Disjoint edge paths between given vertices of a convex polytope

A Gale diagram technique is used to show that if d is positive integer greater than one, then there is a d-polytope P such that there are [$\text{2(d + 4)}\text{5}$] pairs of distinct vertices of P which cannot all be joined by disjoint paths in the graph of P.     

Polarization measurement of the pp → nn charge exchange at 8 Gev/c

The $\text{p}\text{p}\text{→}\text{n}\text{n}$ polarization has been measured at 8 GeV/c and for ?t values ranging from 0 up to 0.8 (GeV/c)². A small and negative polarization has been found.     

Modelling admissions booking of elective in-patients into a treatment centre

As part of the modernisation of the UK National Health Service,specialist centres called treatment centres are being introducedthat cater solely for routine elective treatment for a relativelysmall number of conditions. In principle, such centres can adoptnew methods of operation, e.g. organising booked admissionson a cyclic basis, organised to make efficient use of treatmentresources. Assuming such a mode of operation, explicit cyclicformulae are derived for the mean and variance of bed demand.These take account of systematic differences between the lengthsof stay of different patient groups and also the effects ofemergency admissions. Using these formulae, optimisation methodsare discussed that have the potential for contributing to resourceplanning and to assist the process of booking patient admissions.Such optimisation methods can be used to help reduce overallcapacity needs or, conversely, to make better use of the capacityavailable.     

Monitoring the performance of cardiac surgeons

In the past, simple methods have been used to examine the performance of surgeons by examining the cumulative in-hospital mortality of their patients, without regard to the severity of the cases involved. This paper describes an alternative approach which takes account of an individual cardiac surgeon's case-mix by explicitly incorporating the inherent risk faced by patients due to a combination of factors relating to their age and the degree of disease they have.     

Computing the matrix geometric mean: Riemannian versus Euclidean conditioning,implementation techniques,and a Riemannian BFGS method

This paper addresses the problem of computing the Riemannian center of mass of a collection of symmetric positive definite matrices. We show in detail that the condition number of the Riemannian Hessian of the underlying optimization problem is never very ill conditioned in practice, which explains why the Riemannian steepest descent approach has been observed to perform well. We also show theoretically and empirically that this property is not shared by the Euclidean Hessian. We then present a limited‐memory Riemannian BFGS method to handle this computational task. We also provide methods to produce efficient numerical representations of geometric objects that are required for Riemannian optimization methods on the manifold of symmetric positive definite matrices. Through empirical results and a computational complexity analysis, we demonstrate the robust behavior of the limited‐memory Riemannian BFGS method and the efficiency of our implementation when compared to state‐of‐the‐art algorithms.     

Photoluminescence of mercurous halides

Mercurous halides show strong orange luminescence at 77°K when excited at energies above the fundamental absorption edge. At room temperature this luminescence is strong only in the chloride and bromide. Spectral features, including band maxima and half widths of both excitation and emission spectra are also temperature dependent. At 77°K a strong green luminescence was observed from the Hg₂Cl₂. Both Hg₂F₂ and Hg₂I₂ exhibited weak green emission, while no luminescence was observed from Hg₂Br₂ in this spectral region. The common orange luminescence is tentatively attributed to structural defects unique to mercurous salts, while the green emission is ascribed to an unspecified impurity center.     

Photoluminescence of O2 and S2 ions in synthetic sodalities

Photoluminescence spectra of oxygen-doped chloro- and bromosodalites and sulfur-doped chloro-, bromo- and iodosodalites were measured at temperatures between 4.2 and 300 °K. At 4.2 and 77 °K, the emission spectra of oxygen-doped sodalites consisted of a series of peaks in the wavelength range 400–700 nm, with an average energy separation of ∼ 1000 cm^-1. In addition, fine structure, attributed to lattice modes, was observed in each vibrational band. At 4.2 and 77 °K, the sulfur-doped samples showed a multiband spectrum in the 500–750 nm range, with an average separation of ∼ 570 cm^-1 between bands. The spectrum at 4.2 °K exhibited some asymmetry not observed at 77 °K, but no fine structure was resolved. At 300 °K weak, broad-band luminescence was observed from both oxygen- and sulfur-doped samples, with no vibrational structure evident. The results compared very favorably with those reported for oxygen- and sulfur-doped alkali halides, and by analogy the spectra were attributed to luminescence from O^-₂ and S^-₂ molecular ions.