807 research outputs found
Further results on non-diagonal Bianchi type III vacuum metrics
We present the derivation, for these vacuum metrics, of the Painlev\'e VI
equation first obtained by Christodoulakis and Terzis, from the field equations
for both minkowskian and euclidean signatures. This allows a complete
discussion and the precise connection with some old results due to Kinnersley.
The hyperk\"ahler metrics are shown to belong to the Multi-Centre class and for
the cases exhibiting an integrable geodesic flow the relevant Killing tensors
are given. We conclude by the proof that for the Bianchi B family, excluding
type III, there are no hyperk\"ahler metrics.Comment: 21 pages, no figure
Bianchi type II,III and V diagonal Einstein metrics re-visited
We present, for both minkowskian and euclidean signatures, short derivations
of the diagonal Einstein metrics for Bianchi type II, III and V. For the first
two cases we show the integrability of the geodesic flow while for the third
case a somewhat unusual bifurcation phenomenon takes place: for minkowskian
signature elliptic functions are essential in the metric while for euclidean
signature only elementary functions appear
Celestial mechanics of elastic bodies
We construct time independent configurations of two gravitating elastic
bodies. These configurations either correspond to the two bodies moving in a
circular orbit around their center of mass or strictly static configurations.Comment: 16 pages, 2 figures, several typos removed, erratum appeared in
MathZ.263:233,200
Classical and Quantum Bianchi Type III vacuum Horava - Lifshitz Cosmology
A diagonal Bianchi Type III space-time is treated, both at the classical and
quantum level, in the context of Horava - Lifshitz gravity. The system of the
classical equations of motion is reduced to one independent Abel's equation of
the first kind. Closed form solution are presented for various values of the
coupling constants appearing in the action. Due to the method used, solutions
of Euclidean, Lorentzian and neutral signature are attained. The solutions
corresponding to \lamda 1 are seen to develop curvature singularities as the
other constants approach their Einsteinian values, in contrast to those with
\lamda = 1 which tend to the known Einstein gravity solutions. At the quantum
level, the resulting Wheeler-DeWitt equation is explicitly solved for \lamda =
1, \sigma = 0 and \lamda = 1/3 . The ensuing wave-functions diverge in the
Einsteinian limit.Comment: LaTeX 2e source file, 17 pages, no figure
Relativistic Elastostatics I: Bodies in Rigid Rotation
We consider elastic bodies in rigid rotation, both nonrelativistically and in
special relativity. Assuming a body to be in its natural state in the absence
of rotation, we prove the existence of solutions to the elastic field equations
for small angular velocity.Comment: 25 page
Identification of nonlinearity in conductivity equation via Dirichlet-to-Neumann map
We prove that the linear term and quadratic nonlinear term entering a
nonlinear elliptic equation of divergence type can be uniquely identified by
the Dirichlet to Neuman map. The unique identifiability is proved using the
complex geometrical optics solutions and singular solutions
Definitions, Criteria and Global Classification of Mast Cell Disorders with Special Reference to Mast Cell Activation Syndromes: A Consensus Proposal
Activation of tissue mast cells (MCs) and their abnormal growth and accumulation in various organs are typically found in primary MC disorders also referred to as mastocytosis. However, increasing numbers of patients are now being informed that their clinical findings are due to MC activation (MCA) that is neither associated with mastocytosis nor with a defined allergic or inflammatory reaction. In other patients with MCA, MCs appear to be clonal cells, but criteria for diagnosing mastocytosis are not met. A working conference was organized in 2010 with the aim to define criteria for diagnosing MCA and related disorders, and to propose a global unifying classification of all MC disorders and pathologic MC reactions. This classification includes three types of `MCA syndromes' (MCASs), namely primary MCAS, secondary MCAS and idiopathic MCAS. MCA is now defined by robust and generally applicable criteria, including (1) typical clinical symptoms, (2) a substantial transient increase in serum total tryptase level or an increase in other MC-derived mediators, such as histamine or prostaglandin D 2, or their urinary metabolites, and (3) a response of clinical symptoms to agents that attenuate the production or activities of MC mediators. These criteria should assist in the identification and diagnosis of patients with MCAS, and in avoiding misdiagnoses or overinterpretation of clinical symptoms in daily practice. Moreover, the MCAS concept should stimulate research in order to identify and exploit new molecular mechanisms and therapeutic targets. Copyright (C) 2011 S. Karger AG, Base
Some Spacetimes with Higher Rank Killing-Stackel Tensors
By applying the lightlike Eisenhart lift to several known examples of
low-dimensional integrable systems admitting integrals of motion of
higher-order in momenta, we obtain four- and higher-dimensional Lorentzian
spacetimes with irreducible higher-rank Killing tensors. Such metrics, we
believe, are first examples of spacetimes admitting higher-rank Killing
tensors. Included in our examples is a four-dimensional supersymmetric pp-wave
spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy
a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to
the quantum regime
Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order
The present article reveals important properties of the confluent Heun's
functions. We derive a set of novel relations for confluent Heun's functions
and their derivatives of arbitrary order. Specific new subclasses of confluent
Heun's functions are introduced and studied. A new alternative derivation of
confluent Heun's polynomials is presented.Comment: 8 pages, no figures, LaTeX file, final versio
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