The global attractivity of a higher order rational difference equation

This paper studies global asymptotic stability for positive solutions to the equation

     

Adaptive Lanczos methods for recursive condition estimation

Estimates for the condition number of a matrix are useful in many areas of scientific computing, including: recursive least squares computations, optimization, eigenanalysis, and general nonlinear problems solved by linearization techniques where matrix modification techniques are used. The purpose of this paper is to propose anadaptiveLanczosestimator scheme, which we callale, for tracking the condition number of the modified matrix over time. Applications to recursive least squares (RLS) computations using the covariance method with sliding data windows are considered.ale is fast for relatively smalln-parameter problems arising in RLS methods in control and signal processing, and is adaptive over time, i.e., estimates at timet are used to produce estimates at timet+1. Comparisons are made with other adaptive and non-adaptive condition estimators for recursive least squares problems. Numerical experiments are reported indicating thatale yields a very accurate recursive condition estimator.Research supported by the US Air Force under grant no. AFOSR-88-0285.Research supported by the US Army under grant no. DAAL03-90-G-105.Research supported by the US Air Force under grant no. AFOSR-88-0285.     

Molecular dynamics investigation of structural phase transitions

A two dimensional model exhibiting a structural phase transition is described, and results of molecular dynamics calculations on the model are presented. The static properties indicate a second order phase transition and show the growth of large ordered regions as the transition is approached. The spectral function for the order parameter autocorrelation function has an intense central peak near the transition.     

[3 + 4] Cycloaddition reactions of vinyl carbenoids with furans

The rhodium(II) acetate catalysed decomposition of diethyl 4-diazopent-2-enedioate in the presence of furans results in the formation of products derived from a [3 + 4] cycloaddition.     

A new atomization cell for trace metal determinations by tungsten coil atomic spectrometry

A new metallic atomization cell is used for trace metal determinations by tungsten coil atomic absorption spectrometry and tungsten coil atomic emission spectrometry. Different protecting gas mixtures are evaluated to improve atomic emission signals. Ar, N₂, CO₂ and He are used as solvents, and H₂ and C₂H₂ as solutes. A H₂/Ar mixture provided the best results. Parameters such as protecting gas flow rate and atomization current are also optimized. The optimal conditions are used to determine the figures of merit for both methods and the results are compared with values found in the literature. The new cell provides a better control of the radiation reaching the detector and a small, more isothermal environment around the atomizer. A more concentrated atomic cloud and a smaller background signal result in lower limits of detection using both methods. Cu (324.7 nm), Cd (228.8 nm) and Sn (286.3 nm) determined by tungsten coil atomic absorption spectrometry presented limits of detection as low as 0.6, 0.1, and 2.2 μg L⁻¹, respectively. For Cr (425.4 nm), Eu (459.4 nm) and Sr (460.7 nm) determined by tungsten coil atomic emission spectrometry, limits of detection of 4.5, 2.5, and 0.1 μg L⁻¹ were calculated. The method is used to determine Cu, Cd, Cr and Sr in a water standard reference material. Results for Cu, Cd and Cr presented no significant difference from reported values in a 95% confidence level. For Sr, a 113% recovery was obtained.     

Infinite families of infinite families of congruences for k-regular partitions

Let k∈{10,15,20}, and let b _k (n) denote the number k-regular partitions of n. We prove for half of all primes p and any t≥1 that there exist p?1 arithmetic progressions modulo p ^2t such that b _k (n) is a multiple of 5 for each n in one of these progressions.     

Rhodium catalyzed tandem Diels-Alder/hydrolysis reactions of 2-boron-substituted 1,3-dienes

2-Boron substituted 1,3-dienes have been prepared and used in preliminary experiments to demonstrate that it is possible to effect rhodium catalyzed Diels-Alder/hydrolysis tandem reactions.     

Bulk and surface electron states in ruthenium

Using ab initio pseudopotentials and a mixed basis, we have examined the electronic structure of ruthenium. We have concentrated on the bulk and surface energy bands with specific emphasis on the close packed (0 0 0 1) surface. We present energy band spectra for the surface and bulk bands, and compare these bands to experiment and to other calculations. We find good agreement between our bulk bands and recent photoemission measurements. With respect to our surface bands, the results are in good accord with other calculations both for ruthenium and for “analogous” transition metal surfaces.