For functions u, subharmonic in the plane, let

and let N(r,u) be the integrated counting function. Suppose that is a non-negative non-decreasing convex function of log r for which for all small r and , where 1 < ρ < 2, and define

A sharp upper bound is obtained for and a sharp lower bound is obtained for .

Two samples of Special Hospital patients who had posterior temporal slow wave foci were selected and matched for age, sex, and duration of stay with patients from the same hospital who had normal EEG records. A high prevalence of between 20 and 31% was found. No significant differences were found between the index and control groups with regard to a number of developmental, forensic, psychiatric, behavioural, and psychometric variables. A striking feature was the high average age of almost 30 years of the posterior temporal slow wave patients. This finding suggests that the current maturation defect hypothesis in relation to cerebral function in psychopaths requires revision. The possible role of early social and environmental factors in the genesis of these EEG anomalies is discussed.

This report is concerned with a simple statistical model of the way the brain may function, suggested by the analysis of intelligence test results in two groups of children. The model describes the statistical behaviour of an ideal array of elements, representing the brain, during tests of cognitive ability. Predictions from the model indicate that comparison of the EEC recording taken from groups of children who were good or poor readers would show amplitude differences. These were found between the groups when the eyes were open but not when the eyes were closed–a result explained by the model.

Without prior assumptions about growth, fundamental inequalities for the Taylor series of an entire function are obtained, valid outside a certain exceptional set. The results are vacuous or not depending on the estimate for the exceptional set. Only then does the growth of the function enter.

Let

be an entire function, where (αn) is a strictly increasing sequence of non-negativeintegers. The maximum modulus, M(r), the minimum modulus, m(r), and the maxi-mum term, μ(r), of f defined by

Using data from a cohort study conducted by the Veterinary Laboratories Agency (VLA), evidence of spatial clustering at distances up to 30 km was found for S. Agama and S. Dublin (P values of 0·001) and borderline evidence was found for spatial clustering of S. Typhimurium (P=0·077). The evolution of infection status of study farms over time was modelled using a Markov Chain model with transition probabilities describing changes in status at each of four visits, allowing for the effect of sampling visit. The degree of geographical clustering of infection, having allowed for temporal effects, was assessed by comparing the residual deviance from a model including a measure of recent neighbourhood infection levels with one excluding this variable. The number of cases arising within a defined distance and time period of an index case was higher than expected. This provides evidence for spatial and spatio-temporal clustering, which suggests either a contagious process (e.g. through direct or indirect farm-to-farm transmission) or geographically localized environmental and/or farm factors which increase the risk of infection. The results emphasize the different epidemiology of the three Salmonella serovars investigated.

Post-mortem examinations of harbour porpoises, Phocoena phocoena, regularly reveal heavy parasitic worm burdens. These same post-mortem records show varying levels of polychlorinated biphenyls (PCBs) accumulating in the blubber of porpoises. Although a number of papers have documented geospatial and temporal changes of PCBs and their detrimental effects on marine mammal health, as yet none have examined their role in determining nematode burdens in wild marine mammal populations. Using a data set consisting of harbour porpoises stranded in the UK between 1989 and 2002, we found a significant, positive association between PCB levels and nematode burdens, although the nature of the relationship was confounded with porpoise sex, age and cause of death. It was also apparent that individuals with the heaviest infestations of nematodes did not have the highest PCB level: while PCBs are important, they are clearly not the sole determinants of nematode burdens in wild populations of the harbour porpoise around the UK.

Cryptosporidium has become increasingly recognized as a pathogen responsible for outbreaks of diarrhoeal illness in both immunocompetent and immunocompromised persons. In August 2001, an Illinois hospital reported a cryptosporidiosis cluster potentially linked to a local waterpark. There were 358 case-patients identified. We conducted community-based and waterpark-based case-control studies to examine potential sources of the outbreak. We collected stool specimens from ill persons and pool water samples for microscopy and molecular analysis. Laboratory-confirmed case-patients (n=77) were more likely to have attended the waterpark [odds ratio (OR) 16·0, 95% confidence interval (CI) 3·8–66·8], had pool water in the mouth (OR 6·0, 95% CI 1·3–26·8), and swallowed pool water (OR 4·5, 95% CI 1·5–13·3) than age-matched controls. Cryptosporidium was found in stool specimens and pool water samples. The chlorine resistance of oocysts, frequent swimming exposures, high bather densities, heavy usage by diaper-aged children, and increased recognition and reporting of outbreaks are likely to have contributed to the increasing trend in number of swimming pool-associated outbreaks of cryptosporidiosis. Recommendations for disease prevention include alteration of pool design to separate toddler pool filtration systems from other pools. Implementation of education programmes could reduce the risk of faecal contamination and disease transmission.

It is shown that a condition on the order of a meromorphic function in a result of A. A. Gol’dberg cannot be relaxed.

AMS 2000 Mathematics subject classification: Primary 30D35

Suppose that f is meromorphic in the plane, and that there is a sequence Zn → ∞ and a sequence of positive numbers ∈n → 0, such that ∈n|zn|f#(zn)/log|zn| → ∞. It is shown that if f is analytic and non-zero in the closed discs Δn = {z: |z – zn| ≦∈n|zn|}, n = 1, 2, 3 …, then, given any positive integer K, there are arbitrarily large values of n and there is a point z in Δn such that │f (z)| 〉 |Z│k. Examples are given to show that the hypotheses cannot be relaxed.

This study assessed the ability of otolaryngologists to diagnose and grade reflux disease at rigid endoscopy. Twenty-one out of 25 senior otolaryngologists who were questioned by means of a telephone survey said that if they find evidence of reflux disease at rigid endoscopy of the oesophagus and larynx, their practice is to place the patient on a proton pump inhibitor for six weeks without requesting pH and manometry studies, and without referral to a gastroenterologist. Over a two year period, 21 patients were diagnosed as having reflux disease at rigid endoscopy. This was based on the finding of fluid and erythema in the aerodigestive tract and upper oesophagus. Subsequent oesophageal pH and manometry was performed. Nine out of 21 patients were confirmed as refluxers. This demonstrated an accuracy of less than 50 per cent when using these findings to diagnose gastro-oesophageal reflux at rigid endoscopy.

Two cases of ischaemic optic neuropathy, which occurred as a complication of oncological neck surgery, are reported. These cases are submitted because of the apparent scarcity in the literature of this complication after head and neck surgery. They are also unusual because they presented with different clinical manifestations of ischaemic optic neuropathy after separate forms of bilateral neck dissection. A literature review identifies a small number of similar cases and risk factors and preventative measures are discussed.

The Westaby T-Y tracheobronchial silicone stent can be used for the relief of upper airway obstruction beyond the limit of a standard tracheostomy tube. We report on our experience in the use of the Westaby tube in 10 patients over a five-year period. The general features of the tube, indications for its use, and its method of insertion are described. The versatility and advantages over other stents are discussed. Two cases reports are described and the clinical course and outcomes of the individual patients are outlined.

It is shown that every transcendental entire function f grows transcendentally in a sequence of cercles de remplissage. An example shows that if

formula here

then there may be no sequence of cercles de remplissage the union of which contains infinitely many zeros of f. It is also shown that every transcendental entire function f has a Hayman direction, that is, a direction θ such that, in every open sector containing θ, either f assumes all complex values infinitely often, or else every derivative of f assumes all complex values, except possibly zero, infinitely often.

Abstract: A recurrent nerve palsy occurring in the presence of a goitre is considered to be caused by thyroid malignancy until proven otherwise.

Three cases are described in which benign thyroid disease resulted in recurrent laryngeal nerve paralysis. Recent haemorrhage was implicated histologically as the possible aetiology in all three cases. The importance of identifying and preserving the recurrent laryngeal nerve in the surgical management is highlighted.

Four channels of EEG (T4-T6, P4-02, T3-T5, P3-01) were recorded from several groups of control subjects and schizophrenia patients on analogue tape. They were later digitized and analysed by computer; power spectra were computed for 30 second epochs of EEG per channel; eyes closed, eyes open. No difference between normal controls and neurotic in-patients was apparent. An acute schizophrenic group had less alpha power, this change being confined largely to the temporal areas. A chronic outpatient sample showed less alpha and beta power, while chronic long-stay schizophrenic patients had an excess of delta power. The changes in both chronic patient groups were diffuse rather than local.