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Dedicated to the memory of Leonid R. Volevič. In this paper, we combine results on extensions of operators with recent results on the relation between the M-function and the spectrum, to examine the spectral behaviour of boundary value problems. M-functions are defined for general closed extensions, and associated with realisations of elliptic operators. In(More)
The Homeobox (Hox) genes direct the development of tetrapod digits. The expression of Hox genes may be influenced by endogenous sex steroids during development. Manning (Digit ratio. New Brunswick, NJ: Rutgers University Press, 2002) predicted that the ratio between the lengths of digits 2 (2D) and 4 (4D) should be sexually dimorphic because prenatal(More)
Adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies. However, for only one simple weighting scheme, Gehan or Wilcoxon weights, are estimating equations guaranteed to be(More)
The main objective of this paper is to extend the pioneering work of Sims in [9] on second-order linear differential equations with a complex coefficient, in which he obtains an analogue of the Titchmarsh-Weyl theory and classification. The generalisation considered exposes interesting features not visible in the special case in [9]. An m-function is(More)
Information about accidental injury to children was obtained by studying children who presented at hospitals in South Glamorgan during a 6-month period. Just under 10 000 children who lived in the area presented at hospital, which, if extrapolated means that 20% of children each year might be expected to attend hospital after an accident. The majority (71%)(More)
This paper is concerned with the accurate numerical approximation of the spectral properties of the biharmonic operator on various domains in two dimensions. A number of analytic results concerning the eigenfunctions of this operator are summarized and their implications for numerical approximation are discussed. In particular, the asymptotic behaviour of(More)