A counterexample to gluing theorems for MCP metric measure spaces

Perelman's doubling theorem asserts that the metric space obtained by gluing along their boundaries two copies of an Alexandrov space with curvature $\geq \kappa$ is an Alexandrov space with the same dimension and satisfying the same curvature lower bound. We show that this result cannot be extended to metric measure spaces satisfying synthetic Ricci curvature bounds in the $\mathrm{MCP}$ sense. The counterexample is given by the Grushin half-plane, which satisfies the $\mathrm{MCP}(0,N)$ if and only if $N\geq 4$, while its double satisfies the $\mathrm{MCP}(0,N)$ if and only if $N\geq 5$.Comment: 10 pages, 2 figures. Accepted version, to appear on the Bulletin of the London Mathematical Societ

Growth and slaughtering performance, carcase fleshiness and meat quality according to the plumage colour in Padovana male chickens slaughtered at 18 weeks of age

The aim of this trial was to investigate on the growth and meat quality of Padovana male chickens with different plumage varieties, chamois (PC - light brown feathers with white edge), silver (PS - white feathers with black edge), and their cross. The body weight of PC during the growth period was higher (p<.01) than PS, and it was 1.7 and 1.5 kg, respectively, at 126 d of age. At slaughter, PC showed higher weight of carcase (p<.05), breast and total fleshiness (breast, wings and legs) (p<.01), and thigh meat:bone ratio (p<.05). PS showed higher shanks weight on carcase weight (p<.01), Ilio tibialis a value (p<.01), water losses (p<.01) and shear force (p<.05) in breast meat than PC. Crossing PC males to PS females gave birds with white (Cross- W) and silver (Cross-S) plumage (3:1 ratio, respectively). The offspring genotypes showed similar body weight, and almost all slaughtering, carcase and meat quality traits studied. Cross-W and Cross-S showed significantly higher final body weight, breast and leg weight, total fleshiness and thigh meat:bone ratio than PS. For the Padovana breed, the plumage colour can involve productive and slaughtering performance, and carcase and meat quality, throughout the growing period. At 18 weeks of age, the Padovana male chickens show body weight and carcase fleshiness similar to that of a hybrid laying hen belonging to a light strain

Measure contraction properties of Carnot groups

We prove that any corank 1 Carnot group of dimension $k+1$ equipped with a left-invariant measure satisfies the $\mathrm{MCP}(K,N)$ if and only if $K \leq 0$ and $N \geq k+3$. This generalizes the well known result by Juillet for the Heisenberg group $\mathbb{H}_{k+1}$ to a larger class of structures, which admit non-trivial abnormal minimizing curves. The number $k+3$ coincides with the geodesic dimension of the Carnot group, which we define here for a general metric space. We discuss some of its properties, and its relation with the curvature exponent (the least $N$ such that the $\mathrm{MCP}(0,N)$ is satisfied). We prove that, on a metric measure space, the curvature exponent is always larger than the geodesic dimension which, in turn, is larger than the Hausdorff one. When applied to Carnot groups, our results improve a previous lower bound due to Rifford. As a byproduct, we prove that a Carnot group is ideal if and only if it is fat.Comment: 17 pages, final version, to appear on "Calculus of Variations and PDEs

Radial and cylindrical symmetry of solutions to the Cahn-Hilliard equation

The paper is devoted to the classification of entire solutions to the Cahn-Hilliard equation $-\Delta u = u-u^3-\delta$ in $\R^N$, with particular interest in those solutions whose nodal set is either bounded or contained in a cylinder. The aim is to prove either radial or cylindrical symmetry, under suitable hypothesis

Early b physics at CMS

The CMS experiment at the Large Hadron Collider collected in the first months of operation a luminosity of about 300/nb. The first results in the context of the B physics obtained with these data are presented. The di-muon resonances from J/psi and Y decays are presented and their total and differential cross-sections measured. The inclusive B production have also being investigated and two independent measurements are reported. Muons in jets are used as a way to identify events with B content, the kinematic properties (ptRel) of the muons are used to separate the B production from other processes producing muons in jets. The second measurement of inclusive B production is done using b-tagging techniques and higher energy jets. The two measurements cover different phase spaces, comparison with LO and NLO prediction are also presented.Comment: HCP2010 proceedings. CMS CR-2010/19