We show that the mixing time for the fifteen puzzle in an n× n torus is on the order of n logn.

LiYF4:Eu nanophosphors with a single tetragonal phase are synthesized, and various strategies to enhance the Eu(3+) emission from the nanophosphors are investigated. The optimized Eu(3+) concentration is 35 mol%, and the red emission peaks due to the (5)D0 →(7)FJ (J = 1 and 2) transitions of Eu(3+) ions are further enhanced by energy transfer from a sensitizer pair of Ce(3+) and Tb(3+). The tri...

s, pp. 113 114.Leon WattsFeature

The transition to turbulence in pipe and plane Couette flow differs from the better understood situation of Taylor-Couette or Rayleigh-Bénard flow in that the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when turbulent flow is established, it can spontaneously return to laminar flow. These observations are compatible with the formation o...

By the late 1800s, both phenacetin and acetanilide were used as analgesics and antipyretics, but their acceptance was limited by significant side effects including methemoglobinemia. N-acetyl-p-aminophenol (APAP) is a major metabolite of phenacetin and acetanilide, and is responsible for, both analgesia and antipyresis. APAP was synthesized in 1878 and has a low risk of causing methemoglobinemi...

introduction: gluten is a protein found in grains.  research has shown that the gluten that is in grains of wheat, barley, rye, and oats (to a lesser degree) is toxic to many individuals.  while gluten is essential for the make-up of these 4 grains, our bodies do not need it. is it healthful?  the protein in today’s wheat is poorly digested and can be harmful.  an estimated 95% of prepared food...

Diverticula are thought to arise from defects in the muscularis layer of the intestines (Fig. 35.1) and are related to abnormalities in muscle tone and increased intraluminal pressure; saclike protrusions eventually form at points of weakness. If stool is caught in these sacs, it becomes inspissated and hardened and causes abrasions of the mucosa that lead to inflammation, although the same end...