Okounkov bodies of finitely generated divisors

We show that the Okounkov body of a big divisor with finitely generated section ring is a rational simplex, for an appropriate choice of flag; furthermore, when the ambient variety is a surface, the same holds for every big divisor. Under somewhat more restrictive hypotheses, we also show that the corresponding semigroup is finitely generated.Comment: 9 pages; v2 includes a stronger result in the surface cas

Pattern Avoidance in Reverse Double Lists

In this paper, we consider pattern avoidance in a subset of words on $\{1,1,2,2,\dots,n,n\}$ called reverse double lists. In particular a reverse double list is a word formed by concatenating a permutation with its reversal. We enumerate reverse double lists avoiding any permutation pattern of length at most 4 and completely determine the corresponding Wilf classes. For permutation patterns $\rho$ of length 5 or more, we characterize when the number of $\rho$-avoiding reverse double lists on $n$ letters has polynomial growth. We also determine the number of $1\cdots k$-avoiders of maximum length for any positive integer $k$.Comment: 24 pages, 5 figures, 4 table

Alien Registration- Anderson, Alex (Paris, Oxford County)

https://digitalmaine.com/alien_docs/13487/thumbnail.jp

Transistor-Like Behavior of a Bose-Einstein Condensate in a Triple Well Potential

In the last several years considerable efforts have been devoted to developing Bose-Einstein Condensate (BEC)-based devices for applications such as fundamental research, precision measurements and integrated atom optics. Such devices capable of complex functionality can be designed from simpler building blocks as is done in microelectronics. One of the most important components of microelectronics is a transistor. We demonstrate that Bose-Einstein condensate in a three well potential structure where the tunneling of atoms between two wells is controlled by the population in the third, shows behavior similar to that of an electronic field effect transistor. Namely, it exhibits switching and both absolute and differential gain. The role of quantum fluctuations is analyzed, estimates of switching time and parameters for the potential are presented.Comment: 12 pages, 12 figure

Association between Infant Feeding and Early Postpartum Infant Body Composition: A Pilot Prospective Study

Research studies have produced conflicting results of the impact of breastfeeding on overweight/obesity. This study evaluated the impact of infant feeding on infant body composition. There were two groups of mother-infant pairs (exclusive breastfeeding [EBF; n = 27] and mixed feeding [MF; n = 13]) in this study. At baseline, participants were similar in their demographic characteristics except prepregnancy weight, where MF mothers tended to be heavier than their EBF counterparts (67.3 kg versus 59.9 kg; P = .034). Infant birth weight was slightly higher among the MF group than their EBF counterparts (3.5 kg versus 3.4 kg), although the differences were not statistically significant. At 3 months postpartum, mean infant FMI (4.1 kg/m2 versus 3.8 kg/m2) and percent body fat (24.4% versus 23.1%) were slightly higher among EBF infants than MF infants. In terms of growth velocity, EBF infants gained weight faster than their MF counterparts, although the differences were not statistically significant. The findings from this study suggest that EBF may promote faster weight gain and increase in both fat mass index (FMI) and percent body fat in the early postpartum period in addition to the numerous health benefits enjoyed by the infant and the mother who exclusively breastfeeds her newborn

Increasing the coherence time of Bose-Einstein-condensate interferometers with optical control of dynamics

Atom interferometers using Bose-Einstein condensate that is confined in a waveguide and manipulated by optical pulses have been limited by their short coherence times. We present a theoretical model that offers a physically simple explanation for the loss of contrast and propose the method for increasing the fringe contrast by recombining the atoms at a different time. A simple, quantitatively accurate, analytical expression for the optimized recombination time is presented and used to place limits on the physical parameters for which the contrast may be recovered.Comment: 34 Pages, 8 Figure