and cross-section g g G ¬ t. w x If p is prime, a p-valued field 8, p. 7 is a valued field, of characteristic zero, in which p has minimal positive value and whose residue field has p Ž . elements. A p-valued field F, ̈ is p-adically closed just in case no algebraic extension F9 of F with valuation ̈ 9 extending ̈ is p-valued. The Ž . class of p-adically closed fields is to Q , ̈ as the class of re...

BACKGROUND During sedation for upper gastrointestinal endoscopy, oxygen delivery via a nasal cannula is often necessary. However, the influences of the oxygen delivery route and breathing pattern on the F(IO2) have not been thoroughly investigated. The aim of this simulation study was to investigate the difference in the F(IO2) with a pharyngeal cannula versus nasal cannula during high- or low-...

The problems considered in this paper come as a natural continuation of our program to develop a free analogue of Sz.-Nagy–Foiaş theory, for row contractions. An n-tuple (T1, . . . , Tn) of operators acting on a Hilbert space is called row contraction if T1T ∗ 1 + · · ·+ TnT ∗ n ≤ I. In this study, the role of the unilateral shift is played by the left creation operators on the full Fock space ...

BACKGROUND AND AIMS Acer saccharum and Fagus grandifolia are among the most dominant late-successional tree species in North America. The influence of sapling growth responses to canopy gaps on the co-dominance of the two species in an old-growth forest in southern Quebec, Canada was examined. Two predictions were evaluated: (a) F. grandifolia is more shade tolerant than A. saccharum due to gre...

A 3-connected quadrangulation of a closed surface is said to be K′ 3-irreducible if no faceor cube-contraction preserves simplicity and 3-connectedness. In this paper, we prove that a K′ 3-irreducible quadrangulation of a closed surface except the sphere and the projective plane is either (i) irreducible or (ii) obtained from an irreducible quadrangulation H by applying 4-cycle additions to F0 ...

Let a, b and n be positive integers and let S = {x1, x2, . . . , xn} be a set of distinct positive integers. The n × n matrix (Sf ) = (f ((xi, xj))), having f evaluated at the greatest common divisor (xi, xj) of xi and xj as its ij−entry, is called the GCD matrix associated with f on the set S. Similarly, the n × n matrix [Sf ] = (f ([xi, xj ])) is called the LCM matrix associated with f on S. ...

If X is a convex surface in a Euclidean space, then the squared intrinsic distance function dist(x, y) is DC (d.c., delta-convex) on X×X in the only natural extrinsic sense. An analogous result holds for the squared distance function dist(x,F ) from a closed set F ⊂ X. Applications concerning r-boundaries (distance spheres) and ambiguous loci (exoskeletons) of closed subsets of a convex surface...

1. In this paper we wish to study fields which can be written as intersections of real closed fields. Several more restrictive classes of fields have received careful study (real closed fields by Artin and Schreier, hereditarily euclidean fields by Prestel and Ziegler [8], hereditarily Pythagorean fields by Becker [1]), with this more general class of fields sometimes mentioned in passing. We s...

1. ip is real-analytic; 2. the rank of <p equals p on an everywhere dense subset of U; 3. (f(U) is closed in V; 4. for each compact subset K C <p(U), there exists a compact subset H C U such that <p(H) = K. Then the composition subalgebra A? = {foip: f e C°°(V)} is closed in C°°(U), when this algebra carries its natural Frechet topology (convergence on compact subsets of the function and all it...