Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions

For relatively prime positive integers $u_0$ and $r$, we consider the least common multiple $L_n:=\mathrm{lcm}(u_0,u_1,\ldots, u_n)$ of the finite arithmetic progression $\{u_k:=u_0+kr\}_{k=0}^n$. We derive new lower bounds on $L_n$ which improve upon those obtained previously when either $u_0$ or $n$ is large. When $r$ is prime, our best bound is sharp up to a factor of $n+1$ for $u_0$ properly chosen, and is also nearly sharp as $n\to\infty$.Comment: 10 page

Behind at the Starting Line: Poverty Among Hispanic Infants

In this brief, authors Daniel Lichter, Scott Sanders, and Kenneth Johnson examine the economic circumstances of Hispanic infants using the Census Bureau’s American Community Survey annual microdata files from 2006 through 2010. They report that a disproportionate share of Hispanic infants start life’s race behind the starting line, poor and disadvantaged—an important finding because the proportion of all U.S. births that are Hispanic is growing rapidly. The poverty risk is especially high among rural Hispanic infants and those in new destinations. Despite higher poverty risks, Hispanic infants receive less governmental assistance. High Hispanic infant poverty has immediate and long-term consequences for infants and the nation. Failing to invest in families and children now has long-term consequences because early childhood poverty tends to set into motion a series of lifecycle disadvantages (such as insufficient parenting, bad neighborhoods, underfunded schools, and poor health care) that greatly increases the likelihood of poverty in adulthood. The authors conclude that whether today’s Hispanic children will assimilate into America’s economic mainstream is an open question, but the Hispanic infants who will help reshape America’s future require public policy attention now

The yeast F1-ATPase beta subunit precursor contains functionally redundant mitochondrial protein import information

The NH2 terminus of the yeast F1-ATPase beta subunit precursor directs the import of this protein into mitochondria. To define the functionally important components of this import signal, oligonucleotide-directed mutagenesis was used to introduce a series of deletion and missense mutations into the gene encoding the F1-beta subunit precursor. Among these mutations were three nonoverlapping deletions, two within the 19-amino-acid presequence (delta 5-12 and delta 16-19) and one within the mature protein (delta 28-34). Characterization of the mitochondrial import properties of various mutant F1-beta subunit proteins containing different combinations of these deletions showed that import was blocked only when all three deletions were combined. Mutant proteins containing all possible single and pairwise combinations of these deletions were found to retain the ability to direct mitochondrial import of the F1-beta subunit. These data suggest that the F1-beta subunit contains redundant import information at its NH2 terminus. In fact, we found that deletion of the entire F1-beta subunit presequence did not prevent import, indicating that a functional mitochondrial import signal is present near the NH2 terminus of the mature protein. Furthermore, by analyzing mitochondrial import of the various mutant proteins in [rho-] yeast, we obtained evidence that different segments of the F1-beta subunit import signal may act in an additive or cooperative manner to optimize the import properties of this protein

MINNESOTA PRODUCTION AND CONSUMPTION FORECAST OF MAJOR FEED GRAINS BY MINNESOTA COUNTY FOR 1990 AND 2000

Crop Production/Industries,

Calculating NMR parameters in aluminophosphates : evaluation of dispersion correction schemes

Periodic density functional theory (DFT) calculations have recently emerged as a popular tool for assigning solid-state nuclear magnetic resonance (NMR) spectra. However, in order for the calculations to yield accurate results, accurate structural models are also required. In many cases the structural model (often derived from crystallographic diffraction) must be optimised (i.e., to an energy minimum) using DFT prior to the calculation of NMR parameters. However, DFT does not reproduce weak long-range "dispersion'' interactions well, and optimisation using some functionals can expand the crystallographic unit cell, particularly when dispersion interactions are important in defining the structure. Recently, dispersion-corrected DFT (DFT-D) has been extended to periodic calculations, to compensate for these missing interactions. Here, we investigate whether dispersion corrections are important for aluminophosphate zeolites (AlPOs) by comparing the structures optimised by DFT and DFT-D (using the PBE functional). For as-made AlPOs (containing cationic structure-directing agents (SDAs) and framework-bound anions) dispersion interactions appear to be important, with significant changes between the DFT and DFT-D unit cells. However, for calcined AlPOs, where the SDA-anion pairs are removed, dispersion interactions appear much less important, and the DFT and DFT-D unit cells are similar. We show that, while the different optimisation strategies yield similar calculated NMR parameters (providing that the atomic positions are optimised), the DFT-D optimisations provide structures in better agreement with the experimental diffraction measurements. Therefore, it appears that DFT-D calculations can, and should, be used for the optimisation of calcined and as-made AlPOs, in order to provide the closest agreement with all experimental measurements.PostprintPeer reviewe