Abstract:
We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.

Abstract:
For the class of quasi-periodic solutions of the vortex filament equation, we study connections between the algebro-geometric data used for their explicit construction and the geometry of the evolving curves. We give a complete description of genus one solutions, including geometrically interesting special cases such as Euler elastica, constant torsion curves, and self-intersecting filaments. We also prove generalizations of these connections to higher genus.

Abstract:
Differential equations are derived for a continuous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry.

Abstract:
The Backlund transformation for pseudospherical surfaces, which is equivalent to that of the sine-Gordon equation, can be restricted to give a transformation on space curves that preserves constant torsion. We study its effects on closed curves (in particular, elastic rods) that generate multiphase solutions for the vortex filament flow (also known as the Localized Induction Equation). In doing so, we obtain analytic constant-torsion representatives for a large number of knot types.

Abstract:
We construct integrable hierarchies of flows for curves in centroaffine R^3 through a natural pre-symplectic structure on the space of closed unparametrized starlike curves. We show that the induced evolution equations for the differential invariants are closely connected with the Boussinesq hierarchy, and prove that the restricted hierarchy of flows on curves that project to conics in RP^2 induces the Kaup-Kuperschmidt hierarchy at the curvature level.

Abstract:
We study the relation between the centro-affine geometry of star-shaped planar curves and the projective geometry of parametrized maps into $\RP^1$. We show that projectivization induces a map between differential invariants and a bi-Poisson map between Hamiltonian structures. We also show that a Hamiltonian evolution equation for closed star-shaped planar curves, discovered by Pinkall, has the Schwarzian KdV equation as its projectivization. (For both flows, the curvature evolves by the KdV equation.) Using algebro-geometric methods and the relation of group-based moving frames to AKNS-type representations, we construct examples of closed solutions of Pinkall's flow associated with periodic finite-gap KdV potentials.

Abstract:
We construct integrable hierarchies of flows for curves in centroaffine ${\mathbb R}^3$ through a natural pre-symplectic structure on the space of closed unparametrized starlike curves. We show that the induced evolution equations for the differential invariants are closely connected with the Boussinesq hierarchy, and prove that the restricted hierarchy of flows on curves that project to conics in ${\mathbb{RP}}^2$ induces the Kaup-Kuperschmidt hierarchy at the curvature level.

Abstract:
vertical integration in poultry industry strongly emphasizes the importance of cost control at all levels. in the usual broiler production operations, the costs involved with the production of the hatching egg or the day old chick are negligible if seen in the perspective of the cost per kg of live bird. from a research point of view, anyway, the greatest attention is usually given to the performance of broiler breeders, and most of the research in the field is focused on the improvement of their relative performance, mainly in terms of saleable chicks produced per hen, while less attention has been given to the quality of the chick and to the improvement of its growth performances, even if these last parameters have an effective impact on the overall economics of the poultry growing business. most of the data available is quite dated, as can be seen from some recent reviews, and in general little attention is given to the impact of parental nutrition on the subsequent broiler performance. it is in fact more usual to find data about dam nutrition influence on egg fertility and hatchability than on subsequent progeny performance. the objectives of this review were to assess, on the basis of published reports, the effects of selected nutrients and anti-nutrients normally prevailing in commercial broiler breeder feeds - vitamins, micro-minerals, mycotoxins, - trying to pinpoint which could be the positive and the negative effects of both on the subsequent broiler performance, with a particular attention to the impact on immune function and carcass yield.

Abstract:
We study the local approximation properties in hierarchical spline spaces through multiscale quasi-interpolation operators. This construction suggests the analysis of a subspace of the classical hierarchical spline space (Vuong et al., 2011) which still satisfies the essential properties of the full space. The B-spline basis of such a subspace can be constructed using parent-children relations only, making it well adapted to local refinement algorithms.

Abstract:
We have focused our study on the concentrations of non essential trace metals Pb, Cd and Cr and essential heavy metals Zn and Cu, in the liver and kidney of raptor species from different areas of the Calabria region in Italy, with the aim of obtaining information concerning the quality and the contamination level of their habitat. No significant differences related to sampling areas and gender were found, while significant differences were found in metal concentrations among species. Mean Cd concentrations in the kidneys were generally 1.5-10 fold higher than hepatic ones, while Pb was mostly concentrated in the liver; a different pattern in tissue Cr concentration was observed between species. Referring to essential metals, Cu levels were higher in the liver, whereas higher Zn concentrations were constantly present in the kidneys. The ratio between kidney and liver metal concentrations (K:Ls) was also evaluated. The measured concentrations in toxic elements can be considered as indicative of chronic exposure to low amounts of pollutants. The essential metal concentrations were in the range of physiological values and did not show the presence of any deficiency or excess of metal. The present study can be considered as a starting point in the study of a possible correlation between levels of pollutants and the appearance of any adverse effects in raptor species in the Calabria area.