3,365 research outputs found
On \omega-categorical, generically stable groups
We prove that each \omega-categorical, generically stable group is
solvable-by-finite.Comment: 11 page
Locally finite profinite rings
We investigate the structure of locally finite profinite rings. We classify
(Jacobson-) semisimple locally finite profinite rings as products of complete
matrix rings of bounded cardinality over finite fields, and we prove that the
Jacobson radical of any locally finite profinite ring is nil of finite
nilexponent. Our results apply to the context of small compact -rings, where
we also obtain a description of possible actions of on the underlying ring.Comment: 17 page
The Lascar groups and the 1st homology groups in model theory
Let be a strong type of an algebraically closed tuple over
B=\acl^{\eq}(B) in any theory . Depending on a ternary relation \indo^*
satisfying some basic axioms (there is at least one such, namely the trivial
independence in ), the first homology group can be introduced,
similarly to \cite{GKK1}. We show that there is a canonical surjective
homomorphism from the Lascar group over to . We also notice that
the map factors naturally via a surjection from the `relativised' Lascar group
of the type (which we define in analogy with the Lascar group of the theory)
onto the homology group, and we give an explicit description of its kernel. Due
to this characterization, it follows that the first homology group of is
independent from the choice of \indo^*, and can be written simply as
. As consequences, in any , we show that
unless is trivial, and we give a criterion for the equality of stp and
Lstp of algebraically closed tuples using the notions of the first homology
group and a relativised Lascar group. We also argue how any abelian connected
compact group can appear as the first homology group of the type of a model.Comment: 30 pages, no figures, this merged with the article arXiv:1504.0772
Microscopic Determinations of Fission Barriers, (MEAN-Field and Beyond)
With a help of the selfconsistent Hartree-Fock-Bogoliubov (HFB) approach with
the D1S effective Gogny interaction and the Generator Coordinate Method (GCM)
we incorporate the transverse collective vibrations to the one-dimensional
model of the fission-barrier penetrability based on the traditional WKB method.
The average fission barrier corresponding to the least-energy path in the
two-dimensional potential energy landscape as function of quadrupole and
octupole degrees of freedom is modified by the influence of the transverse
collective vibrations along the nuclear path to fission. The set of transverse
vibrational states built in the fission valley corresponding to a successively
increasing nuclear elongation produces the new energy barrier which is compared
with the least-energy barrier. These collective states are given as the
eigensolutions of the GCM purely vibrational Hamiltonian. In addition, the
influence of the collective inertia on the fission properties is displayed, and
it turns out to be the decisive condition for the possible transitions between
different fission valleys.Comment: 12 pages, 5 figures, presented at XIII Workshop of Nuclear Physics,
Kazimierz Dolny, 2006 (Poland
- …