On curves with one place at infinity

Let $f$ be a plane curve. We give a procedure based on Abhyankar's approximate roots to detect if it has a single place at infinity, and if so construct its associated $\delta$-sequence, and consequently its value semigroup. Also for fixed genus (equivalently Frobenius number) we construct all $\delta$-sequences generating numerical semigroups with this given genus. For a $\delta$-sequence we present a procedure to construct all curves having this associated sequence. We also study the embeddings of such curves in the plane. In particular, we prove that polynomial curves might not have a unique embedding.Comment: 14 pages, 2 figure

Symmetry limit properties of a priori mixing amplitudes for non-leptonic and weak radiative decays of hyperons

We show that the so-called parity-conserving amplitudes predicted in the a priori mixing scheme for non-leptonic and weak radiative decays of hyperons vanish in the strong-flavor symmetry limit

Isolated factorizations and their applications in simplicial affine semigroups

We introduce the concept of isolated factorizations of an element of a commutative monoid and study its properties. We give several bounds for the number of isolated factorizations of simplicial affine semigroups and numerical semigroups. We also generalize $\alpha$-rectangular numerical semigroups to the context of simplicial affine semigroups and study their isolated factorizations. As a consequence of our results, we characterize those complete intersection simplicial affine semigroups with only one Betti minimal element in several ways. Moreover, we define Betti sorted and Betti divisible simplicial affine semigroups and characterize them in terms of gluings and their minimal presentations. Finally, we determine all the Betti divisible numerical semigroups, which turn out to be those numerical semigroups that are free for any arrangement of their minimal generators

Glory revealed in disk-integrated photometry of Venus

Context. Reflected light from a spatially unresolved planet yields unique insight into the overall optical properties of the planet cover. Glories are optical phenomena caused by light that is backscattered within spherical droplets following a narrow distribution of sizes; they are well known on Earth as localised features above liquid clouds. Aims. Here we report the first evidence for a glory in the disk-integrated photometry of Venus and, in turn, of any planet. Methods. We used previously published phase curves of the planet that were reproduced over the full range of phase angles with model predictions based on a realistic description of the Venus atmosphere. We assumed that the optical properties of the planet as a whole can be described by a uniform and stable cloud cover, an assumption that agrees well with observational evidence. Results. We specifically show that the measured phase curves mimic the scattering properties of the Venus upper-cloud micron-sized aerosols, also at the small phase angles at which the glory occurs, and that the glory contrast is consistent with what is expected after multiple scattering of photons. In the optical, the planet appears to be brighter at phase angles of 11-13 deg than at full illumination; it undergoes a maximum dimming of up to 10 percent at phases in between. Conclusions. Glories might potentially indicate spherical droplets and, thus, extant liquid clouds in the atmospheres of exoplanets. A prospective detection will require exquisite photometry at the small planet-star separations of the glory phase angles.Comment: In press. Astronomy & Astrophysics. Letter to the Editor; 201