333 research outputs found
Weak Minimizers, Minimizers and Variational Inequalities for set valued Functions. A blooming wreath?
In the literature, necessary and sufficient conditions in terms of
variational inequalities are introduced to characterize minimizers of convex
set valued functions with values in a conlinear space. Similar results are
proved for a weaker concept of minimizers and weaker variational inequalities.
The implications are proved using scalarization techniques that eventually
provide original problems, not fully equivalent to the set-valued counterparts.
Therefore, we try, in the course of this note, to close the network among the
various notions proposed. More specifically, we prove that a minimizer is
always a weak minimizer, and a solution to the stronger variational inequality
always also a solution to the weak variational inequality of the same type. As
a special case we obtain a complete characterization of efficiency and weak
efficiency in vector optimization by set-valued variational inequalities and
their scalarizations. Indeed this might eventually prove the usefulness of the
set-optimization approach to renew the study of vector optimization
Seesaw mechanism in magnetic compactifications
In this paper, we explore a new avenue to a natural explanation of the
observed tiny neutrino masses with a dynamical realization of the
three-generation structure in the neutrino sector. Under the magnetized
background based on , matter consists of multiply-degenerated zero
modes and the whole intergenerational structure is dynamically determined. In
this sense, we can conclude that our scenario is favored by minimality, where
no degree of freedom remains to deform the intergenerational structure by hand
freely. Under the consideration of brane-localized Majorana-type mass terms for
an singlet neutrino, it is sufficient to introduce one Higgs doublet
for reproducing the observed neutrino data. In all reasonable flux
configurations with three right-handed neutrinos, phenomenologically acceptable
parameter configurations are found.Comment: 20 pages, 3 figures, 4 tables; published version from JHEP (v2
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