On the Nonlocal Equations and Nonlocal Charges Associated with the Harry Dym Hierarchy

A large class of nonlocal equations and nonlocal charges for the Harry Dym hierarchy is exhibited. They are obtained from nonlocal Casimirs associated with its bi-Hamiltonian structure. The Lax representation for some of these equations is also given.Comment: to appear in Journal of Mathematical Physics, 17 pages, Late

Deformed Harry Dym and Hunter-Zheng Equations

We study the deformed Harry Dym and Hunter-Zheng equations with two arbitrary deformation parameters. These reduce to various other known models in appropriate limits. We show that both these systems are bi-Hamiltonian with the same Hamiltonian structures. They are integrable and belong to the same hierarchy corresponding to positive and negative flows. We present the Lax pair description for both the systems and construct the conserved charges of negative order from the Lax operator. For the deformed Harry Dym equation, we construct the non-standard Lax representation for two special classes of values of the deformation parameters. In general, we argue that a non-standard description will involve a pseudo-differential operator of infinite order.Comment: Latex file, 15 page

²¹⁰Pb- ²²⁶Ra chronology reveals rapid growth rate of Madrepora oculata and Lophelia pertusa on world's largest cold-water coral reef

Here we show the use of the 210Pb- 226Ra excess method to determine the growth rate of two corals from the world's largest known cold-water coral reef, Røst Reef, north of the Arctic circle off Norway. Colonies of each of the two species that build the reef, Lophelia pertusa and Madrepora oculata, were collected alive at 350 m depth using a submersible. Pb and Ra isotopes were measured along the major growth axis of both specimens using low level alpha and gamma spectrometry and trace element compositions were studied. 210Pb and 226Ra differ in the way they are incorporated into coral skeletons. Hence, to assess growth rates, we considered the exponential decrease of initially incorporated 210Pb, as well as the increase in 210Pb from the decay of 226Ra and contamination with 210Pb associated with Mn-Fe coatings that we were unable to remove completely from the oldest parts of the skeletons. 226Ra activity was similar in both coral species, so, assuming constant uptake of 210Pb through time, we used the 210Pb- 226Ra chronology to calculate growth rates. The 45.5 cm long branch of M. oculata was 31 yr with an average linear growth rate of 14.4 ± 1.1 mm yr -1 (2.6 polyps per year). Despite cleaning, a correction for Mn-Fe oxide contamination was required for the oldest part of the colony; this correction corroborated our radiocarbon date of 40 yr and a mean growth rate of 2 polyps yr -1. This rate is similar to the one obtained in aquarium experiments under optimal growth conditions. For the 80 cm-long L. pertusa colony, metal-oxide contamination remained in both the middle and basal part of the coral skeleton despite cleaning, inhibiting similar age and growth rate estimates. The youngest part of the colony was free of metal oxides and this 15 cm section had an estimated a growth rate of 8 mm yr -1, with high uncertainty (∼1 polyp every two to three years). We are less certain of this 210Pb growth rate estimate which is within the lowermost ranges of previous growth rate estimates. We show that 210Pb- 226Ra dating can be successfully applied to determine the age and growth rate of framework-forming cold-water corals if Mn-Fe oxide deposits can be removed. Where metal oxides can be removed, large M. oculata and L. pertusa skeletons provide archives for studies of intermediate water masses with an up to annual time resolution and spanning over many decades. © 2012 Author(s)

Interaction entre observateur et observé en écopathologie. Réflexions méthodologiques et épistémologiques

Les maladies des animaux conçues comme des sorties de systèmes complexes que sont les élevages sont l'objet d'étude de l'écopathologie. Le dispositif de recherche utilisé, l'enquête en conditions réelles de production implique fortement les acteurs du système étudié, éleveurs et conseillers, dans l'observation et le recueil des informations. Les interactions biologiques et sociologiques mises en oeuvree dans ce cadre sont nombreuses et diverses. Elles peuvent être source d'interaction entre observateur et observé et avoir des conséquences sur les résultats de la recherche. Cette interaction, reconnue et admise doit être prise en compte depuis la définition du dispositif de recherche jusqu'à l'interprétation des résultats de la recherche. (Résumé d'auteur

Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves

A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative to slab-like macroscopically inhomogeneous porous obstacles. It is shown how to numerically solve such problems, involving both spatially-varying density and compressibility, by means of an iterative scheme initialized with a Born approximation. A numerical solution is obtained for a canonical problem involving a two-layer slab.Comment: submitted to Math.Meth.Appl.Sc

Symmetry, Local Linearization, and Gauge Classification of the Doebner-Goldin Equation

For the family of nonlinear Schr\"odinger equations derived by H.-D.~Doebner and G.A.~Goldin (J.Phys.A 27, 1771) we calculate the complete set of Lie symmetries. For various subfamilies we find different finite and infinite dimensional Lie symmetry algebras. Two of the latter lead to a local transformation linearizing the particular subfamily. One type of these transformations leaves the whole family of equations invariant, giving rise to a gauge classification of the family. The Lie symmetry algebras and their corresponding subalgebras are finally characterized by gauge invariant parameters.Comment: 17 pages, LaTeX, 1 figure, to appear in Reports on Mathematical Physic

Local and non-local equivalent potentials for p-12C scattering

A Newton-Sabatier fixed energy inversion scheme has been used to equate inherently non-local p-${}^{12}$C potentials at a variety of energies to pion threshold, with exactly phase equivalent local ones. Those energy dependent local potentials then have been recast in the form of non-local Frahn-Lemmer interactions.Comment: 15 pages plus 9 figures submitted to Phys. Rev.

Perspectives de la modélisation des systèmes agraires villageois. L'exemple des régions cotonnières du Mali

La recherche agronomique doit se donner les moyens d'expliciter les conditions techniques, économique, sociales et organisationnelles dans lesquelles l'agriculture des régions où elle intervient est susceptible de progresser techniquement et de se développer, ceci pour mieux évaluer les changements dans les politiques macro-économiques et sectorielles qui aideraient à créer ces conditions. Le niveau d'approche proposé pour mobiliser l'information et les connaissances disponibles, par essence hétérogènes, est celui du système agraire local tel qu'il fonctionne à l'échelle des villages. La méthode de formalisation et de calcul retenue est la programmation linéaire bien adaptée pour choisir des activités complémentaires et concurrentes dans un contexte de contraintes sévères. Le cas d'un village du sud du Mali est traité. Il correspond à une situation évoluée avec des problèmes d'équilibre entre une culture de rente (coton) et des cultures céréalières, de relations agriculture-élevage, de pression démographique croissante etc. L'écriture d'un modèle simplifié est décrite pas à pas. Les résultats sont discutés et plusieurs scénarios sont présentés et discutés pour illustrer les possibilités d'analyse et d'évaluation offertes par cette techniqu

Electron Wave Filters from Inverse Scattering Theory

Semiconductor heterostructures with prescribed energy dependence of the transmittance can be designed by combining: {\em a)} Pad\'e approximant reconstruction of the S-matrix; {\em b)} inverse scattering theory for Schro\"dinger's equation; {\em c)} a unitary transformation which takes into account the variable mass effects. The resultant continuous concentration profile can be digitized into an easily realizable rectangular-wells structure. For illustration, we give the specifications of a 2 narrow band-pass 12 layer $Al_cGa_{1-c}As$ filter with the high energy peak more than {\em twice narrower} than the other.Comment: 4 pages, Revtex with one eps figur

Long-Term Recovery After Endothelial Colony-Forming Cells or Human Umbilical Cord Blood Cells Administration in a Rat Model of Neonatal Hypoxic-Ischemic Encephalopathy.

Neonatal hypoxic-ischemic encephalopathy (NHIE) is a dramatic perinatal complication, associated with poor neurological prognosis despite neuroprotection by therapeutic hypothermia, in the absence of an available curative therapy. We evaluated and compared ready-to-use human umbilical cord blood cells (HUCBC) and bankable but allogeneic endothelial progenitors (ECFC) as cell therapy candidate for NHIE. We compared benefits of HUCBC and ECFC transplantation 48 hours after injury in male rat NHIE model, based on the Rice-Vannucci approach. Based on behavioral tests, immune-histological assessment and metabolic imaging of brain perfusion using single photon emission computed tomography (SPECT), HUCBC, or ECFC administration provided equally early and sustained functional benefits, up to 8 weeks after injury. These results were associated with total normalization of injured hemisphere cerebral blood flow assessed by SPECT/CT imaging. In conclusion, even if ECFC represent an efficient candidate, HUCBC autologous criteria and easier availability make them the ideal candidate for hypoxic-ischemic cell therapy. Stem Cells Translational Medicine 2017;6:1987-1996