2,190 research outputs found
-regularity of the -adic valuation of the Fibonacci sequence
We show that the -adic valuation of the sequence of Fibonacci numbers is a
-regular sequence for every prime . For , we determine that
the rank of this sequence is , where is the
restricted period length of the Fibonacci sequence modulo .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 .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
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