Homfly Polynomials of Generalized Hopf Links

Following the recent work by T.-H. Chan in [HOMFLY polynomial of some generalized Hopf links, J. Knot Theory Ramif. 9 (2000) 865--883] on reverse string parallels of the Hopf link we give an alternative approach to finding the Homfly polynomials of these links, based on the Homfly skein of the annulus. We establish that two natural skein maps have distinct eigenvalues, answering a question raised by Chan, and use this result to calculate the Homfly polynomial of some more general reverse string satellites of the Hopf link.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-2.abs.htm

Conjugacy for positive permutation braids

Positive permutation braids on n strings, which are defined to be positive n-braids where each pair of strings crosses at most once, form the elementary but non-trivial building blocks in many studies of conjugacy in the braid groups. We consider conjugacy among these elementary braids which close to knots, and show that those which close to the trivial knot or to the trefoil are all conjugate. All such n-braids with the maximum possible crossing number are also shown to be conjugate. We note that conjugacy of these braids for n<6 depends only on the crossing number. In contrast, we exhibit two such braids on 6 strings with 9 crossings which are not conjugate but whose closures are each isotopic to the (2,5) torus knot

Décès liés au monoxyde de carbone : à propos de Trois cas

L'incidence et la mortalité cumulées mondiales de l'empoisonnement au CO sont actuellement estimées à 137 cas et 4,6 décès par million. En Algérie, ce tueur silencieux, a fait 175 victimes en 2022 selon les données de la protection civil L’objectif est de faire une revue de la littérature sur l’intoxication au CO sur le plan étiologique, clinique ainsi que l'aspect analytique, de rapporter les 3 cas de décès dû au CO qui ont fait l'objet d'une enquête par le service de médecine légale de CHU Mustapha dont le dosage a été réalisée par RAPIDpoint 500ede la marque siemen

The stepwise oxidation of indolino[2,1-b]oxazolidine derivatives

This work presents an original strategy to modulate the electrochemical properties of the indolino[2,1-b]oxazolidine core appropriately substituted in position 5 (para-substitution of the phenyl ring) by acceptor or donor groups (CHO, OMe, Me, F, H, Cl, Br). Supported by spectroelectrochemical experiments and confronted to electrochemical simulations, the stepwise oxidation of indolino[2,1-b]oxazolidine derivatives involves an electrochemical mechanism which depends on the para-substitution of the phenyl ring and leads to either the formation of a stable radical cation, the opening of the oxazolidine ring or an irreversible aryl C-C coupling

Two Dimensional Fractional Supersymmetry from the Quantum Poincare Group at Roots of Unity

A group theoretical understanding of the two dimensional fractional supersymmetry is given in terms of the quantum Poincare group at roots of unity. The fractional supersymmetry algebra and the quantum group dual to it are presented and the pseudo-unitary, irreducible representations of them are obtained. The matrix elements of these representations are explicitly constructed.Comment: 10 pages. Some misprints are corrected. To appear in J. Phys.

A multilayer shallow water system for polydisperse sedimentation

This work considers the flow of a fluid containing one disperse substance consisting of small particles that belong to different species differing in size and density. The flow is modelled by combining a multilayer shallow water approach with a polydisperse sedimentation process. This technique allows one to keep information on the vertical distribution of the solid particles in the mixture, and thereby to model the segregation of the particle species from each other, and from the fluid, taking place in the vertical direction of the gravity body force only. This polydisperse sedimentation process is described by the well-known Masliyah-Lockett-Bassoon (MLB) velocity functions. The resulting multilayer sedimentation-ow model can be written as a hyperbolic system with nonconservative products. The definitions of the nonconservative products are related to the hydrostatic pressure and to the mass and momentum hydrodynamic transfer terms between the layers. For the numerical discretization a strategy of two steps is proposed, where the first one is also divided into two parts. In the _rst step, instead of approximating the complete model, we approximate a reduced model with a smaller number of unknowns. Then, taking advantage of the fact that the concentrations are passive scalars in the system, we approximate the concentrations of the different species by an upwind scheme related to the numerical flux of the total concentration. In the second step, the effect of the transference terms defined in terms of the MLB model is introduced. These transfer terms are approximated by using a numerical ux function used to discretize the 1D vertical polydisperse model (see Bürger, García, Karlsen and Towers, J. Eng. Math. 60 (2008), 387{425). Finally, some numerical examples are presented. Numerical results suggest that the multilayer shallow water model could be adequate in situations where the settling takes place from a suspension that undergoes horizontal movement

Autism spectrum disorder in children and young people with non-epileptic seizures

Purpose: Non-epileptic seizures are paroxysmal events which to an observer resemble epileptic seizures. Proposed risk factors incorporate biopsychosocial aspects including factors in the affected individual. Unexpectedly high rates of autism spectrum disorder (ASD) occurred in the clinical population reported here. Although elevated levels of psychiatric co-morbidity are known to be present in patients with NES, ASD has only been previously described in a single case report. / Methods: This case series captures rates of ASD in 59 children and young people who were referred to a specialist paediatric mental health service at Great Ormond Street Hospital, London, UK for assessment and treatment of non-epileptic seizures between 2012 and 2016. / Results: 10/59 (16.9%) of the children and young people with non-epileptic seizures also had ASD, with 5/10 (50%) of these undiagnosed with ASD before referral. Children and young people with ASD were significantly more likely to have tics or attention-deficit hyperactivity disorder than those without ASD. / Conclusion: ASD may be a common co-morbidity in non-epileptic seizures. Careful clinical assessment with consideration of ASD traits is therefore important in the non-epileptic seizures population. It is beneficial to diagnose ASD early as its presence is likely to require a modified approach to assessment and treatment of non-epileptic seizures. Study of the development of non-epileptic seizures in ASD may suggest hypotheses for the pathogenesis of non-epileptic seizures in the wider population