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Vacuum Einstein metrics with bidimensional Killing leaves. I-Local aspects
The solutions of vacuum Einstein's field equations, for the class of
Riemannian metrics admitting a non Abelian bidimensional Lie algebra of Killing
fields, are explicitly described. They are parametrized either by solutions of
a transcendental equation (the tortoise equation), or by solutions of a linear
second order differential equation in two independent variables. Metrics,
corresponding to solutions of the tortoise equation, are characterized as those
that admit a 3-dimensional Lie algebra of Killing fields with bidimensional
leaves.Comment: LateX file, 33 pages, 2 figure
Separating Solution of a Quadratic Recurrent Equation
In this paper we consider the recurrent equation
for with and given. We give conditions
on that guarantee the existence of such that the sequence
with tends to a finite positive limit as .Comment: 13 pages, 6 figures, submitted to J. Stat. Phy
The local structure of n-Poisson and n-Jacobi manifolds
N-Lie algebra structures on smooth function algebras given by means of
multi-differential operators, are studied. Necessary and sufficient conditions
for the sum and the wedge product of two -Poisson sructures to be again a
multi-Poisson are found. It is proven that the canonical -vector on the dual
of an n-Lie algebra g is n-Poisson iff dim(g) are not greater than n+1. The
problem of compatibility of two n-Lie algebra structures is analyzed and the
compatibility relations connecting hereditary structures of a given n-Lie
algebra are obtained. (n+1)-dimensional n-Lie algebras are classified and their
"elementary particle-like" structure is discovered. Some simple applications to
dynamics are discussed.Comment: 45 pages, latex, no figure
Gravitational fields with a non Abelian bidimensional Lie algebra of symmetries
Vacuum gravitational fields invariant for a bidimensional non Abelian Lie
algebra of Killing fields, are explicitly described. They are parameterized
either by solutions of a transcendental equation (the tortoise equation) or by
solutions of a linear second order differential equation on the plane.
Gravitational fields determined via the tortoise equation, are invariant for a
3-dimensional Lie algebra of Killing fields with bidimensional leaves. Global
gravitational fields out of local ones are also constructed.Comment: 8 pagese, latex, no figure
Evidence, Mechanisms and Improved Understanding of Controlled Salinity Waterflooding Part 1 : Sandstones
Acknowledgements TOTAL are thanked for partial supporting Jackson through the TOTAL Chairs programme at Imperial College London, for supporting Vinogradov through the TOTAL Laboratory for Reservoir Physics at Imperial College London, and for granting permission to publish this work.Peer reviewedPostprin
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