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

Scalar Field Dark Matter mass model and evolution of rotation curves for Lsb galaxies

We study the evolution of gas rotation curves within the scalar field dark matter (SFDM) model. In this model the galactic haloes are astronomical Bose-Einstein Condensate drops of scalar field. These haloes are characterized by a constant-density core and are consistent with observed rotation curves of dark matter dominated galaxies, a missing feature in CDM haloes resulting from DM-only simulations. We add the baryonic component to the SFDM haloes and simulate the evolution of the dark matter tracer in a set of grid-based hydrodynamic simulations aimed to analyse the evolution of the rotation curves and the gas density distribution in the case of dark matter dominated galaxies. Previous works had found that when considering an exact analytic solution for a static SF configuration, the free parameters of the model allows for good fits to the rotation curves, we confirm that in our simulations but now taking into account the evolution of the baryonic component in a static dark matter and stellar disk potential. Including live gas is a step forward from the previous work using SFDM, as for example, the rotation velocity of the gas is not always exactly equal to the circular velocity of a test particle on a circular orbit. Contrasting with the data the cored mass model presented here is preferred instead of a cuspy one.Comment: 8 pages, 8 figures. Accepted for publication in MNRA

Linear recurrences and asymptotic behavior of exponential sums of symmetric boolean functions

In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic behavior of symmetric Boolean functions and provide a formula that allows us to determine if a symmetric boolean function is asymptotically not balanced. In particular, when the degree of the symmetric function is a power of two, then the exponential sum is much smaller than $2^n$.Comment: 18 pages, 3 figure

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