44,917 research outputs found
On the Sr I 4607 A Hanle depolarization signals in the quiet Sun
The Hanle depolarization signals of Sr 4607 A have been used to estimate the
unsigned magnetic flux and magnetic energy existing in the quiet Sun
photosphere. However, the Sr 4607 A Hanle signals are not sensitive to the
unsigned flux and energy. They only bear information on the fraction of
photosphere occupied by magnetic field strengths smaller than the Hanle
saturation, which do not contribute to the unsigned flux and energy. We deduce
an approximate expression for the relationship between magnetic fill factor and
Hanle signal. When applied to existing Hanle depolarization measurements, it
indicates that only 40% of the quiet Sun is filled by magnetic fields with a
strength smaller than 60 G. The remaining 60% of the surface has field
strengths above this limit. Such constraint will be needed to determine the
distribution of magnetic field strengths existing in the quiet Sun.Comment: To appear in A&
On the insertion of n-powers
In algebraic terms, the insertion of -powers in words may be modelled at
the language level by considering the pseudovariety of ordered monoids defined
by the inequality . We compare this pseudovariety with several other
natural pseudovarieties of ordered monoids and of monoids associated with the
Burnside pseudovariety of groups defined by the identity . In
particular, we are interested in determining the pseudovariety of monoids that
it generates, which can be viewed as the problem of determining the Boolean
closure of the class of regular languages closed under -power insertions. We
exhibit a simple upper bound and show that it satisfies all pseudoidentities
which are provable from in which both sides are regular elements
with respect to the upper bound
Generalized Euler-Lagrange equations for variational problems with scale derivatives
We obtain several Euler-Lagrange equations for variational functionals
defined on a set of H\"older curves. The cases when the Lagrangian contains
multiple scale derivatives, depends on a parameter, or contains higher-order
scale derivatives are considered.Comment: Submitted on 03-Aug-2009; accepted for publication 16-March-2010; in
"Letters in Mathematical Physics"
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