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Given a convex or a Jordan domain Ω , let Ω ′ be a subset of this domain, with P (Ω ′) denoting its perimeter and A (Ω ′) its area. If a subset Ωc exists such that h = P (Ω c) / A (Ω c) is a minimum, the subset Ωc is called the Cheeger set of Ω and h, the Cheeger constant of the given domain. If one considers the reciprocal of this minimum or the maximum ratio of the area of the subset to its perimeter, t ∗ = 1 / h. It follows from the work of Mosolov and Miasnikov that the minimum pressure gradient G to sustain the steady flow of a viscoplastic fluid in a pipe, with a cross section defined by Ω , is given by G > τ y / t ∗ , where τy is the constant yield stress of the fluid. In this survey, we summarize several results to determine the constant h when the given domain is self-Cheeger or a Cheeger-regular set that touches each boundary of a convex polygon and when the Cheeger-irregular set does not do so. The determination of the constant h for an arbitrary ellipse, a strip, and a region with no necks is also mentioned. [ABSTRACT FROM AUTHOR]

Background: Brushing cytology is a well established diagnostic procedure used by gynaecologists, physicians and surgeons to obtain representative samples from lesions. Our aim was to evaluate its reliability in ulcerative and tumour-like conditions arising in the skin of the head and neck., Methods: Over 28 months, 86 patients with suspected cutaneous malignant lesions underwent a cytological examination with a cytobrush within the otolaryngology department., Results: Cytological analysis identified 63 out of 64 histologically documented malignant tumours (60 primary basal cell and squamous cell carcinomas and three metastatic adenocarcinomas), and 21 out of 22 benign lesions. There was one false positive and one false negative result., Conclusions: Brushing cytology of suspected cutaneous malignant lesions is a rapid and reliable diagnostic method which helps the clinician to decide on appropriate planning and treatment. The technique can be performed as an out-patient procedure, and smear preparation can be done in the laboratory, even at a peripheral hospital.

An immunocytochemical method was used in male and female ring doves (Streptopelia risoria) to localize progesterone receptor immunoreactivity (PR-ir) in the brain and anterior pituitary gland in nonbreeding, incubating, brooding, and estrogen (E2)-treated nonbreeding birds. Progesterone receptor was found in four regions of the brain in males and females: the preoptic area (POA), nucleus preopticus paraventricularis magnocellularis (PPM), nucleus hypothalami lateralis (PLH), and the tuberal region (TR). Quantitative analysis demonstrated that the density of cell nuclei containing PR-ir in the POA, PPM, and PLH in brooding birds was significantly higher than in E2-treated doves or in birds at other stages of the reproductive cycle. The density of PR-containing cell nuclei in the TR of male ring doves was significantly higher on day 1 of incubation than in nonincubating males. In brooding birds, there was a significant decrease in PR-ir in the TR, particularly in the ventral region where nuclei containing PR-ir disappeared. In the anterior pituitary gland the density of cell nuclei containing PR-ir was higher in females than in males at the onset of incubation. E2 treatment resulted in an increase in the density of PR-containing cell nuclei in both males and females. Brooding females had a lower concentration of PR-containing cell nuclei than did females at other stages of the breeding cycle. It is suggested that progesterone receptor in the POA mediates the expression of incubation behavior while progesterone receptor in the TR is involved in the control of neuroendocrine function. The source of estrogen which increases PR appears to be of central nervous origin in the male and may be predominantly peripheral in the female., (Copyright 1997 Academic Press.)

Brain areas involved in the expression of incubation behaviour were identified in male ring dove at the onset of incubation using quantitative [14C]2-deoxyglucose (2DG) autoradiography. The uptake of 2DG in twenty-eight areas found in the hypothalamus and thalamus, and six areas in the forebrain were compared in control non-breeding and incubating birds. Although 2DG utilisation varied significantly between brain areas, significant differences between non-breeding males and incubating males were observed only in 4 of them. These were the nucleus tuberis, nucleus preopticus medialis, nucleus ovoidalis and paleostriatum primitivum. The uptake of 2DG was increased at the onset of incubation in the nucleus tuberis, nucleus preopticus medialis and nucleus ovoidalis and decrease in the paleostriatum primitivum. These findings are consistent with the hypothesis that these brain areas play a role in the initiation of incubation behaviour.

Quantitative [14C]2-deoxyglucose (2DG) autoradiography was used to identify areas of the ring dove brain involved in the expression of incubation behavior. Compared with non-breeding controls, 2DG uptake was increased in birds of both sexes during late incubation in all areas of the fore, mid- and hind-brain examined. This increase occurred irrespective of whether the birds were sitting on their eggs at the time of 2DG administration. A similar pattern of 2DG uptake into the brain was observed in non-breeding females treated with 30 I.U. ovine prolactin (i.p.) twice daily for 5 days. It is concluded that there is a generalised increase in neural activity in the brain of doves during late incubation which may be dependent on increased concentrations of plasma prolactin.