Some statistics on permutations avoiding generalized patterns

In the last decade a huge amount of articles has been published studying pattern avoidance on permutations. From the point of view of enumeration, typically one tries to count permutations avoiding certain patterns according to their lengths. Here we tackle the problem of refining this enumeration by considering the statistics "first/last entry". We give complete results for every generalized patterns of type $(1,2)$ or $(2,1)$ as well as for some cases of permutations avoiding a pair of generalized patterns of the above types.Comment: 5 figure

The surface accessibility of α-bungarotoxin monitored by a novel paramagnetic probe

The surface accessibility of {alpha}-bungarotoxin has been investigated by using Gd2L7, a newly designed paramagnetic NMR probe. Signal attenuations induced by Gd2L7 on {alpha}-bungarotoxin C{alpha}H peaks of 1H-13C HSQC spectra have been analyzed and compared with the ones previously obtained in the presence of GdDTPA-BMA. In spite of the different molecular size and shape, for the two probes a common pathway of approach to the {alpha}-bungarotoxin surface can be observed with an equally enhanced access of both GdDTPA-BMA and Gd2L7 towards the protein surface side where the binding site is located. Molecular dynamics simulations suggest that protein backbone flexibility and surface hydration contribute to the observed preferential approach of both gadolinium complexes specifically to the part of the {alpha}-bungarotoxin surface which is involved in the interaction with its physiological target, the nicotinic acetylcholine receptor

Enumerative Combinatorics of Intervals in the Dyck Pattern Poset

We initiate the study of the enumerative combinatorics of the intervals in the Dyck pattern poset. More specifically, we find some closed formulas to express the size of some specific intervals, as well as the number of their covering relations. In most of the cases, we are also able to refine our formulas by rank. We also provide the first results on the Möbius function of the Dyck pattern poset, giving for instance a closed expression for the Möbius function of initial intervals whose maximum is a Dyck path having exactly two peaks

Effect of grain refinement on enhancing critical current density and upper critical field in undoped MgB2 ex-situ tapes

Ex-situ Powder-In-Tube MgB2 tapes prepared with ball-milled, undoped powders showed a strong enhancement of the irreversibility field H*, the upper critical field Hc2 and the critical current density Jc(H) together with the suppression of the anisotropy of all of these quantities. Jc reached 104 A/cm2 at 4.2 K and 10 T, with an irreversibility field of about 14 T at 4.2 K, and Hc2 of 9 T at 25 K, high values for not-doped MgB2. The enhanced Jc and H* values are associated with significant grain refinement produced by milling of the MgB2 powder, which enhances grain boundary pinning, although at the same time also reducing the connectivity from about 12% to 8%. Although enhanced pinning and diminished connectivity are in opposition, the overall influence of ball milling on Jc is positive because the increased density of grains with a size comparable with the mean free path produces strong electron scattering that substantially increases Hc2, especially Hc2 perpendicular to the Mg and B planes.Comment: 26 pages, 9 figures, submitted to J. Appl. Phy

Thermal properties of MgB2: the effect of disorder on gap amplitudes and relaxation times of p and s bands

We present thermal conductivity and specific heat measurements on MgB2 and Mg-AlB2 samples. Thermal properties have been analysed by using a two-gap model in order to estimate the gap amplitudes, D(0)p and D(0)s and the intra-band scattering rates, Gss and Gpp. As a function of Al doping and disorder D(0)s rapidly decreases, while D(0)p is rather constant. Gss and Gpp are increased by the disorder, being Gpp more affected than Gss.Comment: 2 pages, 3 figures, presented to the conference M2S-HTSC, 25-30 May 2003, Rio de Janeir

Sustainability, Innovation, and Green Chemistry in the Production and Valorization of Phenolic Extracts from Olea europaea L.

This paper describes a circular economy process based on environmentally and economically sustainable procedures which was applied to the sector of olive oil processing on an industrial scale. Olea europaea L. tissues and by-products represent a renewable and low-cost source of polyphenols, in particular hydroxytyrosol (HTyr), a naturally occurring compound well known for its biological properties. Specifically, green leaves (GL), dried leaves (DL), and pitted olive pulp were treated with water in a pneumatic extractor to obtain the corresponding polyphenolic extracts. Three standardized fractions, named Soft Extract Olea GL, Soft Extract Olea DL, and Soft Extract Olea HTyr resulted after the following two steps: a separation process carried out by membrane technology, and a concentration step performed under reduced pressure and low temperature. The polyphenolic fractions showed antiradical activity and have potential industrial applications in the food, nutraceutical, pharmaceutical, feed, and agronomic fields. Novel functionalized extracts containing hydroxytyrosol methyl carbonate (HTyr-MC) were obtained from Soft Extract Olea HTyr through an innovative approach based on green chemistry procedures, which appear to be a promising tool to increase the applications of the polyphenolic extracts