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On melting of boron phosphide under pressure
Melting of cubic boron phosphide, BP has been studied at pressures to 9 GPa
using synchrotron X-ray diffraction and electrical resistivity measurements. It
has been found that above 2.6 GPa BP melts congruently, and the melting curve
exhibits negative slope -60(7) K/GPa, which is indicative of a higher density
of the melt as compared to the solid phase.Comment: 3 pages, 1 figur
Generically multiple transitive algebraic group actions
With every nontrivial connected algebraic group we associate a positive
integer called the generic transitivity degree of and equal
to the maximal such that there is a nontrivial action of on an
irreducible algebraic variety for which the diagonal action of on
admits an open orbit. We show that (respectively,
) for all solvable (respectively, nilpotent) , and
we calculate for all reductive . We prove that if is
nonabelian reductive, then the above maximal is attained for where
is a proper maximal parabolic subgroup of (but not only for such
homogeneous spaces of ). For every reductive and its proper maximal
parabolic subgroup , we find the maximal such that the diagonal action
of (respectively, a Levi subgroup of ~) on admits an open
-orbit (respectively, -orbit). As an application, we obtain upper bounds
for the multiplicities of trivial components in some tensor product
decompositions. As another application, we classify all the pairs such
that the action of on admits an open orbit, answering a question
of {\sc M. Burger}.Comment: Revised version, 30 page
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