Approximate inverse computation using Frobenius inner product

Parallel preconditioners are presented for the solution of general linear systems of equations. The computation of these preconditioners is achieved by orthogonal projections related to the Frobenius inner product. So, min_M∈??∥AM?I∥ _F and matrix M₀∈?? corresponding to this minimum (?? being any vectorial subspace of ??_n(?)) are explicitly computed using accumulative formulae in order to reduce computational cost when subspace ?? is extended to another one containing it. Every step, the computation is carried out taking advantage of the previous one, what considerably reduces the amount of work. These general results are illustrated with the subspace of matrices M such that AM is symmetric. The main application is developed for the subspace of matrices with a given sparsity pattern which may be constructed iteratively by augmenting the set of non‐zero entries in each column. Finally, the effectiveness of the sparse preconditioners is illustrated with some numerical experiments. Copyright © 2002 John Wiley & Sons, Ltd.     

Local Minimizers of the Ginzburg-Landau Energy with Magnetic Field in Three Dimensions

We establish the existence of locally minimizing vortex solutions to the full Ginzburg-Landau energy in three dimensional simply-connected domains with or without the presence of an applied magnetic field. The approach is based upon the theory of weak Jacobians and applies to nonconvex sample geometries for which there exists a configuration of locally shortest line segments with endpoints on the boundary.Research partially supported by NSERC grant number 261955     

A high performance liquid chromatographic assay for AMP-deaminase activity in the erythrocytes of healthy subjects and patients with inherited purine disorders

A novel method for measuring AMP-deaminase activity in human erythrocytes is presented, based on the determination of the reaction product, IMP, using high performance liquid chromatography. IMP formation was found to be proportional both to the incubation time and the amount of haemolysate over a wide range. The minimal detectable AMP-deaminase activity was more than 1000 times lower than the mean activity found in healthy controls (1083 nmol/h/mg Hb). No marked difference of activity was found in the patients with the following inherited purine disorders: familial juvenile gouty nephropathy and deficiencies of adenosine deaminase, hypoxanthine-guanine phosphoribosyltransferase or adenine phosphoribosyltransferase. The activity in the erythrocytes of patients with chronic renal failure was also similar to controls. The existence of subjects with low erythrocyte AMP-deaminase activity in the population has been confirmed.     

The prediction of coal properties using compressed infrared data from osculating polynomials

Reduction of the representation of infrared spectra from coal samples by osculating polynomials of degree nine is discussed. The reduced representation contains polynomial coefficients of order zero to four. Mathematical models of the original spectra are obtained by linear combination of the coefficients. These compressed models are statistically correlated to coal properties, namely, volatile matter, fixed carbon, ash content, heating value, hydrogen, carbon, sulphur, nitrogen, and maximum vitrinite reflectance, and the results are compared with those previously obtained from second derivatives of the same spectra. The use of compressed data, while giving slightly better correlations for some of the properties, has the advantage of requiring less computational time.     

Ab initio modelling of crosslinking in polymers. A case of chains with furan rings

A quantum chemical model (Abinitio HF-MO and DFT-B3LYP) of polyfurfuryl alcohol crosslinking is shown. Two pathways were considered: (a) a Diels–Alder (D–A) reaction between a dihydrofuran moiety and a furan ring; (b) the addition reaction of electrophilic specimens on conjugated double bonds. The ability for the formation of D–A adducts (dienes and dienophiles) was investigated by the frontier molecular orbital (FMO) theory. Energy gaps between the FMO's of diene and dienophile structures suggest that the occurrence of the D–A reaction is possible. The results suggest that the carbons of the exo double bonds attached to dihydrofuran rings are the sites most likely to be attacked by electrophilic species, while the C₃ and C₄ atoms display the opposite tendency due to their low HOMO electron densities. Results of a thermochemical approach to these reactions at the MP2 level was in agreement with reactivity modelled by MO predictions.     

Characterization of graded-index planar waveguides and analysis of modal coupling for the design of integrated optical components produced by ion-exchange in glass and induced by Kerr effect

An experimental analysis of graded-index (GRIN) planar waveguides produced by ion exchange in soda-lime glass is presented. This study is based on a recent model describing nonlinear diffusion. Likewise the modal coupling between planar waveguides, produced in the same substrate, is analyzed in order to design efficient integrated optical components. Finally, waveguiding structures induced by Kerr effect in glass are proposed and analyzed.     

Defect concentration in Ti-substituted YIG from TG curves

The article discusses theory and experiment about the measurement of defect concentration in Ti-substituted yttrium iron garnet by means of thermogravimetry techniques. The two possible cases arising from oxygen interchange with atmosphere, oxygen vacancies and interstitial cations, may be analyzed quantitatively from the derived expressions. The possibility of another type of defects being present in the samples, not associated to oxygen evolution, is not excluded. Measurements were carried out in air and CO₂ for different Ti contents. The substitution tends to increase slightly the defect parameter θ in YIG, while a CO₂ reducing atmosphere is much more effective than the Ti substitution for increasing θ. Calculations for a given single-phased sample sintered in air show two possibilities: a deficit of one oxygen atom for every 2.5 unit cells of 96 atoms, or one excess cation for every 3.5 cells. Other samples show very similar results. The accuracy involved in the measurements is about 2–3%.