Relatively Congruence-free Regular Semigroups

Yu, Wang, Wu and Ye call a semigroup S τ -congruence-free, where τ is an equivalence relation on S, if any congruence ρ on S is either disjoint from τ or contains τ . A congruence-free semigroup is then just an ω-congruence-free semigroup, where ω is the universal relation. They determined the completely regular semigroups that are τ -congruence-free with respect to each of the Green’s relations. The goal of this paper is to extend their results to all regular semigroups. Such a semigroup is J –congruence-free if and only if it is either a semilattice or has a single nontrivial J -class, J, say, and either J is a subsemigroup, in which case it is congruence-free, or otherwise its principal factor is congruence-free. Given the current knowledge of congruence-free regular semigroups, this result is probably best possible. When specialized to completely semisimple semigroups, however, a complete answer is obtained, one that specializes to that of Yu et al. A similar outcome is obtained for L and R. In the case of H, only the completely semisimple case is fully resolved, again specializing to those of Yu et al

An Upper Bound for the Number of Planar Lattice Triangulations

We prove an exponential upper bound for the number $f(m,n)$ of all maximal triangulations of the $m\times n$ grid: $$f(m,n) < 2^{3mn}.$$ In particular, this improves a result of S. Yu. Orevkov (1999).Comment: 4 pages, 3 figure

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]

On singular moduli that are S-units

Recently Yu. Bilu, P. Habegger and L. K\"uhne proved that no singular modulus can be a unit in the ring of algebraic integers. In this paper we study for which sets S of prime numbers there is no singular modulus that is an S-units. Here we prove that when the set S contains only primes congruent to 1 modulo 3 then no singular modulus can be an S-unit. We then give some remarks on the general case and we study the norm factorizations of a special family of singular moduli.Comment: Version changed according to the referee's comments. The final version appears in Manuscripta Mathematica, https://doi.org/10.1007/s00229-020-01230-

Manifest Duality in Born-Infeld Theory

Born-Infeld theory is formulated using an infinite set of gauge fields, along the lines of McClain, Wu and Yu. In this formulation electromagnetic duality is generated by a fully local functional. The resulting consistency problems are analyzed and the formulation is shown to be consistent.Comment: 15 pages, Late

Hybrid meson masses and the correlated Gaussian basis

We revisited a model for charmonium hybrid meson with a magnetic gluon [Yu. S. Kalashnikova and A. V. Nefediev, Phys. Rev. D {\bf 77}, 054025 (2008)] and improved the numerical calculations. These improvements support the hybrid meson interpretation of X(4260). Within the same model, we computed the hybrid meson mass with an electric gluon which is resolved to be lighter. Relativistic effects and coupling channels decreased also the mass.Comment: 9 pages, 20 figures ; accepted for publication in Phys. Rev.