Dependence of the AES backscattering correction factor on the experimental configuration

We present an analysis of the dependence of the backscattering correction factor (BCF) in Auger-electron spectroscopy (AES) on the analyzer acceptance angle. Illustrative BCF calculations are presented for Pd M₅N₄₅N₄₅ Auger electrons as a function of primary-electron energy for primary-electron angles of incidence, θ₀, of 0° and 80° and for various values of the analyzer acceptance angle. It was necessary to generalize the BCF definition for the case of an analyzer with an arbitrarily large acceptance angle; this was done with a new function, the integral emission depth distribution function. BCFs calculated from an advanced model of electron transport in the surface region of the Pd sample varied weakly with analyzer half-cone angle for θ₀ = 0° but more strongly for θ₀ = 80° where there were BCF differences varying between 19% at a primary energy of 1 keV and 6% at a primary energy of 5 keV. These BCF differences are due in part to variations of the BCF with emission angle and in part to variations of the density of inner-shell ionizations within the information depth for the detected Auger electrons. The latter variations are responsible for differences larger than 10% between BCFs from the widely used simplified BCF model and those from the more accurate advanced model for primary energies less than about 5 keV for θ₀ = 80°. For normal incidence of the primary beam, differences greater than 10% between BCFs from the simplified and advanced models were found for primary energies between 1 keV and 4 keV. These BCF differences indicate that the simplified model can provide only approximate BCF values. In addition, the simplified model does not provide any BCF dependence on Auger-electron emission angle or analyzer acceptance angle.     

A note on quasi-newton formulae for sparse second derivative matrices

In order to apply quasi-Newton methods to solve unconstrained minimization calculations when the number of variables is very large, it is usually necessary to make use of any sparsity in the second derivative matrix of the objective function. Therefore, it is important to extend to the sparse case the updating formulae that occur in variable metric algorithms to revise the estimate of the second derivative matrix. Suitable extensions suggest themselves when the updating formulae are derived by variational methods [1, 3]. The purpose of the present paper is to give a new proof of a theorem of Dennis and Schnabel [1], that shows the effect of sparsity on updating formulae for second derivative estimates.     

Auger evidence of bonding in uranium-titanium alloys

Titanium Auger electron spectra undergo radical changes similar to oxidation in forming the U₂Ti intermetallic compound, whereas uranium spectra are relatively unmodified. These results indicate that Ti is an electron donor species in U₂Ti compound formation.     

Quantitative single point imaging with compressed sensing

A novel approach with respect to single point imaging (SPI), compressed sensing, is presented here that is shown to significantly reduce the loss of accuracy of reconstructed images from under-sampled acquisition data. SPI complements compressed sensing extremely well as it allows unconstrained selection of sampling trajectories. Dynamic processes featuring short NMR signal can thus be more rapidly imaged, in our case the absorption of moisture by a cereal-based wafer material, with minimal loss of image quantification. The absolute moisture content distribution is recovered via a series of images acquired with variable phase encoding times allowing extrapolation to time zero for each image pixel and the effective removal of contrast.     

Fast evaluation of polyharmonic splines in three dimensions

M. J. D. Powell ^{This paper concerns the fast evaluation of radial basis functions.It describes the mathematics of hierarchical and fast multipolemethods for fast evaluation of splines of the form where is a positive integer andp is a low-degree polynomial. Splines s of this form are polyharmonicsplines in 3 and have been found to be very useful for providingsolutions to scattered data interpolation problems in 3. Asit is now well known, hierarchical methods reduce the incrementalcost of a single extra evaluation from O(N) to O(log N) operationsand reduce the cost of a matrix–vector product (evaluationof s at all the centres) from O(N2) to O(N log N) operations.We give appropriate far- and near-field expansions, togetherwith error estimates, uniqueness theorems and translation formulae.A hierarchical code based on these formulae is detailed andsome numerical results are given.}     

Approximate dynamic programming algorithms for optimal dosage decisions in controlled ovarian hyperstimulation

In the controlled ovarian hyperstimulation (COH) treatment, clinicians monitor the patients’ physiological responses to gonadotropin administration to tradeoff between pregnancy probability and ovarian hyperstimulation syndrome (OHSS). We formulate the dosage control problem in the COH treatment as a stochastic dynamic program and design approximate dynamic programming (ADP) algorithms to overcome the well-known curses of dimensionality in Markov decision processes (MDP). Our numerical experiments indicate that the piecewise linear (PWL) approximation ADP algorithms can obtain policies that are very close to the one obtained by the MDP benchmark with significantly less solution time.     

Structure of the α-phase of solid methanol

The crystal structure of α-methanol at 15K has been determined from neutron powder diffraction measurements. The structure is orthorhombic, space group P2₁2₁2₁. The molecular geometry is found to be very similar to that in the gas phase, but the methyl group no longer has ideal 3-fold symmetry. The crystal is formed by infinite hydrogen-bonded chains of molecules with adjacent chains ‘pointing’ in opposite directions. The O-H … O hydrogen bonds are almost linear. No phase intermediate between the low temperature α-phase and the high temperature β-phase was found, but a new, metastable phase was discovered.