Twisted Alexander polynomials detect the unknot

The group of a nontrivial knot admits a finite permutation representation such that the corresponding twisted Alexander polynomial is not a unit.Comment: This is the version published by Algebraic & Geometric Topology on 14 November 200

Parametric Analysis Using the Finite Element Method to Investigate Prosthetic Interface Stresses for Persons with Trans-tibial Amputation

A finite element (FE) model of the below-knee residual limb and prosthetic socket was created to investigate the effects of parameter variations on the interface stress distribution during static stance. This model was based upon geometric approximations of anthropometric residual limb geometry. The model was not specific to an individual with amputation, but could be scaled to approximate the limb of a particular subject. Parametric analyses were conducted to investigate the effects of prosthetic socket design and residual limb geometry on the residual limb/prosthetic socket interface stresses. Behavioral trends were illustrated via sensitivity analysis. The results of the parametric analyses indicate that the residual limb/prosthetic socket interface stresses are affected by variations in both prosthetic design and residual limb geometry. Specifically, the analyses indicate : 1) the residual limb/prosthetic liner interface pressures are relatively insensitive to the socket stiffness ; 2) the stiffness of the prosthetic liner influences the interface stress distribution for both the unrectified and patellar-tendon-bearing (PTB) rectified models-- the external load state appears to influence the interface pressure distribution, while the prosthetic socket rectification appears to influence the interface shear stress distribution ; 3) the interface pressures are - very sensitive to the prosthetic rectification ; 4) the shape and relative bulk of soft tissue may significantly influence the interface pressure distribution ; 5) the interface pressure distribution is also influenced by the residual limb length; and 6) the stiffness/compliance of the residual limb soft tissues may significantly alter the interface pressure distribution

Twisted Alexander Invariants of Twisted Links

Let L be an oriented (d+1)-component link in the 3-sphere, and let L(q) be the d-component link in a homology 3-sphere that results from performing 1/q-surgery on the last component. Results about the Alexander polynomial and twisted Alexander polynomials of L(q) corresponding to finite-image representations are obtained. The behavior of the invariants as q increases without bound is described.Comment: 21 pages, 6 figure

High-temperature gas/liquid stress relaxometers

Two relaxometers allow testing of elastomers in various fluids. First relaxometer uses fork-like loading spacer interposed between loading lever and support ring, so that sample is stretched predetermined amount. In second relaxometer, degree of initial elongation is set by means of adjustable collar, which, when locked in place on piston rod, enables sample to be stretched predetermined length

Twisted Alexander Polynomials and Representation Shifts

For any knot, the following are equivalent. (1) The infinite cyclic cover has uncountably many finite covers; (2) there exists a finite-image representation of the knot group for which the twisted Alexander polynomial vanishes; (3) the knot group admits a finite-image representation such that the image of the fundamental group of an incompressible Seifert surface is a proper subgroup of the image of the commutator subgroup of the knot group.Comment: 7 pages, no figure