Inverse semigroups generated by group congruences. The Möbius functions

The computation of the Möbius function of a Möbius category that arises from a combinatorial inverse semigroup has a distinctive feature. This computation is done on the field of finite posets. In the case of two combinatorial inverse semigroups, order isomorphisms between corresponding finite posets reduce the computation to one of the semigroups. Starting with a combinatorial inverse monoid and using a group congruence we construct a combinatorial inverse semigroup such that the Möbius function becomes an invariant to this construction. For illustration, we consider the multiplicative analogue of the bicyclic semigroup and the free monogenic inverse monoid

Renormalization : A number theoretical model

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200

Problems with equating thermal preference with ‘emotional fever’ and sentience: Comment on ‘fish can show emotional fever: Stress-induced hyperthermia in zebrafish’ by rey et al. (2015)

publishedVersio

A Hot Mars-sized Exoplanet Transiting an M Dwarf

We validate the planetary nature of an ultra-short-period planet orbiting the M dwarf KOI-4777. We use a combination of space-based photometry from Kepler, high-precision, near-infrared Doppler spectroscopy from the Habitable-zone Planet Finder, and adaptive optics imaging to characterize this system. KOI-4777.01 is a Mars-sized exoplanet (R p = 0.51 0.03R ⊕) orbiting the host star every 0.412 days (∼9.9 hr). This is the smallest validated ultra-short period planet known and we see no evidence for additional massive companions using our HPF RVs. We constrain the upper 3σ mass to M p < 0.34 M ⊕ by assuming the planet is less dense than iron. Obtaining a mass measurement for KOI-4777.01 is beyond current instrumental capabilities. © 2021. The Author(s). Published by the American Astronomical Society.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]