Mutant knots with symmetry

Mutant knots, in the sense of Conway, are known to share the same Homfly polynomial. Their 2-string satellites also share the same Homfly polynomial, but in general their m-string satellites can have different Homfly polynomials for m>2. We show that, under conditions of extra symmetry on the constituent 2-tangles, the directed m-string satellites of mutants share the same Homfly polynomial for m<6 in general, and for all choices of m when the satellite is based on a cable knot pattern. We give examples of mutants with extra symmetry whose Homfly polynomials of some 6-string satellites are different, by comparing their quantum sl(3) invariants.Comment: 15 page

A basis for the Birman-Wenzl algebra

An explicit isomorphism is constructed between the Birman-Wenzl algebra, defined algebraically by J. Birman and H. Wenzl using generators and relations, and the Kauffman algebra, constructed geometrically by H. R. Morton and P. Traczyk in terms of tangles. The isomorphism is obtained by constructing an explicit basis in the Birman-Wenzl algebra, analogous to a basis previously constructed for the Kauffman algebra using 'Brauer connectors'. The geometric isotopy arguments for the Kauffman algebra are systematically replaced by algebraic versions using the Birman-Wenzl relations.Comment: This is a lightly edited version of an article written in 1989 but never fully completed. It was originally intended as a joint paper with A. J.Wassermann. 33 pages, 20 figure

Ticket to Work and Self-Sufficiency Program: Overview and Current Issues

[Excerpt] Title I of the Ticket to Work and Work Incentives Improvement Act of 1999 (P.L. 106-170) established the Ticket to Work and Self-Sufficiency program (hereafter referred to as the Ticket to Work or Ticket program), which is administered by the Social Security Administration (SSA). The purpose of this program is to enhance work incentives for Social Security Disability Insurance (SSDI) and Supplemental Security Income (SSI) beneficiaries. The legislation created a “ticket” system to expand choices in the numbers and types of providers that SSDI and SSI beneficiaries may choose to assist them in receiving employment services. The legislation also expanded Medicare and Medicaid coverage for individuals with a disability who are working or could work. Most notably, the Ticket to Work program created a market for public and private providers of support services known as employment networks (ENs) to which Social Security disability beneficiaries can voluntarily assign their tickets in exchange for a range of employment support services. The goal of the Ticket program is to reduce dependence on disability benefits and help Social Security disability beneficiaries enter or reenter the workforce. ENs would then be eligible to receive payments from SSA based on ticket holders achieving employment “milestones” or outcomes. This report provides an overview of how the Ticket to Work program operates and addresses several issues related to the Ticket program. First, it provides a brief background on the SSDI and SSI programs and a legislative history on how the Ticket program evolved. Second, this report provides an in-depth explanation on the various components and regulations of the Ticket to Work program in its current form and prior to major regulatory changes in July 2008. Third, it examines other work incentive programs created by Ticket to Work legislation and concludes with a discussion on the issues surrounding implementation of the Ticket program

Concurrent Receipt of Social Security Disability Insurance (SSDI) and Unemployment Insurance (UI): Background and Legislative Proposals in the 113th Congress

[Excerpt] Although Social Security Disability Insurance (SSDI) and Unemployment Insurance (UI) both provide income support to eligible individuals, the two programs serve largely separate populations. SSDI provides monthly cash benefits to statutorily disabled individuals who worked in jobs covered by Social Security and to their dependents. UI, on the other hand, provides temporary cash assistance to involuntarily unemployed workers who meet the requirements of state law. Under certain circumstances, however, some individuals may be concurrently (simultaneously) eligible for benefits under both programs. Numerous proposals have been introduced in the 113th Congress to prevent or offset concurrent receipt of SSDI and UI benefits. Proponents of these bills contend that concurrent receipt of SSDI and UI benefits is “double dipping” or duplicative, inasmuch as each payment serves the same function of replacing lost earnings. Opponents, however, argue that dual receipt of UI and SSDI benefits is consistent and appropriate under law, because the SSDI program actively encourages beneficiaries to return to work through various work incentives. This report provides background on SSDI and UI and explains how individuals may be eligible for both programs at the same time. It also summarizes the competing arguments for and against concurrent eligibility and examines many of the legislative proposals formally introduced in the 113th Congress to eliminate or reduce concurrent receipt of SSDI and UI benefits

The Burau matrix and Fiedler's invariant for a closed braid

It is shown how Fiedler's `small state-sum' invariant for a braid can be calculated from the 2-variable Alexander polynomial of the link which consists of the closed braid together with the braid axis.Comment: 7 pages LaTeX2e. To appear in Topology and its Application

Concurrent Receipt of Social Security Disability Insurance (SSDI) and Unemployment Insurance (UI): Background and Legislative Proposals

[Excerpt] Although Social Security Disability Insurance (SSDI) and Unemployment Insurance (UI) both provide income support to eligible individuals, the two programs serve largely separate populations. SSDI provides long-term benefits to statutorily disabled individuals who worked in jobs covered by Social Security and to their eligible dependents. In contrast, UI provides temporary benefits to involuntarily unemployed workers who meet the requirements of state law. Under certain circumstances, however, individuals are eligible for both programs. Several proposals have been introduced in the 114th Congress to prevent or reduce concurrent receipt of SSDI and UI benefits. Proponents of these bills contend that concurrent receipt is “double dipping” or duplicative, inasmuch as each payment serves the same function of replacing lost earnings. Opponents argue that concurrent receipt of SSDI and UI benefits is consistent and appropriate under law, because the SSDI program actively encourages beneficiaries to return to work through various work incentives. This report provides background on SSDI and UI and explains how individuals may be eligible for both programs concurrently. It also summarizes the competing arguments for and against concurrent eligibility and examines the legislative proposals introduced in the 114th Congress to deny or offset the SSDI benefits of individuals in receipt of UI. The report ends with a discussion of potential issues in implementing such proposals. of potential issues in implementing such proposals

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

The effect of elliptic shape on the period ratio P-1/P-2 of emerging coronal loops

Aims. We determine the effect of an elliptical shape on the period ratio for the standing transversal oscillations of a longitudinally stratified coronal loop throughout its emergence from the low solar atmosphere into the ubiquitously magnetised corona. Methods. Under the assumption that elliptical curvature has a negligible effect on eigenfrequencies, the equation that describes the projection of a density profile onto a magnetic flux tube with elliptical shape is obtained in a gravitationally stratified atmosphere. The effect of the elliptical shape on the period ratio of the fundamental mode to the first harmonic (P-1/P-2) at various stages of emergence is determined, assuming that the oscillation periods are much shorter than the characteristic time scale of loop emergence. Results. We find that there are two separate cases of elliptical shape that occur, the minor ellipse and the major ellipse. It is then shown how the period ratio P-1/P-2 is dependent upon the ellipticity (epsilon), the parameter characterising the stage of emergence (lambda) and the density scale height (H). Ellipticity is found to make an important contribution to P-1/P-2 for the minor ellipse when compared to its counterpart of standing oscillations of stratified loops with semi-circle or circle-arc shape. The major ellipse was found to have a lesser effect on the period ratio of standing oscillations. We also find the value of P-1/P-2 is dependent upon the stage of emergence of the loop, where the greatest contribution from emergence to the ratio of P-1/P-2 is when the loop is almost fully emerged. The important implication for magneto-seismological interpretations of the observations of oscillating coronal loops is that measurements of ellipticity and stage of emergence should supplement observations of oscillation periods and should be considered when applying observed frequencies of the fundamental mode and first harmonic to determine the diagnostic properties of these oscillating loops, e. g. the density scale height or strength of magnetic field. Neglecting the determination of ellipticity and stage of emergence may result in a 35% error in estimating density scale height

Magnetohydrodynamic waves in a compressible magnetic flux tube with elliptical cross-section

Aims. The propagation of magnetohydrodynamic (MHD) waves in a finite, compressible magnetic flux tube with an elliptical cross-section embedded in a magnetic environment is investigated. Methods. We present the derivation of the general dispersion relation of linear magneto-acoustic wave propagation for a compressible magnetic flux tube with elliptical cross-section in a plasma with finite beta. The wave modes of propagation for the n = 0 (symmetric) sausage and n = 1 (anti-symmetric) kink oscillations are then examined within the limit of the thin flux tube approximation. Results. It is shown that a compressible magnetic tube with elliptical cross-section supports slow and fast magneto-acoustic waves. In the thin tube approximation, the slow sausage mode and the slow and fast kink modes are found in analogue to a circular cross-section. However, the kink modes propagate with different phase speeds depending on whether the axial displacement takes place along the major or minor axis of the ellipse. This feature is present in both the slow and the fast bands, providing two infinite sets of slow kink modes and two infinite sets of fast kink modes, i.e. each corresponding cylindrical mode splits into two sets of modes due to the ellipticity. The difference between the phase speeds along the different axis is dependent on the ratio of the lengths of the two axes. Analytical expressions for the phase speeds are found. We show that the sausage modes do not split due to the introduced ellipticity and only the phase speed is modified when compared to the appropriate cylindrical counterpart. The percentage difference between the periods of the circular and elliptical cross-sections is also calculated, which reaches up to 21% for oscillations along the major axis. The level of difference in period could be very important in magneto-seismological applications, when observed periods are inverted into diagnostic properties (e. g. magnetic field strength, gravitational scale height, tube expansion parameter). Also shown is the perturbation of focal points of the elliptical cross-section for different modes. It is found that the focal points are unperturbed for the sausage mode, but are perturbed for all higher modes