Mixed block elimination for linear systems with wider borders

The paper is about the stable solution of possibly ill-conditionedbordered linear systems. Given stable solvers for matrix A andfor A^T, we prove that the Govaerts Mixed Block Elimination (BEM)method constitutes a stable solver for the matrix consistingof A or A^T with a border of width 1, and hence by recursionfor a border of any width. We express the algorithm in an efficient,iterative, form. We analyse its operation count, and verifythe theory by extensive numerical experiments. ^*Senior Research Associate of the Belgian National Fund of ScientificResearch NFWO.     

Studies on solution cast perfluorocarbonsulfonic acid ionomers

The thermal properties of perfluorocarbonsulfonic acid ionomer films cast from solution and their temperature-dependent far infrared spectra have been investigated. In addition to the endotherms and spectral changes associated with the loss of solvent as the films were heated, a significant exotherm has been observed and assigned to the relaxation associated with rearrangements resulting in partially crystallized phases in insoluble thermally treated membranes. © 1993 John Wiley & Sons, Inc.     

Measurement of the spin and temperature dependence of ddµ molecule formation rate in solid and liquid deuterium

The ddµ molecule formation rate is experimentally measured for the two hyperfine states of the dµ-atom in the temperature range of 5–30 K. Results are consistent with a preliminary measurement by the TRIUMF group and contradict theoretical predictions. The work has been performed on the JINR phasotron (Dubna).     

Surface characterization of fluorinated polymers (PTFE, PVDF, PFA) for use in ultratrace analysis

Surface characterization of new unused PTFE, PFA and PVDF labware has been carried out by light microscopy, scanning electron microscopy, profilometry and atomic force microscopy. It has been found that in spite of higher micro-roughness, PFA exhibits the lowest nano-roughness and hence seems best suited as vessel material for relatively mild pressureless chemical operations for sample preparation of ultrapure substances, as container material for storage of ultrapure liquids, and for transport of such liquids, e.g., from the producer in the chemical to the end user in the microelectronics industry. This suitability refers only to the surface quality of the investigated materials. PTFE-surfaces, due to the sintering process of production, exhibit the most unfavourable surface quality of the investigated fluorinated polymers.     

Velocity inversion: A case study in infinite-dimensional optimization

The goal of seismic velocity inversion is the estimation of seismic wave velocities inside the earth by attempting to predict, in a least-error sense, seismic waveforms measured at its surface. We present velocity inversion as a case study in the various infinite-dimensional pathologies which may afflict practically important problems of distributed parameter identification, treated as optimization problems in function spaces. These features differentiate various problem formulations far beyond the degree one would expect for finite- (small-) dimensional problems. We illustrate this differentiation by comparing the characteristics of three different least-squares formulations of velocity inversion.     

Synthesis and crystal and molecular structure of newN-substituted γ-hydroxybutyramides

TheN-(2-phenylethyl)amide of-(1, 1-ethylenedioxy)-ethyl--hydroxybutyric acid (II) and theN-(p-methoxybenzyl)amide of-(1, 1-ethylenedioxy)-ethyl--hydroxybutyric acid (III) have been synthesized and the crystal structure ofIII has been solved. CompoundIII, C₁₆H₂₃O₅N, crystallizes in the monoclinic space groupP2₁/c witha=12.572(2),b=11.149(2),c=12.317(2) Å and=106.53(1)°. The structure was solved by direct methods, and refined by full-matrix least squares to giveR=0.040 (R _w =0.047) for 2004 intensities. The dioxolane ring has a deformed half-chair conformation.     

Covering the Plane with Congruent Copies of a Convex Body

It is shown that every plane compact convex set K with an interiorpoint admits a covering of the plane with density smaller thanor equal to 8(23 – 3)/3 = 1.2376043.... For comparison,the thinnest covering of the plane with congruent circles isof density 2 / 27 = 1.209199576.... (see R. Kershner [3]), whichshows that the covering density bound obtained here is closeto the best possible. It is conjectured that the best possibleis 2 / 27. The coverings produced here are of the double-latticekind consisting of translates of K and translates of —K.