We use the Birman–Ko–Lee presentation of braid group to show that all closures strongly quasipositive braids whose normal form contains a positive power dual Garside element [Formula: see text] are fibered. classify links which admit such representative in geometric terms as boundaries plumbings Hopf bands disk. Rudolph constructed fibered words on certain generating sets and we prove Rudolph’s...

Let M be a map on a surface S. The edge-width of M is the length of a shortest non-contractible cycle of M . The face-width (or, representativity) of M is the smallest number of intersections a noncontractible curve in S has with M . (The edge-width and face-width of a planar map may be de ned to be in nity.) A map is an LEW-embedding if its maximum face valency is less than its edge-width. For...

It was proven by Emma Lehmer that for almost all odd primes p, F2p is a Fibonacci pseudoprime. In this paper, we generalize this result to Lucas sequences {Uk}. In particular, we find Lucas sequences {Uk} for which either U2p is a Lucas pseudoprime for almost all odd primes p or Up is a Lucas pseudoprime for almost all odd primes p.

It is well known that Huxley’s density estimates [5] for the zeros of the Riemann zeta-function yield J(x, h) = o(xh2(log x)−2), but only for h ≥ x1/6(log x) , for some C > 0. The weaker result with h ≥ x1/6+ε is proved in Saffari and Vaughan [8], Lemma 5, and in [13], where an identity of Heath-Brown (Lemma 1 of [3]) is used. This paper is inspired by Heath-Brown’s extension [4] of Huxley’s Th...

We investigated the variation of drilled regions of expert and trainee surgeons performing virtual temporal bone surgery to identify their compliance with standard drilling procedures. To this end, we recruited seven expert and six trainee ENT surgeons, who were asked to perform the surgical preparations for cochlear implantation on a virtual temporal bone. The temporal bone was divided into si...

The phenomenon of expertise produces two problems for liberal democratic theory: the first is whether it creates inequalities that undermine citizen rule or make it a sham; the second is whether the state can preserve its neutrality in liberal “government by discussion” while subsidizing, depending on, and giving special status to the opinions of experts and scientists. A standard Foucauldian c...