Stochastic monotonicity and duality for continuous time Markov chains with general q-Matrix

The key problems in discussing stochastic monotonicity and duality for continuous time Markov chains are to give the criteria for existence and uniqueness and to construct the associated monotone processes in terms of their infinitesimal q -matrices. In their recent paper, Chen and Zhang [6] discussed these problems under the condition that the given q-matrix Q is conservative. The aim of this paper is to generalize their results to a more general case, i.e., the given q-matrix Q is not necessarily conservative. New problems arise 'in removing the conservative assumption. The existence and uniqueness criteria for this general case are given in this paper. Another important problem, the construction of all stochastically monotone Q-processes, is also considered.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

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.