Contours of constant Δ and Ψ in the 2–4 plane for the ellipsometric functions

Contour graphs of ₂ vs ₄ for different film thicknesses and a range of angles of incidence have been plotted for the ellipsometric functions Δ and Ψ in both the reflection and transmission modes. In the case of reflection ellipsometry, when the plots for Δ_R and Ψ_R are superimposed, the two sets of contours cross nearly at right angles over a large part of the field, this being indicative of the high accuracy obtainable in using this technique to determine ₄ and ₂ and hence the optical constants, n and k, for the film material. The reflection ellipsometric technique is accurate over angles of incidence between 30° and 75° and for a range of film thicknesses between λ/30 and 5λ. Transmission ellipsometry is less useful, due to anomalies in both X_s and X_p where sudden phase changes of ±π occur in regions of interest. There is also the possibility of multiple solutions, although the use of a multiangle technique would enable the “correct” values to be more easily determined.     

Secondary transverse instabilities in optical parametric oscillators

We investigate the effect of coupling between diffraction and walk-off on secondary instabilities in nondegenerate optical parametric oscillators. We show that traveling waves that propagate in the walk-off direction, which are generated at the onset of absolute instability, experience Eckhaus and zigzag phase instabilities. Each of these secondary instabilities splits into absolute and convective instabilities that modify the Eckhaus and zigzag instability boundaries. As a consequence, the stability domain of modulated traveling waves is enlarged and may coexist with uniform steady states. The predictions are consistent with the numerical solutions of the optical parametric oscillator model.     

Achievable accuracy of parameter estimation for multidimensional NMR experiments

A fundamental issue in NMR spectroscopy is the estimation of parameters such as the Larmor frequencies of nuclei, J coupling constants, and relaxation rates. The Cramer-Rao lower bound provides a method to assess the best achievable accuracy of parameter estimates resulting from an unbiased estimation procedure. We show how the Cramer-Rao lower bound can be calculated for data obtained from multidimensional NMR experiments. The Cramer-Rao lower bound is compared to the variance of parameter estimates for simulated data using a least-squares estimation procedure. It is also shown how our results on the Cramer-Rao lower bound can be used to analyze whether an experimental design can be improved to provide experimental data which can result in parameter estimates with higher accuracy. The concept of nonuniform averaging in the indirect dimension is introduced and studied in connection with nonuniform sampling of the data.     

Approximation properties of zonal function networks using scattered data on the sphere

A zonal function (ZF) network is a function of the form x↦∑ _k=1 ⁿ c _k (x · y _k), where x and the y _k's are on the unit sphere in q+1 dimensional Euclidean space, and where the y _k's are scattered points. In this paper, we study the degree of approximation by ZF networks. In particular, we compare this degree of approximation with that obtained with the classical spherical harmonics. In many cases of interest, this is the best possible for a given amount of information regarding the target function. We also discuss the construction of ZF networks using scattered data. Our networks require no training in the traditional sense, and provide theoretically predictable rates of approximation. This revised version was published online in June 2006 with corrections to the Cover Date.     

MR imaging of the liver and spleen: a comparison of the effects on signal intensity of two superparamagnetic iron oxide agents

We compared the effects of two superparamagnetic iron oxide (SPIO) contrast agents, ferumoxides and SHU-555A, in MR imaging of the liver and spleen. Thirty-six patients with known malignant lesions of the liver underwent T2W turbo spin-echo (TSE) and T1WGRE FLASH opposed-phase imaging before and after SPIO injection on a 1.0 T MR system. Post-ferumoxides images were obtained in 18 patients 90 min after infusion of 15 micrommol Fe/kg of the agent. In 18 other patients SHU-555A was administered as a rapid bolus at a dose of 7.0-12.9 micrommol Fe/kg. T1WGRE FLASH images were obtained immediately, 30 s and 480 s and T2WTSE images 10 min after injection. Signal intensity of the liver, spleen, and malignant liver lesions before and after SPIO was measured with operator-defined regions of interest. The effects of ferumoxides and SHU-555A were measured as the percentage signal intensity change (PSIC) and in the malignant liver lesions additionally as changes in lesion-to-liver contrast-to-noise ratio (deltaDCNR). On T2W TSE images, there was no significant difference between the two agents in signal loss of liver parenchyma (p > 0.05). The signal loss in the spleen produced by ferumoxides was greater than with SHU-555A (p < 0.05). Both SPIO agents produced a significant increase in the CNR of malignant liver lesions. Delta CNR was slightly greater with ferumoxides than with SHU-555A (p < 0.05). On T1WGRE FLASH images, a slight decrease of liver SI induced by both agents was found on late post-SPIO images. No significant difference of liver PSIC between the two SPIO agents was noted on T1W images. The SI of spleen was significantly increased with both agents on T1W images and no difference in PSIC of spleen was noted (p > 0.05). The T1 and T2 effects produced by ferumoxides and SHU-555A were comparable in the liver although ferumoxides produced a stronger T2 effect in the spleen.     

Infinite-dimensional gauge groups and special nonlinear gravitons

A gauge theory in flat space—time, in which the gauge algebra is the (infinite-dimensional) algebra of vector fields on a surface, determines a curved space—time metric. This note deals with some completely integrable examples, concentrating on the N → ∞ limit of the Euler—Arnol'd equations [geodesics on SO(N)]. In this case, the metric turns out to be flat, which points the way to a coordinate transformation that solves the original equations.     

Periodic Points for Expansive Actions of Zd on Compact Abelian Groups

In this note we show that the periodic points of an expansiveZ^d action on a compact abelian group are uniformly distributedwith respect to Haar measure if the action has completely positiveentropy. In the general expansive case, we show that any measureobtained as the distribution of periodic points along some sequenceof periods necessarily has maximal entropy but need not be Haarmeasure.     

Calibration procedure for gel permeation chromatography

A novel procedure is presented for calibrating a gel permeation chromatograph by using broad polymer fractions. The limit in accuracy is set by the accuracy of number-average and weight-average molecular weight measurements and the reproducibility of the chromatograph. In the particular calibration for linear polyethylene described here, low molecular weight fractions were prepared by nitric acid oxidation of annealed single crystals. The calibration is then of particular value in morphological studies of polyethylene. The influence in the calibration of polar endgroups on the polymer, as produced in these oxidized samples is discussed.