Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.

The art of auscultation: evaluating a patient's respiratory pathology

This article considers national policy drivers promoting the development of advanced assessment skills and practical procedures for the safe and effective use of the stethoscope in the clinical area. The evidence base underpinning effective use of the stethoscope in clinical practice is explored, including the preparation of the patient and the environment, applying infection control policies, and placing an emphasis on privacy and dignity. This is followed by a practical guide to auscultation technique of the respiratory system for nurses developing advanced practice skills.

Respiratory auscultation: how to use a stethoscope

This article outlines the correct procedure for respiratory assessments using a stethoscope, how to use a stethoscope and how to interpret your findings.

Early growth and adult respiratory function in men and women followed from the fetal period to adulthood

While some studies suggest that poor fetal growth rate, as indicated by lower birth weight, is associated with poor respiratory function in childhood, findings among adults remain inconsistent. A study was undertaken to determine the association between early growth and adult respiratory function.