Some identities on derangement and degenerate derangement polynomials

In combinatorics, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derangement number. In this paper, as natural companions to derangement numbers and degenerate versions of the companions we introduce derangement polynomials and degenerate derangement polynomials. We give some of their properties, recurrence relations and identities for those polynomials which are related to some special numbers and polynomials.Comment: 12 page

Insect herbivores should follow plants escaping their relatives

Neighboring plants within a local community may be separated by many millions of years of evolutionary history, potentially reducing enemy pressure by insect herbivores. However, it is not known how the evolutionary isolation of a plant affects the fitness of an insect herbivore living on such a plant, especially the herbivore's enemy pressure. Here, we suggest that evolutionary isolation of host plants may operate similarly as spatial isolation and reduce the enemy pressure per insect herbivore. We investigated the effect of the phylogenetic isolation of host trees on the pressure exerted by specialist and generalist enemies (parasitoids and birds) on ectophagous Lepidoptera and galling Hymenoptera. We found that the phylogenetic isolation of host trees decreases pressure by specialist enemies on these insect herbivores. In Lepidoptera, decreasing enemy pressure resulted from the density dependence of enemy attack, a mechanism often observed in herbivores. In contrast, in galling Hymenoptera, enemy pressure declined with the phylogenetic isolation of host trees per se, as well as with the parallel decline in leaf damage by non-galling insects. Our results suggest that plants that leave their phylogenetic ancestral neighborhood can trigger, partly through simple density-dependency, an enemy release and fitness increase of the few insect herbivores that succeed in tracking these plants

Phenytoin Pharmacokinetics After Intravenous Administration to Patients Receiving Enteral Tube-Feeding

Serial plasma samples were collected after administration of 13 intravenous dose of phenytoin to 11 patients with head injury; 5 to patients who had been receiving enteral feeds for less than 5 days (group 1), and 8 to patients who had been receiving enteral feeds for loner than 5 days (group 2). Average plasma phenytoin concentrations were higher in group 1 than in group 2 (0.003). The median intravenous study dose was the same (300 mg) in both groups (p=0.17). Group 2 received slightly higher doses expressed as mg/kg (median of 5.45 mg/kg compared to 4.29 mg/kg in group 1, p=0.21). Phenytoin was more rapidly eliminated following intravenous dosing patients receiving long-term enteral feeding. V-max was higher in group 2 than in group 1 (medians, 709 versus 394 mg/day) and K-m smaller (medians, 2.5 versus 3.9 mg/l), but volume of distribution was similar in both groups (p=0.88). The kinetic parameters of phenytoin in group 1 were similar to previously published population pharmacokinetic parameters. In order to maintain phenytoin concentrations adequate for seizure prophylaxis in patients receiving long-term enteral feeding it would be advisable to decrease the dosing interval as well as increasing the phenytoin dose when the drug is administered intravenously