Edward Davies

Non-Self-Adjoint Differential Operators

A description is given of methods that have been used to analyze the spectrum of non-self-adjoint differential operators, emphasizing the differences from the self-adjoint theory. It transpires that even in cases in which the eigenfunctions can be determined explicitly, they often do not form a basis; this is closely related to a high degree of instability of the eigenvalues under small perturbations of the operator.

Complement activation during bypass in acquired C1 esterase inhibitor deficiency.

Serial complement estimations during cardiopulmonary bypass are reported in a patient with acquired C1 esterase inhibitor deficiency. Although the extent of classic and alternative pathway activation appeared appropriate, exaggerated common pathway activation with massive increase in the C3d:C3 ratio occurred. A fatal hemostatic disorder, pulmonary edema, and circulatory collapse ensued despite prophylaxis and therapy.

Trace properties of the Dirichlet Laplacian

On obtient des bornes superieures et inferieures pour tr[exp(−Ht)] en termes de la fonction r(x)

Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle

We prove that for any n × n matrix, A, and z with |z| ≥ ||A||, we have that ||(z - A)-1|| ≤ cot(π/4n) dist(z, spec(A))-1. We apply this result to the study of random orthogonal polynomials on the unit circle.

Perturbations of Jordan matrices

We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In the case of random perturbations we obtain explicit estimates which show that as the size of the matrix increases, most of the eigenvalues of the perturbed matrix converge to a certain circle with centre at the origin. In the case of finite rank perturbations we completely determine the spectral asymptotics as the size of the matrix increases.

Bury the bill

The proposed reforms to the Health and Social Care Bill would leave it unfit for any purpose

FETAL C-REACTIVE PROTEIN

C-reactive protein (CRP) was measured in fetal blood obtained by cordocentesis from 17 patients with preterm prelabour rupture of the membranes (PPROM). CRP was detected in the blood of eight of the 17 fetuses. Six fetuses, five of whom may have been infected had CRP > or = 0.8 mg dl-1. The remaining 11 fetuses as well as 25 healthy term infants who had cord blood taken immediately post delivery had CRP < 0.6 mg dl-1. These results suggest that elevation of fetal CRP levels may be a useful indicator of fetal infection in pregnancies complicated by PPROM.

Singular Schrödinger operators in one dimension

We consider a class of singular Schrodinger operators H that act in L 2 (0;1), each of which is constructed from a positive function on (0;1). Our analysis is direct and elementary. In particular it does not mention the potential directly or make any assumptions about the magnitudes of the rst derivatives or the existence of second derivatives of . For a large class of H that have discrete spectrum, we prove that the eigenvalue asymptotics of H does not depend on rapid oscillations of or of the potential. Similar comments apply to our treatment of the existence and completeness of the wave operators.

Emergency hospital evacuation as Hurricane Sandy hits New York

More than 200 patients had to be evacuated from a major New York hospital on 29 October when two backup power generators failed as Hurricane Sandy hit New York City. The patients, including 20 babies from the neonatal intensive care unit, were evacuated by a fleet of ambulances from all over the city, lined up outside New York University Tisch Hospital at the Langone Medical Centre. Doctors …

Ultracontractive Semigroups and Some Problems in Analysis

Publisher Summary This chapter discusses the ultracontractive semigroups and some problems in analysis. The chapter discusses some results involving the relation of some abstract theory of L P properties of semigroups. The concrete problems addressed in the chapter are (1) Sobolev estimates up to the boundary, (2) conditioned Brownian paths, and (3) ultracontractivity of Schrodinger semigroups. Since their introduction as tools in constructive quantum field theory, the hypercontractive estimates have provoked a large mathematical literature. The chapter combines the known results of Gross and Rosen to reduce ultracontractive estimates to a single family of operator inequalities. The chapter also proves ultracontractivity under suitable geometric hypotheses.