Abstract:
This article offers a simple but rigorous proof that the curl defined as a limit of circulation density is a vector-valued function with the standard Cartesian expression.

Abstract:
Let $m,ngeq 1$ be integers. Define $mathcal{T}_{m,n}$ to be the transportation polytope consisting of the $m imes n$ non-negative real matrices whose rows each sum to $1$ and whose columns each sum to $m/n$. The special case $mathcal{B}_n = mathcal{T}_{n,n}$ is the much-studied Birkhoff-von Neumann polytope of doubly-stochastic matrices. Using a recent asymptotic enumeration of non-negative integer matrices (Canfield and McKay, 2007), we determine the asymptotic volume of $mathcal{T}_{m,n}$ as $n oinfty$ with $m = m(n)$ such that $m/n$ neither decreases nor increases too quickly. In particular, we give an asymptotic formula for the volume of $mathcal{B}_n$.

Abstract:
Let m,n be positive integers. Define T(m,n) to be the transportation polytope consisting of the m x n non-negative real matrices whose rows each sum to 1 and whose columns each sum to m/n. The special case B(n)=T(n,n) is the much-studied Birkhoff-von Neumann polytope of doubly-stochastic matrices. Using a recent asymptotic enumeration of non-negative integer matrices (Canfield and McKay, 2007), we determine the asymptotic volume of T(m,n) as n goes to infinity, with m=m(n) such that m/n neither decreases nor increases too quickly. In particular, we give an asymptotic formula for the volume of B(n).

Abstract:
Let s,t,m,n be positive integers such that sm=tn. Let M(m,s;n,t) be the number of m x n matrices over {0,1,2,...} with each row summing to s and each column summing to t. Equivalently, M(m,s;n,t) counts 2-way contingency tables of order m x n such that the row marginal sums are all s and the column marginal sums are all t. A third equivalent description is that M(m,s;n,t) is the number of semiregular labelled bipartite multigraphs with m vertices of degree s and n vertices of degree t. When m=n and s=t such matrices are also referred to as n x n magic squares with line sums equal to t. We prove a precise asymptotic formula for M(m,s;n,t) which is valid over a range of (m,s;n,t) in which m,n become infinite while remaining approximately equal and the average entry is not too small. This range includes the case where m/n, n/m, s/n and t/m are bounded from below.

Abstract:
Submicron scale vanadia/silica hybrid nanofiber mats have been produced by electrospinning silica sol-gel precursor containing vanadium oxytriisopropoxide (VOTIP), followed by calcinations at high temperature. The properties of the resulting inorganic hybrid nanofiber mats are compared to those of electrospun pure silica nanofibers. SEM images show fibers are submicron in diameter and their morphology is maintained after calcination. Physisorption experiments reveal that silica nanofiber mats have a high specific surface area of 63 m2/g. FT-IR spectra exhibit Si—O vibrations and indicate the presence of V2O5 in the fibers. XPS studies reveal that the ratio of Si to O is close to 0.5 on the surface of fibers and the amount of vanadium on the surface of fibers increases with calcination. XRD diffraction patterns show that silica nanofibers are amorphous and orthorhombic V2O5 crystals have formed after calcination. EFTEM images demonstrate the growth of crystals on the surface of fibers containing vanadium after calcination. SEM images of fibers with high-vanadium content (50 mol% V : Si) show that vanadia crystals are mostly aligned along the fiber axis. XPS shows an increase in vanadium contents at the surface, and XRD patterns exhibit an increase in the degree of crystallinity. A coaxial electrospinning scheme has successfully been employed to selectively place V2O5 in the skin layer.

Abstract:
There is an emerging body of work indicating that genes, epigenetics, and the in utero environment can impact whether or not a child is obese. While certain genes have been identified that increase one’s risk for becoming obese, other factors such as excess gestational weight gain, gestational diabetes mellitus, and smoking can also influence this risk. Understanding these influences can help to inform which behaviors and exposures should be targeted if we are to decrease the prevalence of obesity. By helping parents and young children change certain behaviors and exposures during critical time periods, we may be able to alter or modify one’s genetic predisposition. However, further research is needed to determine which efforts are effective at decreasing the incidence of obesity and to develop new methods of prevention. In this paper, we will discuss how genes, epigenetics, and in utero influences affect the development of obesity. We will then discuss current efforts to alter these influences and suggest future directions for this work.

Abstract:
ential impact of chronotype on weekday and weekend sleep timing and duration Original Research (3441) Total Article Views Authors: Stephanie E Roepke, Jeanne F Duffy Published Date September 2010 Volume 2010:2 Pages 213 - 220 DOI: http://dx.doi.org/10.2147/NSS.S12572 Stephanie E Roepke1, Jeanne F Duffy1,2 1Division of Sleep Medicine, Department of Medicine, Brigham and Women’s Hospital, Boston, MA, USA; 2Division of Sleep Medicine, Harvard Medical School, Boston, MA, USA Abstract: Most recommendations are that adults should obtain 7–8 hours of sleep per night, although there are individual differences in self-reported sleep need. Chronotype (preference for early or late sleep timing), in combination with social demands, may affect the ability to obtain adequate sleep. This questionnaire study assessed perceived sleep need and self-reported sleep timing and duration during the week and on the weekend with respect to chronotype in visitors to the Museum of Science in Boston. Increasing age was associated with greater morningness. After adjusting for age, we found no significant association between chronotype and self-reported sleep need, or between chronotype and weekday sleep duration. However, we did find that greater eveningness was associated with a larger gap between self-reported sleep need and weekday sleep duration. On weekends, greater eveningness was associated with a longer sleep duration and greater extension of sleep, with the sleep extension achieved by later wake times. Together, these findings suggest that evening types accumulate a sleep debt during the week, despite reporting a similar sleep need and duration as morning types, and evening types then attempt to make up for that lost weekday sleep on the weekends. Studies of sleep need and sleep duration should take chronotype into account, and studies of chronotype may be confounded by the association between age and morningness, and must account for this potential confound in selection criteria and/or analysis.