Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions

We show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.Comment: 19 pages, 1 figure. New version corrects misprints and adds pertaining reference

Renormalization Group Flow of the Two-Dimensional Hierarchical Coulomb Gas

We consider a quasilinear parabolic differential equation associated with the renormalization group transformation of the two-dimensional hierarchical Coulomb system in the limit as the size of the block L goes to 1. We show that the initial value problem is well defined in a suitable function space and the solution converges, as t goes to infinity, to one of the countably infinite equilibrium solutions. The nontrivial equilibrium solution bifurcates from the trivial one. These solutions are fully described and we provide a complete analysis of their local and global stability for all values of inverse temperature. Gallavotti and Nicolo's conjecture on infinite sequence of ``phases transitions'' is also addressed. Our results rule out an intermediate phase between the plasma and the Kosterlitz-Thouless phases, at least in the hierarchical model we consider.Comment: 34pages,2figures, to appear in CM

A multi-domain approach to asteroid families identification

Previous works have identified families halos by an analysis in proper elements domains, or by using Sloan Digital Sky Survey-Moving Object Catalog data, fourth release (SDSS-MOC4) multi-band photometry to infer the asteroid taxonomy, or by a combination of the two methods. The limited number of asteroids for which geometric albedo was known until recently discouraged in the past the extensive use of this additional parameter, which is however of great importance in identifying an asteroid taxonomy. The new availability of geometric albedo data from the Wide-field Infrared Survey Explorer (WISE) mission for about 100,000 asteroids significantly increased the sample of objects for which such information, with some errors, is now known. In this work we proposed a new method to identify families halos in a multi-domain space composed by proper elements, SDSS-MOC4 (a*,i-z) colors, and WISE geometric albedo for the whole main belt (and the Hungaria and Cybele orbital regions). Assuming that most families were created by the breakup of an undifferentiated parent body, they are expected to be homogeneous in colors and albedo. The new method is quite effective in determining objects belonging to a family halo, with low percentages of likely interlopers, and results that are quite consistent in term of taxonomy and geometric albedo of the halo members.Comment: 23 pages, 18 figures, 6 tables. Accepted for publication in MNRA

Recent results on graphs with convex quadratic stability number

The main results about graphs with convex quadratic stability number (that is, graphs for which the stability number can be determined by convex quadratic programming) are surveyed including the most recently obtained. Furthermore, a few algorithmic techniques for the recognition of this type of graphs in particular families are presented

Reconhecimento de grafos com número de estabilidade quadrático convexo

São apresentados os principais e mais recentes resultados sobre grafos com número de estabilidade quadrático convexo (que são grafos cujo número de estabilidade pode ser determinado através de técnicas de programação quadrática convexa) e descritas algumas estratégias algorítmicas para o reconhecimento de grafos deste tipo em famílias particulares

Modulation of tomato pericarp firmness through pH and calcium: Implications for the texture of fresh-cut fruit

The effect of pH and calcium on pericarp firmness and pectin solubility was investigated in tomato fruit (Lycopersicon esculentum Mill. ‘Tavira’). Pericarp disks were vacuum-infiltrated with 50mM CaCI₂ or with distilled water and incubated for 4 h in buffer solutions at pH 4.5 and 7.0, and subsequently stored at 2 ◦C for 5 days. CaCl2 treatment had a significant effect on firmness retention in disks from turning and ripe fruit. Pericarp disks from mature-green fruit infiltrated with CaCl2 were firmer than untreated tissue after a 4 h incubation period, but the effect of calcium did not persist during storage at 2 ◦C. pH had a significant effect on the firmness of pericarp disks excised from turning and ripe fruit, but not on mature-green tissue. Treatments at pH 7.0 caused a reduction of the softening rate in disks from turning and ripe fruit, but had no significant effect at the mature-green stage. Water-soluble pectins decreased significantly in mature-green and ripe pericarp tissue following treatment with CaCl2 at pH 7.0, suggesting that pH affects pectin dissolution. Firmness changes induced by pH and calcium after a 4 h incubation treatment were highly correlated with pectin dissolution. The results indicate that, besides calcium, pH contributes to textural changes in tomato fruit pericarp. Since wounding inflicted during processing and acidic solutions used to prevent enzymic browning and microbial growth are likely to acidify the apoplast of fresh-cut fruit, the ability to maintain an apoplastic pH near 7.0 can significantly contribute to enhanced firmness of fresh-cut fruit