The White Line of Hilton

On a conjecture of Hilton

We show that if AI, A 2 ," " Ak are collections of distinct subsets from an n-element set such that these collections are incomparable and uncomplemented, then 2::7=1 IAI :::; 2 1 under certain conditions. Upper bounds are also given for 2::7=1 lAd with or without the "uncomplemented" condition.

Blast Xiii Meeting Hilton

John Hilton, 1805–1878

This Classic article is a reprint of the original work by John Hilton, On Rest and Pain: Lecture XIV. An accompanying biographical sketch on John Hilton, MD, is available at DOI 10.1007/s11999-009-0927-2 . The Classic Article is reprinted with courtesy from Hilton J. On The Influence of Mechanical and Physiological Rest in the Treatment of Accidents and Surgical Diseases, and the Diagnostic Val...

The Geometry of the Hilton Splitting

One of the important theorems in homotopy theory is the Hilton Splitting Theorem which states: there is an isomorphismH = ⊕γ∈ΓHγ from them-th homotopy group of the wedge of a number of spheres to the direct sum of the m-th homotopy groups of some spheres, see [Hi]. In this paper we will construct geometrically all Hilton homomorphisms Hγ and prove a family of sharper symmetry relations between ...

2-Paper Hilton

This paper presents in-plane electrostatic comb-drive actuators with stroke as large as 245 μm that is achieved by employing a novel Clamped Paired Double Parallelogram (C-DPDP) flexure mechanism. For a given flexure beam length, comb gap, and actuation voltage, this is currently the largest comb-drive actuator stroke reported in the literature. The C-DP-DP flexure mechanism design offers high ...