Performance limitations of bilateral force reflection imposed by operator dynamic characteristics

A linearized, single-axis model is presented for bilateral force reflection which facilitates investigation into the effects of manipulator, operator, and task dynamics, as well as time delay and gain scaling. Structural similarities are noted between this model and impedance control. Stability results based upon this model impose requirements upon operator dynamic characteristics as functions of system time delay and environmental stiffness. An experimental characterization reveals the limited capabilities of the human operator to meet these requirements. A procedure is presented for determining the force reflection gain scaling required to provide stability and acceptable operator workload. This procedure is applied to a system with dynamics typical of a space manipulator, and the required gain scaling is presented as a function of environmental stiffness

Involutory quandles of (2,2,r)-Montesinos links

In this paper we show that Montesinos links of the form L(1/2, 1/2, p/q;e), which we call (2,2,r)-Montesinos links, have finite involutory quandles. This generalizes an observation of Winker regarding the (2, 2, q)-pretzel links. We also describe some properties of these quandles.Comment: 19 pages, 8 figure

Commensurability classes of twist knots

In this paper we prove that if $M_K$ is the complement of a non-fibered twist knot $K$ in $\mathbb S^3$, then $M_K$ is not commensurable to a fibered knot complement in a $\mathbb Z/ 2 \mathbb Z$-homology sphere. To prove this result we derive a recursive description of the character variety of twist knots and then prove that a commensurability criterion developed by D. Calegari and N. Dunfield is satisfied for these varieties. In addition, we partially extend our results to a second infinite family of 2-bridge knots.Comment: 10 pages, 3 figure

Twisted Alexander polynomials of 2-bridge knots

We investigate the twisted Alexander polynomial of a 2-bridge knot associated to a Fox coloring. For several families of 2-bridge knots, including but not limited to, torus knots and genus-one knots, we derive formulae for these twisted Alexander polynomials. We use these formulae to confirm a conjecture of Hirasawa and Murasugi for these knots.Comment: 29 pages, 2 figure

Epimorphisms and Boundary Slopes of 2-Bridge Knots

In this article we study a partial ordering on knots in the 3-sphere where K_1 is greater than or equal to K_2 if there is an epimorphism from the knot group of K_1 onto the knot group of K_2 which preserves peripheral structure. If K_1 is a 2-bridge knot and K_1 > K_2, then it is known that K_2 must also be 2-bridge. Furthermore, Ohtsuki, Riley, and Sakuma give a construction which, for a given 2-bridge knot K_{p/q}, produces infinitely 2-bridge knots K_{p'/q'} with K_{p'/q'}>K_{p/q}. After characterizing all 2-bridge knots with 4 or less distinct boundary slopes, we use this to prove that in any such pair, K_{p'/q'} is either a torus knot or has 5 or more distinct boundary slopes. We also prove that 2-bridge knots with exactly 3 distinct boundary slopes are minimal with respect to the partial ordering. This result provides some evidence for the conjecture that all pairs of 2-bridge knots with K_{p'/q'}>K_{p/q} arise from the Ohtsuki-Riley-Sakuma construction.Comment: 24 pages, 4 figure

Boundary slopes of 2-bridge links determine the crossing number

A diagonal surface in a link exterior M is a properly embedded, incompressible, boundary incompressible surface which furthermore has the same number of boundary components and same slope on each component of the boundary of M. We derive a formula for the boundary slope of a diagonal surface in the exterior of a 2-bridge link which is analogous to the formula for the boundary slope of a 2-bridge knot found by Hatcher and Thurston. Using this formula we show that the diameter of a 2-bridge link, that is, the difference between the smallest and largest finite slopes of diagonal surfaces, is equal to the crossing number.Comment: 16 pages, 6 figure

The Contribution of Sectoral Productivity Differentials to Inflation in Greee

This paper estimates the magnitude of the Balassa-Samuelson effect for Greece. We calculate the effect directly, using sectoral national accounts data, which permits estimation of total factor productivity (TFP) growth in the tradeables and nontradeables sectors. Our results suggest that it is difficult to produce one estimate of the BS effect. Any particular estimate is contingent on the definition of the tradeables sector and the assumptions made about labour shares. Moreover, there is also evidence that the effect has been declining through time as Greek standards of living have caught up on those in the rest of the world and as the non-tradeables sector within Greece catches up with the tradeables.Balassa-Samuelson effect, inflation, productivity