Limits and Continuity

SOME RESULTS OF CONTINUITY ?f

The dynamical behavior of a map on the unit interval has been the subject of much contemporary research. In this paper, we will consider the relation between the continuity of the map cof and cof for some positive integer k, where f is a continuous map from the unit interval to itself, and ?f is a function which takes any element of the unit interval to the set of all subsequential limits o...

Notes on Limits of Sobolev Spaces and the Continuity of Interpolation Scales

We extend lemmas by Bourgain-Brezis-Mironescu (2001), and Maz’ya-Shaposhnikova (2002), on limits of Sobolev spaces, to the setting of interpolation scales. This is achieved by means of establishing the continuity of real and complex interpolation scales at the end points. A connection to extrapolation theory is developed, and a new application to limits of Sobolev scales is obtained. We also gi...

Contents 0 Foreword 3 1 Function Limits and Continuity 3 2 Continuity 4 3 Continuous Functions on Closed Intervals 5

Semi-continuity of Siegel Disks under Parabolic Implosion

We transfer the lower semi-continuity of Siegel disks with fixed Brjuno type rotation numbers to geometric limits. Here, we restrict to Lavaurs maps associated to quadratic polynomials with a parabolic fixed point.

Analysis of Continuity and Proximity Effect Conductivity Limits in ''in Situ'' Multifilamentary Superconducting Wires

We focus on the question of whether continuity or the proximity effect is the dominant factor for the high critical current in "in situ" materials. The analysis of the experiments indicate that proximity plays a role at low Nb concentration while continuity is the dominant factor for high Nb concentration.

Re-framing continuity of care for this century.

I t is widely accepted that ‘‘continuity of care’’ is vital to its quality and safety. The traditional approach to achieving this in the inpatient setting has been to minimize transfers among providers to reduce interruptions in the care process. In recent years the effort to limit duty hours for resident physicians (junior doctors) in the US, UK, and EU has highlighted the fact that continuity...