Characterizing fully principal congruence representable distributive lattices

Motivated by a recent paper of G. Gr\"atzer, a finite distributive lattice $D$ is said to be fully principal congruence representable if for every subset $Q$ of $D$ containing $0$, $1$, and the set $J(D)$ of nonzero join-irreducible elements of $D$, there exists a finite lattice $L$ and an isomorphism from the congruence lattice of $L$ onto $D$ such that $Q$ corresponds to the set of principal congruences of $L$ under this isomorphism. Based on earlier results of G. Gr\"atzer, H. Lakser, and the present author, we prove that a finite distributive lattice $D$ 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 $L$ 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

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]

Maximal Acceleration Limits on the Mass of the Higgs Boson

Caianiello's quantum geometrical model with maximal acceleration places the upper limit $\mu\leq 719.5$ 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 $\mu$ and independent symmetry breaking and mass generating mechanisms. These may further restrict the value of $\mu$.Comment: LaTex file, 13 pages, to be published in Il Nuovo Cimento