379,551 research outputs found
Euclidean Windows
In this paper we study number fields which are Euclidean with respect to a
function different from the absolute value of the norm. We also show that the
Euclidean minimum with respect to weighted norms may be irrational and not
isolated
Euclidean Supergravity
Supergravity with eight supercharges in a four-dimensional Euclidean space is
constructed at the full non-linear level by performing an off-shell time-like
reduction of five-dimensional supergravity. The resulting four-dimensional
theory is realized off-shell with the Weyl, vector and tensor supermultiplets
and a corresponding multiplet calculus. Hypermultiplets are included as well,
but they are themselves only realized with on-shell supersymmetry. The
off-shell reduction leads to a full understanding of the Euclidean theory. A
complete multiplet calculus is presented along the lines of the Minkowskian
theory. Unlike in Minkowski space, chiral and anti-chiral multiplets are real
and supersymmetric actions are generally unbounded from below. Precisely as in
the Minkowski case, where one has different formulations of Poincar\'e
supergravity by introducing different compensating supermultiplets, one can
also obtain different versions of Euclidean supergravity.Comment: 42 page
Combing Euclidean buildings
For an arbitrary Euclidean building we define a certain combing, which
satisfies the `fellow traveller property' and admits a recursive definition.
Using this combing we prove that any group acting freely, cocompactly and by
order preserving automorphisms on a Euclidean building of one of the types
A_n,B_n,C_n admits a biautomatic structure.Comment: 32 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper2.abs.htm
Efficient estimation of Banach parameters in semiparametric models
Consider a semiparametric model with a Euclidean parameter and an
infinite-dimensional parameter, to be called a Banach parameter. Assume: (a)
There exists an efficient estimator of the Euclidean parameter. (b) When the
value of the Euclidean parameter is known, there exists an estimator of the
Banach parameter, which depends on this value and is efficient within this
restricted model. Substituting the efficient estimator of the Euclidean
parameter for the value of this parameter in the estimator of the Banach
parameter, one obtains an efficient estimator of the Banach parameter for the
full semiparametric model with the Euclidean parameter unknown. This hereditary
property of efficiency completes estimation in semiparametric models in which
the Euclidean parameter has been estimated efficiently. Typically, estimation
of both the Euclidean and the Banach parameter is necessary in order to
describe the random phenomenon under study to a sufficient extent. Since
efficient estimators are asymptotically linear, the above substitution method
is a particular case of substituting asymptotically linear estimators of a
Euclidean parameter into estimators that are asymptotically linear themselves
and that depend on this Euclidean parameter. This more general substitution
case is studied for its own sake as well, and a hereditary property for
asymptotic linearity is proved.Comment: Published at http://dx.doi.org/10.1214/009053604000000913 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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