The production in the EU of the oilseeds, rapeseed and sunflower, has
increased dramatically over the last 20 years. Much of the oil produced after crushing is used for culinary purposes; this enhanced intake of vegetable oil has led to a substantial change of fatty
acid (FA) supply. This has been conclusively demonstrated by taking the UK oil
supply data and by use of the FA profile of the key oils converting the supply
data into a FA profile of the UK market place for 2008-2012. The most marked
changes are a reduction in saturated fat (SFA) and an increase in monounsaturated fatty acids (MUFA) available for consumption. Furthermore the introduction of varieties of hi-oleic sunflower oil
can further affect the market FA profile. The
fat profiles of rapeseed and sunflower oils are considered healthy and they can have a
positive impact when included in the diet, particularly as a replacement for
oils or fats rich in SFA. In the UK and much
of Europe, adult SFA intake continues to exceed recommendations. While
reductions in the UK population’s SFA intake have occurred over the last 20
years, these are modest and it may be timely to identify ways in which SFA
intake can be further reduced. To do this, the UK market FA supply data has
been analysed alongside the profile of FA intake from adults recording their intake
in national dietary surveys in order to
identify if the market supply affects overall FA consumption. There is
an indication that market oil supply is reflected in adults dietary intake of
the main groups of FA. Consequently changes made to the oil profile of oilseeds
by plant breeders and use of the resulting healthier oils by food manufacturers
could have important roles to play in helping adults to achieve the recommended
intake of SFA and also improve the overall fat quality in their diet leading
to enhanced long-term health and well-being.
Thus changes made in pri

Abstract:
A topological lower bound on the Skyrme energy which depends explicity on the pion mass is derived. This bound coincides with the previously best known bound when the pion mass vanishes, and improves on it whenever the pion mass is non-zero. The new bound can in particular circumstances be saturated. New energy bounds are also derived for the Skyrme model on a compact manifold, for the Faddeev-Skyrme model with a potential term, and for the Aratyn-Ferreira-Zimerman and Nicole models.

Abstract:
We consider topological solitons in the CP^n sigma models in two space dimensions. In particular, we study "kinks", which are independent of one coordinate up to a rotation of the target space, and "chains", which are periodic in one coordinate up to a rotation of the target space. Kinks and chains both exhibit constituents, similar to monopoles and calorons in SU(n) Yang-Mills-Higgs and Yang-Mills theories. We examine the constituent structure using Lie algebras.

Abstract:
We construct families of SO(3)-symmetric charge 1 instantons and calorons on the space H^3 x R. We show how the calorons include instantons and hyperbolic monopoles as limiting cases. We show how Euclidean calorons are the flat space limit of this family.

Abstract:
We construct SU(2) calorons, with non-trivial holonomy, instanton charge 2 and magnetic charge 0 or -1; these calorons have two constituent monopoles, with charges (2,2) or (2,1). Our calorons are U(1)-symmetric and are constructed via the Nahm transform. They fall into distinct families which can be classified using representation theory. We consider large scale and large period limits of these calorons; in particular, the large scale limit may be a monopole, or a caloron with different topological charges.

Abstract:
The Carmichael lambda function $\lambda(n)$ is defined to be the smallest positive integer $m$ such that $a^m$ is congruent to 1 modulo $n,$ for all $a$ and $n$ relatively prime. The function $\lambda_k(n)$ is defined to be the $k$th iterate of $\lambda(n).$ Previous results show a normal order for $n/\lambda_k(n)$ where $k=1,2.$ We will show a normal order for all $k.$

Abstract:
The Carmichael lambda function $\lambda(n)$ is defined to be the smallest positive integer $m$ such that $a^m \equiv 1 \pmod{n}$ for all $(a,n)=1.$ $\lambda_k(n)$ is defined to be the $k$th iterate of $\lambda(n).$ Let L(n) be the smallest $k$ for which $\lambda_k(n)=1.$ It's easy to show that $L(n) \ll \log n.$ It's conjectured that $L(n)\asymp \log\log n,$ but previously it was not known to be $o(\log n)$ for almost all $n.$ We will show that $L(n) \ll (\log n)^{\delta}$ for almost all $n,$ for some $\delta <1.$ We will also show $L(n) \gg \log\log n$ for almost all $n$ and conjecture a normal order for L(n).

Abstract:
We consider the large N limit of the Nahm transform, which relates charge N monopoles to solutions to the Nahm equation involving NxN matrices. In the large N limit the former approaches a magnetic bag, and the latter approaches a solution of the Nahm equation based on the Lie algebra of area-preserving vector fields on the 2-sphere. We show that the Nahm transform simplifies drastically in this limit.

Abstract:
The emergence of the pandemic 2009 H1N1 influenza A virus in humans and subsequent discovery that it was of swine influenza virus lineages raised concern over the safety of pork. Pigs experimentally infected with pandemic 2009 H1N1 influenza A virus developed respiratory disease; however, there was no evidence for systemic disease to suggest that pork from pigs infected with H1N1 influenza would contain infectious virus. These findings support the WHO recommendation that pork harvested from pandemic influenza A H1N1 infected swine is safe to consume when following standard meat hygiene practices.

Abstract:
Solitons in the Skyrme-Faddeev model on R^2xS^1 are shown to undergo buckling transitions as the circumference of the S^1 is varied. These results support a recent conjecture that solitons in this field theory are well-described by a much simpler model of elastic rods.