This short note attempts to shed light on some of the surgical procedures referred to in Martial's epigram 10.56 by consulting pertinent Graeco-Roman medical texts. A fuller understanding of one such intervention (treatment of infected/inflamed uvula) supports Martial's text as transmitted.

As an application of the theory of graph-like Legendrian unfoldings, relations of the hidden structures of caustics, and wave front propagations are revealed.

We study the Minkowski symmetry set of a closed smooth curve γ in the Minkowski plane. We answer the following question, which is analogous to one concerning curves in the Euclidean plane that was treated by Giblin and O’Shea (1990): given a point p on γ, does there exist a bi-tangent pseudo-circle that is tangent to γ both at p and at some other point q on γ? The answer is yes, but as pseudo-circles with non-zero radii have two branches (connected components) it is possible to refine the above question to the following one: given a point p on γ, does there exist a branch of a pseudo-circle that is tangent to γ both at p and at some other point q on γ? This question is motivated by the earlier quest of Reeve and Tari (2014) to define the Minkowski Blum medial axis, a counterpart of the Blum medial axis of curves in the Euclidean plane.

The cosmic web is a complex spatial pattern of walls, filaments, cluster nodes and underdense void regions. It emerged through gravitational amplification from the Gaussian primordial density field. Here we infer analytical expressions for the spatial statistics of caustics in the evolving large-scale mass distribution. In our analysis, following the quasi-linear Zel'dovich formalism and confined to the 1D and 2D situation, we compute number density and correlation properties of caustics in cosmic density fields that evolve from Gaussian primordial conditions. The analysis can be straightforwardly extended to the 3D situation. We moreover, are currently extending the approach to the non-linear regime of structure formation by including higher order Lagrangian approximations and Lagrangian effective field theory.

Associé à des singularités mathématiques, le phénomène optique des caustiques représente l'ensemble des valeurs singulières de la projection d'une sous-variété lagrangienne de l'espace de phases (i.e. système de rayon) sur l'espace de configurations défini par le champ des déplacements. Dans ce cas, en supposant que la transition entre le domaine élastique et le domaine plastique qui entoure la pointe de fissure se fait par un changement de la configuration du champ de déplacements, nous nous proposons d'analyser les modifications que cela entraîne dans la formation des caustiques.

Caustic ingestion can lead to oesophageal stenosis. We studied 251 patients, 205 of whom were children, in a sixteen-year period. Seventeen patients, of whom one was an adult, acquired deep burns in the oesophagus which had to be treated, to prevent the development of oesophageal strictures. These patients were treated with long-term stenting of the oesophagus with specially designed, silicone rubber stents, impregnated with silicone oil 20 cS, designed by one of us (R.N.P.B.) as the only treatment. Of all models, the twin-tube dilatator was the most satisfactory. No corticosteroids were administered. Only one patient developed a mild stenosis. It is therefore our opinion that, when life-saving operations are not indicated, twin-tube stenting of the oesophagus is helpful in treating caustic lesions of the oesophagus and will prevent stricture formation. Corticosteroids were not given in this series, and should be abandoned in the treatment of caustic lesions.