Mutual braiding and the band presentation of braid groups

This paper is concerned with detecting when a closed braid and its axis are 'mutually braided' in the sense of Rudolph. It deals with closed braids which are fibred links, the simplest case being closed braids which present the unknot. The geometric condition for mutual braiding refers to the existence of a close control on the way in which the whole family of fibre surfaces meet the family of discs spanning the braid axis. We show how such a braid can be presented naturally as a word in the `band generators' of the braid group discussed by Birman, Ko and Lee in their recent account of the band presentation of the braid groups. In this context we are able to convert the conditions for mutual braiding into the existence of a suitable sequence of band relations and other moves on the braid word, and derive a combinatorial method for deciding whether a braid is mutually braided.Comment: 13 pages, 10 figures. To appear in the proceedings of 'Knots in Hellas 98

Geometrical relations and plethysms in the Homfly skein of the annulus

The oriented framed Homfly skein C of the annulus provides the natural parameter space for the Homfly satellite invariants of a knot. It contains a submodule C+ isomorphic to the algebra of the symmetric functions. We collect and expand formulae relating elements expressed in terms of symmetric functions to Turaev's geometrical basis of C+. We reformulate the formulae of Rosso and Jones for quantum sl(N) invariants of cables in terms of plethysms of symmetric functions, and use the connection between quantum sl(N) invariants and C+ to give a formula for the satellite of a cable as an element of C+. We then analyse the case where a cable is decorated by the pattern which corresponds to a power sum in the symmetric function interpretation of C+ to get direct relations between the Homfly invariants of some diagrams decorated by power sums.Comment: 28 pages, 15 figure

Non-axisymmetric oscillations of stratified coronal magnetic loops with elliptical cross-sections

We study non-axisymmetric oscillations of a straight magnetic tube with an elliptic cross-section and density varying along the tube. The governing equations for kink and fluting modes in the thin tube approximation are derived. We found that there are two kink modes, polarised along the large and small axes of the elliptic cross-section. We have shown that the ratio of frequencies of the first overtone and fundamental harmonic is the same for both kink modes and independent of the ratio of the ellipse axes. On the basis of this result we concluded that the estimates of the atmospheric scale height obtained using simultaneous observations of the fundamental harmonic and first overtone of the coronal loop kink oscillations are independent of the ellipticity of the loop cross-section

Early Origins of Adult Cancer Risk Among Men and Women: Influence of Childhood Misfortune?

Objective—To examine the effect of five childhood misfortune domains—parental behavior, socioeconomic status, infectious diseases, chronic diseases, and impairments—on all-site and selected site-specific cancer prevalence and all-site cancer incidence. Method—Panel data from the Health and Retirement Study (2004–2012) were used to investigate cancer risk among adults above the age of 50. Results—Risky parental behavior and impairment in childhood were associated with higher odds of all-site cancer prevalence, and childhood chronic disease was associated with prostate cancer, even after adjusting for adult health and socioeconomic factors. Moreover, having one infectious disease in childhood lowered the odds of colon cancer. Cancer trends varied by race and ethnicity, most notably, higher prostate cancer prevalence among Black men and lower all-site cancer among Hispanic adults. Discussion—These findings underscore the importance of examining multiple domains of misfortune because the type and amount of misfortune influence cancer risk in different ways

Torsional Alfvén waves: magneto-seismology in static and dynamic coronal plasmas

Aims: We study the properties of torsional Alfvén waves in coronal loops so that they may be exploited for coronal seismological applications. Methods: The governing equation is obtained for standing torsional Alfvén waves of a dynamic, gravitationally stratified plasma. The footpoints are assumed to obey line-tying conditions necessary for standing oscillations. Solutions are found in a number of different but typical scenarios to demonstrate the possibilities for both temporal and spatial magneto-seismology exploitation of waveguides with the standing torsional Alfvén oscillations. Results: It is found that the frequency of the standing Alfvén oscillation increases as the stratification of the plasma increases. The ratio of the periods of the fundamental modeand the first overtone is also found to change as the stratification of the plasma increases. Further, the eigenfunctions of the higher overtones of the standing oscillations are found to experience a shift of their anti-nodes. The influence of a dynamic plasma on the amplitudes of the mode is also investigated. The amplitude of the torsional Alfvén mode is found to increase as the plasma within the coronal loop experiences cooling

An investigation of social activities of neurologically healthy older adults and relevance of the Social Activities Checklist (SOCACT-2)

Purpose: This preliminary study aimed to describe the type, range, partner and frequency of social activity among neurologically healthy older people in order to evaluate the content validity of the SOCial ACTivities Checklist (SOCACT-2). Method: Ten neurologically healthy older people were recruited. Participants’ social activities were investigated through the completion of the SOCACT-2. Naturalistically occurring social activities were then recorded in a social activity diary over 28 consecutive days. Items recorded in the diaries were compared with SOCACT-2 items, and new items not included in the SOCACT-2 were noted. Frequency and location of participation was also recorded. Results: All SOCACT-2 items were recorded in the diaries, with the exception of two. Findings suggest that another two SOCACT-2 items could be rephrased to more accurately reflect naturalistically occurring social activities, and two new categories of social activities were identified. Conclusions: The results provide preliminary evidence for the relevance of the majority of SOCACT items. Revisions to four existing items included in the SOCACT-2, as well as the inclusion of two additional items may be indicated to capture the range of activities participated in by older people

An Approach to Onshore Facility Hazard Analysis

PresentationOnshore oil and gas operators face challenging cost efficiency targets while pressing for higher production volumes. Within this tension is a need to reduce planned facility foot prints while maintaining primary focus of personnel and environmental protection. This will be examined in this paper

Thin-film flow in helically wound rectangular channels with small torsion

Laminar gravity-driven thin-film flow down a helically-wound channel of rectangular cross-section with small torsion in which the fluid depth is small is considered. Neglecting the entrance and exit regions we obtain the steady-state solution that is independent of position along the axis of the channel, so that the flow, which comprises a primary flow in the direction of the axis of the channel and a secondary flow in the cross-sectional plane, depends only on position in the two-dimensional cross-section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity and pressure in terms of the free-surface shape, the latter satisfying a non-linear ordinary differential equation that has a simple exact solution in the special case of a channel of rectangular cross-section. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier–Stokes equations. The present work has particular relevance to spiral particle separators used in the mineral-processing industry. The validity of an assumption commonly used in modelling flow in spiral separators, namely that the flow in the outer region of the separator cross-section is described by a free vortex, is shown to depend on the problem parameters