Calculation of energy levels and transition amplitudes for barium and radium

The radium atom is a promising system for studying parity and time invariance violating weak interactions. However, available experimental spectroscopic data for radium is insufficient for designing an optimal experimental setup. We calculate the energy levels and transition amplitudes for radium states of significant interest. Forty states corresponding to all possible configurations consisting of the $7s$, $7p$ and $6d$ single-electron states as well as the states of the $7s8s$, $7s8p$ and $7s7d$ configurations have been calculated. The energies of ten of these states corresponding to the $6d^2$, $7s8s$, $7p^2$, and $6d7p$ configurations are not known from experiment. Calculations for barium are used to control the accuracy.Comment: 12 pages, 4 table

Tzitz\'eica transformation is a dressing action

We classify the simplest rational elements in a twisted loop group, and prove that dressing actions of them on proper indefinite affine spheres give the classical Tzitz\'eica transformation and its dual. We also give the group point of view of the Permutability Theorem, construct complex Tzitz\'eica transformations, and discuss the group structure for these transformations

Small oscillations and the Heisenberg Lie algebra

The Adler Kostant Symes [A-K-S] scheme is used to describe mechanical systems for quadratic Hamiltonians of $\mathbb R^{2n}$ on coadjoint orbits of the Heisenberg Lie group. The coadjoint orbits are realized in a solvable Lie algebra $\mathfrak g$ that admits an ad-invariant metric. Its quadratic induces the Hamiltonian on the orbits, whose Hamiltonian system is equivalent to that one on $\mathbb R^{2n}$. This system is a Lax pair equation whose solution can be computed with help of the Adjoint representation. For a certain class of functions, the Poisson commutativity on the coadjoint orbits in $\mathfrak g$ is related to the commutativity of a family of derivations of the 2n+1-dimensional Heisenberg Lie algebra $\mathfrak h_n$. Therefore the complete integrability is related to the existence of an n-dimensional abelian subalgebra of certain derivations in $\mathfrak h_n$. For instance, the motion of n-uncoupled harmonic oscillators near an equilibrium position can be described with this setting.Comment: 17 pages, it contains a theory about small oscillations in terms of the AKS schem

The conceptual and practical ethical dilemmas of using health discussion board posts as research data.

Increasing numbers of people living with a long-term health condition are putting personal health information online, including on discussion boards. Many discussion boards contain material of potential use to researchers; however, it is unclear how this information can and should be used by researchers. To date there has been no evaluation of the views of those individuals sharing health information online regarding the use of their shared information for research purposes

Algebraic construction of the Darboux matrix revisited

We present algebraic construction of Darboux matrices for 1+1-dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case. We discuss different approaches to the Darboux-Backlund transformation, based on different lambda-dependencies of the Darboux matrix: polynomial, sum of partial fractions, or the transfer matrix form. We derive symmetric N-soliton formulas in the general case. The matrix spectral parameter and dressing actions in loop groups are also discussed. We describe reductions to twisted loop groups, unitary reductions, the matrix Lax pair for the KdV equation and reductions of chiral models (harmonic maps) to SU(n) and to Grassmann spaces. We show that in the KdV case the nilpotent Darboux matrix generates the binary Darboux transformation. The paper is intended as a review of known results (usually presented in a novel context) but some new results are included as well, e.g., general compact formulas for N-soliton surfaces and linear and bilinear constraints on the nonisospectral Lax pair matrices which are preserved by Darboux transformations.Comment: Review paper (61 pages). To be published in the Special Issue "Nonlinearity and Geometry: Connections with Integrability" of J. Phys. A: Math. Theor. (2009), devoted to the subject of the Second Workshop on Nonlinearity and Geometry ("Darboux Days"), Bedlewo, Poland (April 2008

Grassmannian flows and applications to nonlinear partial differential equations

We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting linear evolutionary flows on a Stiefel manifold onto a coordinate chart of the underlying Grassmann manifold. Our method relies on extending this idea to the infinite dimensional case. The key is an integral equation analogous to the Marchenko equation in integrable systems, that represents the coodinate chart map. We show explicitly how to generate such solutions to scalar partial differential equations of arbitrary order with nonlocal quadratic nonlinearities using our approach. We provide numerical simulations that demonstrate the generation of solutions to Fisher--Kolmogorov--Petrovskii--Piskunov equations with nonlocal nonlinearities. We also indicate how the method might extend to more general classes of nonlinear partial differential systems.Comment: 26 pages, 2 figure

Drivers and outcomes of work alienation: reviving a concept

This article sheds new light on an understudied construct in mainstream management theory, namely, work alienation. This is an important area of study because previous research indicates that work alienation is associated with important individual and organizational outcomes. We tested four antecedents of work alienation: decision-making autonomy, task variety, task identity, and social support. Moreover, we examined two outcomes of alienation: deviance and performance, the former measured 1 year after the independent variables were measured, and the latter as rated by supervisors. We present evidence from a sample of 283 employees employed at a construction and consultancy organization in the United Kingdom. The results supported the majority of our hypotheses, indicating that alienation is a worthy concept of exploration in the management sciences

Conformally parametrized surfaces associated with CP^(N-1) sigma models

Two-dimensional conformally parametrized surfaces immersed in the su(N) algebra are investigated. The focus is on surfaces parametrized by solutions of the equations for the CP^(N-1) sigma model. The Lie-point symmetries of the CP^(N-1) model are computed for arbitrary N. The Weierstrass formula for immersion is determined and an explicit formula for a moving frame on a surface is constructed. This allows us to determine the structural equations and geometrical properties of surfaces in R^(N^2-1). The fundamental forms, Gaussian and mean curvatures, Willmore functional and topological charge of surfaces are given explicitly in terms of any holomorphic solution of the CP^2 model. The approach is illustrated through several examples, including surfaces immersed in low-dimensional su(N) algebras.Comment: 32 page

A prospective, multicenter, phase I matched-comparison group trial of safety, pharmacokinetics, and preliminary efficacy of riluzole in patients with traumatic spinal cord injury.

A prospective, multicenter phase I trial was undertaken by the North American Clinical Trials Network (NACTN) to investigate the pharmacokinetics and safety of, as well as obtain pilot data on, the effects of riluzole on neurological outcome in acute spinal cord injury (SCI). Thirty-six patients, with ASIA impairment grades A-C (28 cervical and 8 thoracic) were enrolled at 6 NACTN sites between April 2010 and June 2011. Patients received 50 mg of riluzole PO/NG twice-daily, within 12 h of SCI, for 14 days. Peak and trough plasma concentrations were quantified on days 3 and 14. Peak plasma concentration (Cmax) and systemic exposure to riluzole varied significantly between patients. On the same dose basis, Cmax did not reach levels comparable to those in patients with amyotrophic lateral sclerosis. Riluzole plasma levels were significantly higher on day 3 than on day 14, resulting from a lower clearance and a smaller volume of distribution on day 3. Rates of medical complications, adverse events, and progression of neurological status were evaluated by comparison with matched patients in the NACTN SCI Registry. Medical complications in riluzole-treated patients occurred with incidences similar to those in patients in the comparison group. Mild-to-moderate increase in liver enzyme and bilirubin levels were found in 14-70% of patients for different enzymes. Three patients had borderline severe elevations of enzymes. No patient had elevated bilirubin on day 14 of administration of riluzole. There were no serious adverse events related to riluzole and no deaths. The mean motor score of 24 cervical injury riluzole-treated patients gained 31.2 points from admission to 90 days, compared to 15.7 points for 26 registry patients, a 15.5-point difference (p=0.021). Patients with cervical injuries treated with riluzole had more-robust conversions of impairment grades to higher grades than the comparison group