A New Family of Solvable Self-Dual Lie Algebras

A family of solvable self-dual Lie algebras is presented. There exist a few methods for the construction of non-reductive self-dual Lie algebras: an orthogonal direct product, a double-extension of an Abelian algebra, and a Wigner contraction. It is shown that the presented algebras cannot be obtained by these methods.Comment: LaTeX, 12 page

Waste management in the stingless bee Melipona beecheii Bennett (Hymenoptera: Apidae)

Waste management is important in insect societies because waste can be hazardous to adults, brood and food stores. The general organization of waste management and the influence of task partitioning, division of labor and age polyethism on waste processing were studied in three colonies of the tropical American stingless bee Melipona beecheii Bennett in Yucatán, Mexico. Waste generated in the colony (feces, old brood cells, cocoons, dead adults and brood) was collected by workers throughout the nest and taken to specific waste dumps within the nest. During the day, workers based at the waste dumps formed waste pellets, which they directly transferred in 93% of cases, to other workers who subsequently removed them from the nest. This is an example of task partitioning and is hypothesized to improve nest hygiene as has been found in leafcutting ants, Atta. To investigate division of labor and age polyethism we marked a cohort of 144 emerging workers. Workers forming waste pellets were on average 31.2±6.5 days old (±SD, N= 40, range of 18-45 days). The life span of M. beecheii workers was 49.0±14.0 days (N= 144). There was no difference in the life span of workers who formed (52.2±11.6 days, N= 40) or did not form (49.9±11.5 days, N= 97) waste pellets, suggesting that waste work did not increase mortality. Although waste was probably not hazardous to adults and brood, because the dumps are located outside the brood chamber, its presence inside the nests can attract phorid flies and predators, which can harm the colony

pp-regularity of the pp-adic valuation of the Fibonacci sequence

We show that the $p$-adic valuation of the sequence of Fibonacci numbers is a $p$-regular sequence for every prime $p$. For $p \neq 2, 5$, we determine that the rank of this sequence is $\alpha(p) + 1$, where $\alpha(m)$ is the restricted period length of the Fibonacci sequence modulo $m$.Comment: 7 pages; publication versio