Top properties in ttˉt\bar{t} events at CMS (includes mass)

Selected results from the following topics are presented: Measurements of several top quark properties are obtained from the CMS data collected in 2011 at a center-of-mass energy of 7 TeV. The results include measurements of the top quark mass, the W helicity in top decays, the top quark charge, and of the $t\bar{t}$ spin correlation and the search for anomalous couplings.Comment: 5 pages, 10 figures. Presented at HCP 2012 Hadron Collider Physics Symposium 201

On discrete integrable equations of higher order

We study 2D discrete integrable equations of order 1 with respect to one independent variable and $m$ with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The examples are related to the B\"acklund--Darboux transformations for the lattice equations of Bogoyavlensky type.Comment: 20 pages, 2 figure

Some incidence theorems and integrable discrete equations

Several incidence theorems of planar projective geometry are considered. It is demonstrated that generalizations of Pascal theorem due to M\"obius give rise to double cross-ratio equation and Hietarinta equation. The construction corresponding to the double cross-ratio equation is a reduction to a conic section of some planar configuration $(20_3 15_4)$. This configuration provides a correct definition of the multidimensional quadrilateral lattices on the plane.Comment: 12 p, 7 fi