We find an optimal Sobolev-type space on R all of whose functions admit a trace on subspaces of R of given dimension. A corresponding trace embedding theorem with sharp range is established.

Let s(n) be the threshold for which each directed path of order smaller than s ( n ) is extendible from one of its endpoints in some tournament T,. It is shown that s(n) is asymptotic to 3n/4, with an error term at most 3 for infinitely many n. There are six tournaments with s (n) = n.

The basis of potentiometry is the Nernst equation, which relates the concentration of electroactive species at the surface of an electrode (C) to the potential of that electrode (E); that is, for the reaction O + e = R where E is the formal redox potential of the electron transfer reaction. In a potentiometry experiment, the open-circuit potential (i.e., there is no measurable current through t...

background: this study aimed to compare intermittent intravenous (iv) pantoprazole and ranitidine for control of gastric acid secretion and the possible prevention of upper gastrointestinal bleeding (ugib) in critical care patients. methods: this was a randomized, double blind clinical trial study of iv pantoprazole (40 mg every12 hour) or intermittent iv ranitidine (50 mg bolus every 8 hour) i...

Noncompliance with study medications is an important issue in the design of endpoint clinical trials. Including noncompliant patient data in an intention-to-treat analysis could seriously decrease study power. Standard methods for calculating sample size account for noncompliance, but all assume that noncompliance is noninformative, i.e., that the risk of discontinuation is independent of the r...