Random Walks on Thompson\u27s Group F

In this paper we consider the statistical properties of random walks on Thompson’s group F . We use two-way forest diagrams to represent elements of F . First we describe the random walk of F by relating the steps of the walk to the possible interactions between two-way forest diagrams and the elements of {x0,x1}, the finite generating set of F, and their inverses. We then determine the long-term probabilistic and recurrence properties of the walk

Raman excitation spectroscopy of carbon nanotubes: effects of pressure medium and pressure

Raman excitation and emission spectra for the radial breathing mode (RBM) are reported, together with a preliminary analysis. From the position of the peaks on the two-dimensional plot of excitation resonance energy against Raman shift, the chiral indices (m, n) for each peak are identified. Peaks shift from their positions in air when different pressure media are added - water, hexane, sulphuric acid - and when the nanotubes are unbundled in water with surfactant and sonication. The shift is about 2 - 3 cm-1 in RBM frequency, but unexpectedly large in resonance energy, being spread over up to 100meV for a given peak. This contrasts with the effect of pressure. The shift of the peaks of semiconducting nanotubes in water under pressure is orthogonal to the shift from air to water. This permits the separation of the effects of the pressure medium and the pressure, and will enable the true pressure coefficients of the RBM and the other Raman peaks for each (m, n) to be established unambiguously.Comment: 6 pages, 3 Figures, Proceedings of EHPRG 2011 (Paris

Pressure coefficients of Raman modes of carbon nanotubes resolved by chirality: Environmental effect on graphene sheet

Studies of the mechanical properties of single-walled carbon nanotubes are hindered by the availability only of ensembles of tubes with a range of diameters. Tunable Raman excitation spectroscopy picks out identifiable tubes. Under high pressure, the radial breathing mode shows a strong environmental effect shown here to be largely independent of the nature of the environment . For the G-mode, the pressure coefficient varies with diameter consistent with the thick-wall tube model. However, results show an unexpectedly strong environmental effect on the pressure coefficients. Reappraisal of data for graphene and graphite gives the G-mode Grueuneisen parameter gamma = 1.34 and the shear deformation parameter beta = 1.34.Comment: Submitted to Physical Review

Promoting healthy eating and physical activity among school children: findings from Health-E-PALS, the first pilot intervention from Lebanon

Background: In Lebanon, childhood obesity doubled during the past decade. Preventive measures should start early in life and Schools are considered an important environment to promote energy balance health behaviours. School-based programmes promoting healthy lifestyles are lacking. The purpose of this study was to evaluate the feasibility and effectiveness of a multicomponent school-based intervention to promote healthy eating and physical activity (and prevent obesity) with school children aged 9–11 years in Lebanon. Methods: The intervention was developed based on the constructs of the Social Cognitive Theory and adapted to the culture of Lebanese and Arab populations. It consisted of three components: class curriculum, family involvement and food service. Eight schools were purposively selected from two communities of different socioeconomic status (SES) in Beirut and, within each school type, were matched on SES, religious sect profile, and then randomly assigned to either the intervention or control group. Anthropometric measurements and questionnaires on determinants of behavioural change, eating and physical activity habits were completed by the students in both groups at baseline and post intervention. Focus group interviews were conducted in intervention schools at the end of the study. Challenges encountered during the programme implementation were also identified, since Lebanon is considered a country with political unrest and no similar research projects were conducted in the area. Results: Students in the intervention group reported purchasing and consuming less chips and sweetened drinks post-intervention compared with controls (86% & 88% less respectively p < 0.001). Knowledge and self-efficacy scores increased for the intervention (+2.8 & +1.7 points respectively p < 0.001) but not for the control group. There was no difference in physical activity and screen time habits and no changes in BMI between groups at post intervention. Interview data from focus groups showed that the programme was generally well accepted. Limitations for better outcomes include the length of the programme and the school environment. Conclusion: “Health-E-PALS” intervention is a promising innovative, theory-based, culturally sensitive intervention to promote healthy eating habits and physical activity in Lebanese school children with a potential to be scaled up, replicated and sustained

On the Initial Singularity Problem in Two Dimensional Quantum Cosmology

The problem of how to put interactions in two-dimensional quantum gravity in the strong coupling regime is studied. It shows that the most general interaction consistent with this symmetry is a Liouville term that contain two parameters $(\alpha, \beta)$ satisfying the algebraic relation $2\beta - \alpha =2$ in order to assure the closure of the diffeomorphism algebra. The model is classically soluble and it contains as general solution the temporal singularity. The theory is quantized and we show that the propagation amplitude fall tozero in $\tau =0$. This result shows that the classical singularities are smoothed by quantum effects and the bing-bang concept could be considered as a classical extrapolation instead of a physical concept.Comment: 9pp, Revtex 3.0. New references added. To appear in Phys. Rev.

Implications of invariance of the Hamiltonian under canonical transformations in phase space

We observe that, within the effective generating function formalism for the implementation of canonical transformations within wave mechanics, non-trivial canonical transformations which leave invariant the form of the Hamilton function of the classical analogue of a quantum system manifest themselves in an integral equation for its stationary state eigenfunctions. We restrict ourselves to that subclass of these dynamical symmetries for which the corresponding effective generating functions are necessaarily free of quantum corrections. We demonstrate that infinite families of such transformations exist for a variety of familiar conservative systems of one degree of freedom. We show how the geometry of the canonical transformations and the symmetry of the effective generating function can be exploited to pin down the precise form of the integral equations for stationary state eigenfunctions. We recover several integral equations found in the literature on standard special functions of mathematical physics. We end with a brief discussion (relevant to string theory) of the generalization to scalar field theories in 1+1 dimensions.Comment: REVTeX v3.1, 13 page

Quantum equivalence of sigma models related by non Abelian Duality Transformations

Coupling constant renormalization is investigated in 2 dimensional sigma models related by non Abelian duality transformations. In this respect it is shown that in the one loop order of perturbation theory the duals of a one parameter family of models, interpolating between the SU(2) principal model and the O(3) sigma model, exhibit the same behaviour as the original models. For the O(3) model also the two loop equivalence is investigated, and is found to be broken just like in the already known example of the principal model.Comment: As a result of the collaboration of new authors the previously overlooked gauge contribution is inserted into eq.(43) changing not so much the formulae as part of the conclusion: for the models considered non Abelian duality is OK in one loo

Hamiltonian quantization of General Relativity with the change of signature

We show in this article how the usual hamiltonian formalism of General Relativity should be modified in order to allow the inclusion of the Euclidean classical solutions of Einstein's equations. We study the effect that the dynamical change of signature has on the superspace and we prove that it induces a passage of the signature of the supermetric from ($-+++++$) to ($+-----$). Next, all these features are more particularly studied on the example of minisuperspaces. Finally, we consider the problem of quantization of the Euclidean solutions. The consequences of different choices of boundary conditions are examined.Comment: 32 pages, GCR-93/11/01, To appear in Phys. Rev.

Prescription opioid use disorder and heroin use among 12-34 year-olds in the United States from 2002 to 2014

Trend analyses of prescription opioids in the U.S. indicate use, especially use of prescription opioids stronger than morphine, has more than doubled among adults since the early 1990's (Frenk, Porter, & Paulozzi, 2015). Prescription opioids, like Oxycontin®, are effective pharmacological treatments for acute and chronic pain (Fitzcharles and Shir, 2009 ; Gallagher and Rosenthal, 2008). When used as indicated, these medications can be an important component of pain management. However, their high abuse potential presents concerns regarding their nonmedical use, which can be defined as ‘use of a prescription opioid that was not prescribed, or taken for the experience or feeling it caused’ (SAMHSA, 2014). In the United States, nonmedical use of prescription opioids (NMPO) is increasingly recognized as a serious public health problem among adults (Blanco et al., 2007; Han et al., 2015 ; Huang et al., 2006). Nonmedical prescription drug use, specifically nonmedical use of prescription opioids, is also a growing problem in other countries such as Canada (Fischer et al., 2014 ; Fischer et al., 2013) and Australia (Degenhardt et al., 2006 ; Rintoul et al., 2011)