Rigid motions: action-angles, relative cohomology and polynomials with roots on the unit circle

Revisiting canonical integration of the classical solid near a uniform rotation, canonical action angle coordinates, hyperbolic and elliptic, are constructed in terms of various power series with coefficients which are polynomials in a variable $r^2$ depending on the inertia moments. Normal forms are derived via the analysis of a relative cohomology problem and shown to be obtainable without the use of ellitptic integrals (unlike the derivation of the action-angles). Results and conjectures also emerge about the properties of the above polynomials and the location of their roots. In particular a class of polynomials with all roots on the unit circle arises.Comment: 26 pages, 1 figur

Local stability of a gravitating filament: a dispersion relation

Filamentary structures are ubiquitous in astrophysics and are observed at various scales. On a cosmological scale, matter is usually distributed along filaments, and filaments are also typical features of the interstellar medium. Within a cosmic filament, matter can contract and form galaxies, whereas an interstellar gas filament can clump into a series of bead-like structures which can then turn into stars. To investigate the growth of such instabilities, we derive a local dispersion relation for an idealized self-gravitating filament, and study some of its properties. Our idealized picture consists of an infinite self-gravitating and rotating cylinder with pressure and density related by a polytropic equation of state. We assume no specific density distribution, treat matter as a fluid, and use hydrodynamics to derive the linearized equations that govern the local perturbations. We obtain a dispersion relation for axisymmetric perturbations and study its properties in the (k_R, k_z) phase space, where k_R and k_z are respectively the radial and longitudinal wavenumbers. While the boundary between the stable and unstable regimes is symmetrical in k_R and k_z and analogous to the Jeans criterion, the most unstable mode displays an asymmetry that could constrain the shape of the structures that form within the filament. Here the results are applied to a fiducial interstellar filament, but could be extended for more astrophysical systems such as cosmological filaments and tidal tails.Comment: 8 pages, 1 figure, published in A&

Algebraic Linearization of Dynamics of Calogero Type for any Coxeter Group

Calogero-Moser systems can be generalized for any root system (including the non-crystallographic cases). The algebraic linearization of the generalized Calogero-Moser systems and of their quadratic (resp. quartic) perturbations are discussed.Comment: LaTeX2e, 13 pages, no figure

Quadratic Algebra associated with Rational Calogero-Moser Models

Classical Calogero-Moser models with rational potential are known to be superintegrable. That is, on top of the r involutive conserved quantities necessary for the integrability of a system with r degrees of freedom, they possess an additional set of r-1 algebraically and functionally independent globally defined conserved quantities. At the quantum level, Kuznetsov uncovered the existence of a quadratic algebra structure as an underlying key for superintegrability for the models based on A type root systems. Here we demonstrate in a universal way the quadratic algebra structure for quantum rational Calogero-Moser models based on any root systems.Comment: 19 pages, LaTeX2e, no figure

The relationship between international humanitarian law and human rights law from the perspective of a human rights treaty body

The debate about the simultaneous applicability of international humanitarian law and human rights law also affects human rights treaty bodies. The article first considers the difficulty for a human rights body in determining whether international humanitarian law is applicable; second, it examines the problems in practice in applying the lex specialis doctrine and the question of derogation in this particular context. The author finally outlines the impact of the debate as to the extent of extraterritorial applicability of human rights law

Short-pulse photoassociation in rubidium below the D1_1 line

Photoassociation of two ultracold rubidium atoms and the subsequent formation of stable molecules in the singlet ground and lowest triplet states is investigated theoretically. The method employs laser pulses inducing transitions via excited states correlated to the $5S+5P_{1/2}$ asymptote. Weakly bound molecules in the singlet ground or lowest triplet state can be created by a single pulse while the formation of more deeply bound molecules requires a two-color pump-dump scenario. More deeply bound molecules in the singlet ground or lowest triplet state can be produced only if efficient mechanisms for both pump and dump steps exist. While long-range $1/R^3$-potentials allow for efficient photoassociation, stabilization is facilitated by the resonant spin-orbit coupling of the $0_u^+$ states. Molecules in the singlet ground state bound by a few wavenumbers can thus be formed. This provides a promising first step toward ground state molecules which are ultracold in both translational and vibrational degrees of freedom

The first derivative of the period function of a plane vector field

The algorithm of the successive derivatives introduced in \cite{5} was implemented in \cite{7}, \cite{8}. This algorithm is based on the existence of a decomposition of 1-forms associated to the relative cohomology of the Hamiltonian function which is perturbed. We explain here how the first step of this algorithm gives also the first derivative of the period function. This includes, for instance, new presentations of formulas obtained by Carmen Chicone and Marc Jacobs in \cite{3}

Allied Health Professions in the Health-sector Job Structure

This article reviews the characteristics of allied health professions in the U.S., Massachusetts, and Boston health sectors. These occupations are considered in the broader context of the multitiered job structure of the health sector and their gender and ethnic composition. The discussion includes surveys of vacancy rates and wage levels for selected allied health professions in Massachusetts hospitals. The article concludes with a more detailed, albeit national, picture of these occupations in the hospital sector per se, their demographic composition, and earnings level