
Covariants,joint invariants and the problem of equivalence in the invariant theory of Killing tensors defined in pseudo-Riemannian spaces of constant curvature
The invariant theory of Killing tensors (ITKT) is extended by introducing the
new concepts of covariants and joint invariants of (product) vector spaces of
Killing tensors defined in pseudo-Riemannian spaces of constant curvature. The
covariants are employed to solve the problem of classification of the
orthogonal coordinate webs generated by non-trivial Killing tensors of valence
two defined in the Euclidean and Minkowski planes. Illustrative examples are
provided.Comment: 60 pages. to appear in J. Math. Phy
Significance Tests for Periodogram Peaks
We discuss methods currently in use for determining the significance of peaks
in the periodograms of time series. We discuss some general methods for
constructing significance tests, false alarm probability functions, and the
role played in these by independent random variables and by empirical and
theoretical cumulative distribution functions. We also discuss the concept of
"independent frequencies" in periodogram analysis. We propose a practical
method for estimating the significance of periodogram peaks, applicable to all
time series irrespective of the spacing of the data. This method, based on
Monte Carlo simulations, produces significance tests that are tailor-made for
any given astronomical time series.Comment: 22 pages, 11 Encapsulated Postscript figures, AAS LaTeX v5.2
Submitted to Ap
The Principle of Symmetric Criticality in General Relativity
We consider a version of Palais' Principle of Symmetric Criticality (PSC)
that is applicable to the Lie symmetry reduction of Lagrangian field theories.
PSC asserts that, given a group action, for any group-invariant Lagrangian the
equations obtained by restriction of Euler-Lagrange equations to
group-invariant fields are equivalent to the Euler-Lagrange equations of a
canonically defined, symmetry-reduced Lagrangian. We investigate the validity
of PSC for local gravitational theories built from a metric. It is shown that
there are two independent conditions which must be satisfied for PSC to be
valid. One of these conditions, obtained previously in the context of
transverse symmetry group actions, provides a generalization of the well-known
unimodularity condition that arises in spatially homogeneous cosmological
models. The other condition seems to be new. The conditions that determine the
validity of PSC are equivalent to pointwise conditions on the group action
alone. These results are illustrated with a variety of examples from general
relativity. It is straightforward to generalize all of our results to any
relativistic field theory.Comment: 46 pages, Plain TeX, references added in revised versio
Rufinamide in refractory childhood epileptic encephalopathies other than Lennox-Gastaut syndrome.
Background: To report on the first multicenter Italian experience with rufinamide as
adjunctive drug in children, adolescents and young adults with refractory childhoodonset
epileptic encephalopathies other than Lennox–Gastaut syndrome.
Methods: Thirty-eight patients (19 males, 19 females), aged between 4 and 34 (mean
13.7 ± 8.3, median 12.5), all affected by different types of childhood-onset refractory
epileptic encephalopathies other than Lennox–Gastaut syndrome, were treated with
rufinamide as adjunctive drug for a mean period of 11.4 months (range 3–26 months).
Results: Fifteen of 38 patients (39.5%) had a ‡50% seizure reduction in countable
seizures. Complete seizure freedom was achieved in one of these patients (2.6%).
Three patients (7.9%) had a 25–49% seizure reduction, whilst seizure frequency
remained unchanged in 15 (39.5%) and increased in five patients (13.1%). Eleven
patients (28.9%) reported adverse side effects. Vomiting was reported in five patients
(13.1%); drowsiness, decreased appetite and irritability with migraine manifested in
other four patients. They were transient and mild in all cases.
Conclusion: Rufinamide may be an effective and well-tolerated adjunctive drug for
the treatment of refractory childhood-onset epileptic encephalopathies other than
Lennox–Gastaut syndrome. Rufinamide was most effective in patients with dropattacks
and (bi)frontal spike–wave discharges.
Introduction
Rufinamide is a structurally triazole-derivative (1-[2,6-
difluorophenyl)methyl]-1hydro-1,2,3-triazole-carboxamide)
novel antiepileptic drug, structurally unrelated to
the existing antiepileptic drugs, and approved by the
Food and Drug Administration for the treatment of
Lennox–Gastaut syndrome in patients aged 4 and over,
and for the treatment of partial seizures in adults and
adolescents.
The proposed mechanism of action is the limitation
of excessiv
Killing Vector Fields in Three Dimensions: A Method to Solve Massive Gravity Field Equations
Killing vector fields in three dimensions play important role in the
construction of the related spacetime geometry. In this work we show that when
a three dimensional geometry admits a Killing vector field then the Ricci
tensor of the geometry is determined in terms of the Killing vector field and
its scalars. In this way we can generate all products and covariant derivatives
at any order of the ricci tensor. Using this property we give ways of solving
the field equations of Topologically Massive Gravity (TMG) and New Massive
Gravity (NMG) introduced recently. In particular when the scalars of the
Killing vector field (timelike, spacelike and null cases) are constants then
all three dimensional symmetric tensors of the geometry, the ricci and einstein
tensors, their covariant derivatives at all orders, their products of all
orders are completely determined by the Killing vector field and the metric.
Hence the corresponding three dimensional metrics are strong candidates of
solving all higher derivative gravitational field equations in three
dimensions.Comment: 25 pages, some changes made and some references added, to be
published in Classical and Quantum Gravit
Semiclassical States in Quantum Cosmology: Bianchi I Coherent States
We study coherent states for Bianchi type I cosmological models, as examples
of semiclassical states for time-reparametrization invariant systems. This
simple model allows us to study explicitly the relationship between exact
semiclassical states in the kinematical Hilbert space and corresponding ones in
the physical Hilbert space, which we construct here using the group averaging
technique. We find that it is possible to construct good semiclassical physical
states by such a procedure in this model; we also discuss the sense in which
the original kinematical states may be a good approximation to the physical
ones, and the situations in which this is the case. In addition, these models
can be deparametrized in a natural way, and we study the effect of time
evolution on an "intrinsic" coherent state in the reduced phase space, in order
to estimate the time for this state to spread significantly.Comment: 21 pages, 1 figure; Version to be published in CQG; The discussion
has been slightly reorganized, two references added, and some typos correcte
- …