INTRODUCTION Nasal cannulas are commonly used to deliver oxygen in acute and chronic care settings; however, there are few data available on delivered fraction of inspired oxygen (F(IO(2))). The purposes of this study were to determine the delivered F(IO(2)) on human subjects using low-flow and high-flow nasal cannulas, and to determine the effects of mouth-closed and mouth-open breathing on F(...

In this very short paper, we show that the average overlap density of a union-closed family $\mathcal{F}$ subsets $\{1,2,\ldots,n\}$ may be as small \[\Theta((\log_2 \log_2 |\mathcal{F}|)/(\log_2 |\mathcal{F}|)),\] for infinitely many positive integers $n$.

In 1979 Frankl conjectured that in a finite union-closed family F of finite sets, F = {∅} there has to be an element that belongs to at least half of the sets in F . We prove this when | F| 10.

Under the assumption that δ is a Woodin cardinal and GCH holds, I show that if F is any class function from the regular cardinals to the cardinals such that (1) κ < cf(F (κ)), (2) κ < λ implies F (κ) ≤ F (λ), and (3) δ is closed under F , then there is a cofinality-preserving forcing extension in which 2 = F (γ) for each regular cardinal γ < δ, and in which δ remains Woodin. Unlike the analogou...

Suppose M is a topological m-manifold, X is a generalized nmanifold satisfying the disjoint disks property (DDP ), m > n ≥ 5, f : M → X is an approximate fibration, with fiber the shape of a closed topological manifold F , and Y is a closed, 1-LCC, codimension three subset of X. We examine conditions under which f is controlled homeomorphic to an approximate fibration g : M → X such that g|g−1(...

This thesis consists of three contributions to the theory of complex approximation on Riemann surfaces. It is known that if E is a closed subset of an open Riemann surface R and f is a holomorphic function on a neighbourhood of E, then it is “usually” not possible to approximate f uniformly by functions holomorphic on all of R. In Chapter 2, we show, however, that for every open Riemann surface...

Let (M, g) be a closed Riemannian manifold of dimension n ≥ 3 and let f ∈ C∞(M), such that the operator Pf := ∆g + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of Pf as the constant term in the expansion of the Green function of Pf at p. In this paper, we establish many results on the mass of such operators. In particular, if f := n−2 4(n−1) sg, ...

Structural analyses of actin binding regions comprising tandem calponin homology domains alone and when bound to F-actin have revealed a number of different conformations with calponin homology domains in 'open' and 'closed' positions. In an attempt to resolve these issues we have examined the properties of the utrophin actin binding domain in open and closed conformations in order to verify th...

Let Mφ denote the set of Borel probability measures invariant under a topological action φ on a compact metrizable space X. For a continuous function f : X → R, a measure μ ∈ Mφ is called f -maximizing if ∫ f dμ = sup{ ∫ f dm : m ∈Mφ}. It is shown that if μ is any ergodic measure in Mφ, then there exists a continuous function whose unique maximizing measure is μ. More generally, if E is a non-e...

We define Euclidean scissor congruence groups for an arbitrary algebraically closed field F and formulate a conjecture describing them. Using the Euclidean and NonEuclidean F–scissor congruence groups we construct a category which is conjecturally equivalent to a subcategory of the category MT (Fε) of mixed Tate motives over the dual numbers Fε := F [ε]/ε . 1. Euclidean scissor congruence group...