Resolvent Estimates for High-Contrast Elliptic Problems with Periodic Coefficients

We study the asymptotic behaviour of the resolvents (Aε+I)−1 of elliptic second-order differential operators Aε in Rd with periodic rapidly oscillating coefficients, as the period ε goes to zero. The class of operators covered by our analysis includes both the “classical” case of uniformly elliptic families (where the ellipticity constant does not depend on ε ) and the “double-porosity” case of coefficients that take contrasting values of order one and of order ε2 in different parts of the period cell. We provide a construction for the leading order term of the “operator asymptotics” of (Aε+I)−1 in the sense of operator-norm convergence and prove order O(ε) remainder estimates

Spectral Analysis of One-Dimensional High-Contrast Elliptic Problems with Periodic Coefficients

We study the behavior of the spectrum of a family of one-dimensional operators with periodic high-contrast coefficients as the period goes to zero, which may represent, e.g., the elastic or electromagnetic response of a two-component composite medium. Compared to the standard operators with moderate contrast, they exhibit a number of new effects due to the underlying nonuniform ellipticity of the family. The effective behavior of such media in the vanishing period limit also differs notably from that of multidimensional models investigated thus far by other authors, due to the fact that neither component of the composite forms a connected set. We then discuss a modified problem, where the equation coefficient is set to a positive constant on an interval that is independent of the period. Formal asymptotic analysis and numerical tests with finite elements suggest the existence of localized eigenfunctions (``defect modes''), whose eigenvalues are situated in the gaps of the limit spectrum for the unperturbed problem

Introduction to Knowledge Flows, Transfer, Sharing and Exchange Minitrack

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Periventricular-intraventricular haemorrhage in low-birth-weight infants at Baragwanath Hospital

The prevalence of periventricular-intraventricular haemorrhage (PV-IVH) aInong very-low-birthweight infants at Baragwanath Hospital has not been well docwnented. In this prospective study, a total of 282 live-born infants with birth weights of 1 000 - 1 749 g were studied over a 41/2-month period. Every infant had at least one cranial ultrasound examination at 7 - 10 days of age, while one third of non-ventilated and all ventilated infants had ultrasound examinations on days 3, 7 and 14. Where possible, all infants had a follow-up ultrasound scan at 40 weeks' post-conceptional age. The overall prevalence of PV-IVH was 53% for infants weighing less than 1 500 g at birth and 52% for infants born at less than 35 weeks' gestation, but only 12% had either grade III or grade IV haemorrhages. The prevalence and severity of PV-IVH increased with both decreasing birth weight and decreasing gestational age and was also predicted by the need for active resuscitation at birth, mechanical ventilation and the development of pneumothorax. A total of 93% ofinfants without PV-IVH survived, but survival decreased with increasing grade of PV-IVH. Germinal matrix cysts were noted on follow-up in 55% of surviving infants with grade I PV-IVH. Very-low-birthweight infants at Baragwanath Hospital therefore seem to have a higher prevalence of PV-IVH when compared with reported figures, but this is due mainly to an increase in smaller haemorrhages

Antigen-Presenting Activity of Non-Langerhans Epidermal Cells in Contact Hypersensitivity Reactions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72263/1/j.1365-3083.1990.tb02914.x.pd

Soft x-ray spectroscopy experiments on the near K-edge of B in MB2 (M=Mg, Al, Ta, and Nb)

Soft X-ray absorption and emission measurements are performed for the K- edge of B in MB$_2$ (M=Mg, Al, Ta and Nb). Unique feature of MgB$_2$ with a high density of B 2$p_{xy}(\sigma)$-state below and above the Fermi edge, which extends to 1 eV above the edge, is confirmed. In contrast, the B 2$p$ density of states in AlB$_2$ and TaB$_2$, both of occupied and unoccupied states, decreased linearly towards the Fermi energy and showed a dip at the Fermi energy. Furthermore, there is a broadening of the peaks with $p\sigma$-character in XES and XAS of AlB$_2$, which is due to the increase of three dimensionality in the $p\sigma$-band in AlB$_2$. The DOS of NbB$_2$ has a dip just below the Fermi energy. The present results indicate that the large DOS of B-2$p\sigma$ states near the Fermi energy are crucial for the superconductivity of MgB$_2$.Comment: 3 pages text and 4 pages figures. accepted for publication to Phys. Rev.

Diagnostic accuracy of biopsy versus full excision for diagnosis of oral cancer: a systematic review

Objectives: To review studies assessing diagnostic accuracy of biopsy of oral lesions for diagnosis of oral cancer and potentially malignant disorders, compared with full excision. Methods: Systematic review: four databases were searched for studies conducted within developed countries and published between 2009 and January 2020. Results: Six studies met inclusion criteria, with wide variation in methods and results. For identifying dysplasia or malignancy, sensitivity of biopsy (versus excision) ranged from 42% to 86% and specificity from 75% to 100% across two studies, while concordance varied from 27% to 89% across four studies. For identifying malignant-only lesions, sensitivity was 71% and 94% in two studies, while specificity ranged from 17% to 100% across four studies. Conclusions: There are few published studies assessing biopsy accuracy, with varying results. Further research should evaluate factors impacting accuracy, such as biopsy depth; multiple biopsies of large lesions; discordance between pathologists; and regular follow-up

Diagnostic accuracy of conventional oral examination for detecting oral cavity cancer and potentially malignant disorders in patients with clinically evident oral lesions: Systematic review and meta‐analysis

This systematic review evaluates the diagnostic accuracy of conventional oral examination (COE) versus incisional or excisional biopsy for the diagnosis of malignant and/or dysplastic lesions in patients with clinically evident lesions. Searches were conducted across five electronic databases from inception to January 2020. Meta-analyses were undertaken, where appropriate. Among 18 included studies, 14 studies were included in the meta-analysis, giving summary estimates for COE of 71% sensitivity and 85% specificity for the diagnosis of dysplastic and/or malignant lesions. The pooled diagnostic accuracy of identifying malignant-only lesions was reported in seven studies, giving a pooled estimate of 88% sensitivity and 81% specificity. Diagnostic accuracy of different types of dental/medical professionals in identifying dysplastic or malignant lesions gave varying estimates of sensitivity and specificity across three studies. Further research is needed to improve the diagnostic accuracy of COE for early detection of dysplastic and malignant oral lesions