On the numerical radius of the truncated adjoint Shift

A celebrated thorem of Fejer (1915) asserts that for a given positive trigonometric polynomial $\sum_{j=-n+1}^{n-1}c_{j}e^{ijt}$, we have $\lvert c_{1}\lvert\leqslant c_{0}\cos\frac{\pi}{n+1}$. A more recent inequality due to U. Haagerup and P. de la Harpe asserts that, for any contraction $T$ such that $T^{n}=0$, for some $n\geq2$, the inequality $\omega_{2}(T)\leqslant\cos\frac{\pi}{n+1}$ holds, and $\omega_{2}(T)=\cos\frac{\pi}{n+1}$ when T is unitarily equivalent to the extremal operator {S}^{\ast}_{n}={\bbs}_{\lvert{\C}^{n}}={\bbs}_{\lvert Ker (u_{n}(\bbs))} where $u_{n}(z)=z^{n}$ and \bbs is the adjoint of the shift operator on the Hilbert space of all square summable sequences. Apparently there is no relationship between them. In this mathematical note, we show that there is a connection between Taylor coefficients of positive rational functions on the torus and numerical radius of the extremal operator \bbs(\phi)=\bbs_{\lvert Ker(\phi(\bbs))} for a precise inner function $\phi$. This result completes a line of investigation begun in 2002 by C. Badea and G. Cassier \cite{Cassier}. An upper and lower bound of the numerical radius of \bbs(\phi) are given where $\phi$ is a finite Blashke product with unique zero

Patterns of antihypertensive prescribing, discontinuation and switching among a Hong Kong Chinese population from over one million prescriptions

Hypertension is an alarming public health problem among Chinese. The present study evaluated the prescribing patterns, discontinuation and switching profiles of antihypertensive agents and their associated factors in one Hong Kong Chinese population. Data were retrieved from computerized records for patients prescribed anti-hypertensive agents in government primary care clinics of Hong Kong from January, 2004 to June, 2007. A total of 1,069,836 antihypertensive drug visits, representing 67,028 patients, were analyzed. The most commonly prescribed drugs were Calcium Channel Blockers (CCBs) (49%), b-Blockers (BBs) (46%) and Angiotensin-Converting Enzyme Inhibitors (ACEIs) (19%). Thiazide diuretic prescribing was low (13%) and on the decline (14% in 2004 to 12% in 2007). Prescribing of ACEIs was rising (16% in 2004 to 23% in 2007). Patients’ age, gender, and socio-economic status were independent predictors of class of anti-hypertensive prescribed but explained less than 3.5% of the variation observed. Drug discontinuation was highest for BBs (21%) and lowest for CCBs (12%). The high rates of discontinuation in BBs remained apparent after controlling for confounding variables. Switching was less common than discontinuation and was most likely with thiazide diuretics. To summarize, prescribing of CCBs and BBs were high and that of thiazide diuretics particularly low in this Chinese population when compared with international trends. CCBs may be a particularly favorable antihypertensive treatment in Chinese, given the high discontinuation rates of BBs and international guidelines advising against the use of BBs as first-line therapy. The low use of thiazide diuretics warrants further clinical and cost effectiveness studies among Chinese

Beta-blokers in patients with cirrhosis and infection: don't blame too soon.

We found that PPI-users had a higher rate and BBs-users a lower rate of infections. The lower infection rate and better prognosis of BB-users can not be attributed, as suggested by Schiavon et al., to a higher proportion of variceal bleeding in this group; in fact, the large majority of patients hospitalized for bleeding were excluded from the study as they came to our ward already on systemic antibiotic treatment (which is usually started in the Emergency room) and this would have represented a confounding factor. Only few patients with variceal bleeding were included: they developed bleeding after enrolment and were equally distributed between those taking and not taking BBs. Following the recent debate about the ‘therapeutic window’ of BBs in cirrhotic patients (2–4), we were also interested in evaluating possible harmful effects of BBs in cirrhotic patients with infections. This was a secondary aim of our study and we certainly recognize that the study was underpowered for this purpose

Beta-blocker under-use in COPD patients

Background: Cardiovascular (CVS) comorbidities are common in COPD and contribute significantly to morbidity and mortality, especially following acute exacerbations of COPD (AECOPD). Beta-blockers (BBs) are safe and effective in COPD patients, with demonstrated survival benefit following myocardial infarction. We sought to determine if BBs are under-prescribed in patients hospitalized with AECOPD. We also sought to determine inpatient rates of CVS and cerebrovascular complications, and their impact on patient outcomes. Methods: Retrospective hospital data was collected over a 12-month period. The medical records of all patients 40 years of age coded with a diagnosis of AECOPD were analyzed. Prevalent use and incident initiation of BBs were assessed. Comorbidities including indications and contraindications for BB use were analyzed. Results: Of the 366 eligible patients, 156 patients (42.6%) had at least one indication for BB use – of these patients, only 53 (34.0%) were on BB therapy and 61 (39.1%) were not on BB therapy but had no listed contraindication. Prevalent use of BBs at the time of admission in all 366 patients was 19.7%, compared with 45.6%, 39.6% and 45.9% use of anti-platelets, statins and angiotensin-converting enzyme inhibitor/angiotensin II receptor blockers, respectively. CVS and cerebrovascular complications were common in this population (57 patients, 16%) and were associated with longer length of stay (p,0.01) and greater inpatient mortality (p=0.02). Conclusions: BBs are under-prescribed in COPD patients despite clear indication(s) for their use. Further work is required to explore barriers to BB prescribing in COPD patients