Partial regularity and t-analytic sets for Banach function algebras

In this note we introduce the notion of t-analytic sets. Using this concept, we construct a class of closed prime ideals in Banach function algebras and discuss some problems related to Alling’s conjecture in H infinity. A description of all closed t-analytic sets for the disk-algebra is given. Moreover, we show that some of the assertions in [8] concerning the O-analyticity and S-regularity of certain Banach function algebras are not correct. We also determine the largest set on which a Douglas algebra is pointwise regular

Clark measures and a theorem of Ritt

We determine when a finite Blaschke product B can be written, in a non-trivial way, as a composition of two finite Blaschke products (Ritt's problem) in terms of the Clark measure for B. Our tools involve the numerical range of compressed shift operators and the geometry of certain polygons circumscribing the numerical range of the relevant operator. As a consequence of our results, we can determine, in terms of Clark measures, when two finite Blaschke products commute

Norms of Truncated Toeplitz Operators and Numerical Radii of Restricted Shifts

This paper gives a new approach to the calculation of the numerical radius of a restricted shift operator by linking it to the norm of a truncated Toeplitz operator (TTO), which can be calculated by various methods. Further results on the norm of a TTO are derived, and a conjecture on the existence of continuous symbols for compact TTO is resolved

3D Printing - To print or not to print? Aspects to consider before adoption - A supply chain perspective

3D printing is believed by many to be the next industrial revolution. The technology is already deployed in production. However, supply chain literature is still in its infancy regarding this topic, despite 3D printings radical impact on supply chains. A framework has been developed to assess various aspects that need to be considered when deploying such technology as part of the production process. Literature has been drawn from cross-discipline (e.g. social sciences, engineering, and business). The challenge for businesses will be whether to incur the cost impact today or the opportunity cost of tomorrow if 3D printing is not adopted

Inner functions and operator theory

This tutorial paper presents a survey of results, both classical and new, linking inner functions and operator theory. Topics discussed include invariant subspaces, universal operators, Hankel and Toeplitz operators, model spaces, truncated Toeplitz operators, restricted shifts, numerical ranges, and interpolation

Lithium distribution across the membrane of motoneurons in the isolated frog spinal cord

Lithium sensitive microelectrodes were used to investigate the transmembrane distribution of lithium ions (Li+) in motoneurons of the isolated frog spinal cord. After addition of 5 mmol·l–1 LiCl to the bathing solution the extracellular diffusion of Li+ was measured. At a depth of 500 m, about 60 min elapsed before the extracellular Li+ concentration approached that of the bathing solution. Intracellular measurements revealed that Li+ started to enter the cells soon after reaching the motoneuron pool and after up to 120 min superfusion, an intra — to extracellular concentration ratio of about 0.7 was obtained. The resting membrane potential and height of antidromically evoked action potentials were not altered by 5 mmol·l–1 Li+

Effects of lithium on electrical activity and potassium ion distribution in the vertebrate central nervous system

Three different regions of the vertebrate central nervous system maintained in vitro (frog spinal cord, guinea pig olfactory cortex and hippocampus) have been used to investigate how Li+ influences membrane potential, membrane resistance, action potentials, synaptic potentials and the transmembrane K+-distribution of neurons and glial cells. In view of the therapeutic action of Li+ in manicdepressive disease, a special effort was made to determine the threshold concentration for the actions of Li+ on the parameters described above. It was observed that Li+ induced a membrane depolarization of both neurons and glial cells, a decrease of action potential amplitudes, a facilitation of monosynaptic excitatory postsynaptic potentials and a depression of polysynaptic reflexes. The membrane resistance of neurons was not altered. Li+ also induced an elevation of the free extracellular potassium concentration and a decrease of the free intracellular potassium concentration. Furthermore, in the presence of Li+ a slowing of the recovery of the membrane potential of neurons and glial cells, and of the extracellular potassium concentration after repetitive synaptic stimulation was observed. The threshold concentrations for the effects of Li+ were below 5 mmol/l in the frog spinal cord and below 2 mmol/l in the guinea pig olfactory cortex and hippocampus. The basic mechanism underlying the action of Li+ may be an interaction with the transport-function of the Na+/K+ pump

Health-related quality of life after myocardial infarction is associated with level of left ventricular ejection fraction

<p>Abstract</p> <p>Background</p> <p>The objective was to explore the relationship between left ventricular ejection fraction (LVEF) assessed during hospitalization for acute myocardial infarction (MI) and later health-related quality of life (HRQoL).</p> <p>Methods</p> <p>We used multivariable linear regression to assess the relationship between LVEF and HRQoL in 256 MI patients who responded to the Kansas City Cardiomyopathy Questionnaire (KCCQ), the EQ-5D Index, and the EuroQol Visual Analogue Scale (EQ-VAS) 2.5 years after the index MI.</p> <p>Results</p> <p>167 patients had normal LVEF (>50%), 56 intermediate (40%–50%), and 33 reduced (<40%). The mean (SD) KCCQ clinical summary scores were 85 (18), 75 (22), and 68 (21) (<it>p </it><0.001) in the three groups, respectively. The corresponding EQ-5D Index scores were 0.83 (0.18), 0.72 (0.27), and 0.76 (0.14) (<it>p </it>= 0.005) and EQ-VAS scores were 72 (18), 65 (21), and 57 (20) (<it>p </it>= 0.001). In multivariable linear regression analysis age ≥ 70 years, known chronic obstructive pulmonary disease (COPD), subsequent MI, intermediate LVEF, and reduced LVEF were independent determinants for reduced KCCQ clinical summary score. Female sex, medication for angina pectoris at discharge, and intermediate LVEF were independent determinants for reduced EQ-5D Index score. Age ≥ 70 years, COPD, and reduced LVEF were associated with reduced EQ-VAS score.</p> <p>Conclusion</p> <p>LVEF measured during hospitalization for MI was a determinant for HRQoL 2.5 years later.</p

Development of a questionnaire to measure health-related quality of life (HRQoL) in patients with atrial fibrillation (AF-QoL)

<p>Abstract</p> <p>Background</p> <p>The Health-Related Quality of Life (HRQoL) assessment in atrial fibrillation (AF) patients has traditionally been carried out in a poorly standardised fashion, or via the use of non disease-specific HRQoL questionnaires. The development of a HRQoL questionnaire with a good measuring performance will allow for a standardised assessment of the impact of this disease on the patient's daily living.</p> <p>Methods</p> <p>A bibliography review was conducted to identify the most relevant domains of daily living in AF patients. Subsequently, a focus group was created with the aid of cardiologists, and 17 patients were interviewed to identify the most-affected HRQoL domains. A qualitative analysis of the interview answers was performed, which was used to develop a pilot questionnaire administered to a 112-patient sample. Based on patient responses, an analysis was carried out following the statistical procedures defined by the Classical Test Theory (CTT) and the Item Response Theory (IRT). Reliablility was assessed via Cronbach's coefficient alpha and item-total score correlations. A factorial analysis was performed to determine the number of domains. For each domain, a Rasch analysis was carried out, in order to reduce and stand hierarchically the questionnaire items.</p> <p>Results</p> <p>By way of the bibliography review and the expert focus group, 10 domains were identified. The patient interviews allowed for the identification of 286 items that later were downsized to 40 items. The resultant preliminary questionnaire was administered to a 112-patient sample (pilot study). The Rasch analysis led to the definition of two domains, comprising 7 and 11 items respectively, which corresponded to the psychological and physical domains (18 items total), thereby giving rise to the initial AF-QoL-18 questionnaire. Cronbach's coefficient alpha was acceptable (0.91).</p> <p>Conclusion</p> <p>An initial HRQoL questionnaire, AFQoL-18, has been developed to assess HRQoL in AF patients.</p