6,769,518 research outputs found
Characterizing fully principal congruence representable distributive lattices
Motivated by a recent paper of G. Gr\"atzer, a finite distributive lattice
is said to be fully principal congruence representable if for every subset
of containing , , and the set of nonzero join-irreducible
elements of , there exists a finite lattice and an isomorphism from the
congruence lattice of onto such that corresponds to the set of
principal congruences of under this isomorphism. Based on earlier results
of G. Gr\"atzer, H. Lakser, and the present author, we prove that a finite
distributive lattice is fully principal congruence representable if and
only if it is planar and it has at most one join-reducible coatom. Furthermore,
even the automorphism group of can arbitrarily be stipulated in this case.
Also, we generalize a recent result of G. Gr\"atzer on principal congruence
representable subsets of a distributive lattice whose top element is
join-irreducible by proving that the automorphism group of the lattice we
construct can be arbitrary.Comment: 20 pages, 8 figure
A Rejoinder on Quaternionic Projective Representations
In a series of papers published in this Journal (J. Math. Phys.), a
discussion was started on the significance of a new definition of projective
representations in quaternionic Hilbert spaces. The present paper gives what we
believe is a resolution of the semantic differences that had apparently tended
to obscure the issues.Comment: AMStex, 6 Page
Maximal Acceleration Limits on the Mass of the Higgs Boson
Caianiello's quantum geometrical model with maximal acceleration places the
upper limit GeV on the mass of the Higgs boson. The model also
provides an equation linking the mass of the W boson to the Higgs mass
and independent symmetry breaking and mass generating mechanisms. These may
further restrict the value of .Comment: LaTex file, 13 pages, to be published in Il Nuovo Cimento
Comments to On the Accuracy of Lamb Shift Measurements in Hydrogen (Physica Scripta, 55 (1997) 33-40) by V. G. Pal'chikov, Yu. L. Sokolov, and V. P. Yakovlev
The work is a comments on the article of V. G. Pal'chikov, Yu. L. Sokolov,
and V. P. Yakovlev, devoted to the measurement of the Lamb shift in the
hydrogen atom and published in Physica Scripta, 55 (1997) 33-40.Comment: 4 pages; [email protected]
Neutrinos in Physics and Astrophysics
The observed flavor oscillations of solar and atmospheric neutrinos determine
several elements of the leptonic mixing matrix, but leave open the small mixing
angle Theta_13, a possible CP-violating phase, the mass ordering, the absolute
mass scale m_nu, and the Dirac vs. Majorana property. Progress will be made by
long-baseline, tritium endpoint, and 2-beta decay experiments. The best
constraint on m_nu obtains from cosmological precision observables, implying
that neutrinos contribute very little to the dark matter. However, massive
Majorana neutrinos may well be responsible for ordinary matter by virtue of the
leptogenesis mechanism for creating the baryon asymmetry of the universe. In
future, neutrinos could play an important role as astrophysical messengers if
point sources are discovered in high-energy neutrino telescopes. In the
low-energy range, a high-statistics observation of a galactic supernova would
allow one to observe directly the dynamics of stellar collapse and perhaps to
discriminate between certain mixing scenarios. An observation of the relic
neutrinos from all past supernovae has come within reach.Comment: Proceedings Texas in Tuscany, Dec. 2002. Updated cosmological mass
limits in replacemen
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