We show that the maximal number of singular moves required to pass between any two regularly homotopic plane or spherical curves with at most n crossings grows quadratically with respect to n. Furthermore, for any two regularly homotopic curves with at most n crossings, there exists such a sequence of singular moves, satisfying the quadratic bound, for which all curves along the way have at mos...

Conclusion Recall that our goal was a system that is as secure as time–sharing. We feel we have met this goal. The way you are authenticated in a time–sharing system is by knowing your password. In our system, the same is true. In time–sharing the person you trust is your system administrater, who does not do anything dirty such as change your passwd entry so they can impersonate you. In our sy...

Jech and Shelah [2] studied full reflection below אω, and produced a model in which the extent of full reflection is maximal in a certain sense. We produce a model in which full reflection is maximised in a different direction.

We determine the maximal set of moves for 2-pile take-away games with prescribed P -positions (bαnc, bβnc) for n ∈ Z≥1 where α ∈ (1, 2) is irrational, 1/α+1/β = 1. This was done in [3] for the special case α = golden ratio. We generalize the infinite Fibonacci word to an infinite wordW with alphabet Σ = {a, b}, in which α replaces the golden ratio, and we analyze the set {s ∈ Z≥0 : W(s) = b, W(...

Let H be the Heisenberg group and let μt be the normalized surface measure for the sphere of radius t in R. Consider the maximal function defined by Mf = supt>0 |f ∗μt|. We prove for n ≥ 2 that M defines an operator bounded on L(H) provided that p > 2n/(2n − 1). This improves an earlier result by Nevo and Thangavelu, and the range for L boundedness is optimal. We also extend the result to a mor...