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.     

Pulse radiolysis study of the initial steps of the polymerization of cyclohexyl acrylate and cyclohexyl methacrylate

Pulse radiolysis with kinetic spectroscopic detection was applied to study the kinetics of the first steps of radiation induced polymerization of cyclohexyl acrylate and cyclohexyl methacrylate in cyclohexane solvent. The reactions were initiated by cyclohexyl radicals produced in the radiolysis of the solvent. The transient absorption spectra of the -carboxyalkyl type radicals produced in addition reaction show maxima around 300 nm. This shifts to longer wavelength with time after the pulse. This phenomenon was explained by the oligomerization reaction. From the kinetic curves average rate coefficients of termination for the oligomer radicals (2k_t) were determined as a function of time elapsed after the electron pulse. The values obtained were compared with those calculated for other (acrylate and methacrylate type) monomers.     

Phase separation in blends of two homopolymers and a diblock copolymer during film casting

Demixing during film casting of blends of polystyrene, polymethylmethacrylate, and a symmetric diblock copolymer of styrene and methylmethacrylate is discussed. The concentration fluctuations in the homogeneous solutions were calculated in mean field approximation. The structures in the homogeneous and demixed solutions and in the dry films were measured by small-angle x-ray scattering, and the morphologies of the dry films were characterized by transmission electron microscopy. The structure of the dry blends is evidently already pre-formed in solution.     

Viscoelastic properties of amorphous polymers 3: low molecular weight poly(methylphenylsiloxane)

By making creep and recoverable creep measurements of a nearly monodisperse low molecular weight poly(methyl phenyl siloxane) sample, we have found on decreasing temperature towardsT _g that there is continuously a change in the viscoelastic spectrum concomitant with a decrease of the steadystate recoverable compliance. This behavior is exactly the same as previously observed in low molecular weight poly(styrene), proving that this spectacular anomaly in the viscoelasticity of low molecular weight polymers is general and deserves an explanation. Photon correlation spectroscopic measurements performed on the same sample have extended the observation of the viscoelastic response to shorter times and the result corroborates the trend of variation established by the creep data.Dedicated to Prof.Dr. E. W. Fischer on his 65th Birthday. Prof.Dr. Fischer is known for his valuable contribution to fosterine, international collaboration of research in polymer science. This work is an example of his contribution because it would not be possible without him bringing us together. One of us (KLN) would like to take this opportunity to thank Prof. Dr. Fischer for his unwaiving support of the 1st (Crete) and the 2nd (Alicante) International Discussion Meeting on Relaxations in Complex Systems     

T1Effects in Sequential Dynamic Susceptibility Contrast Experiments

Residual effects of an initial bolus of gadolinium contrast agent have been previously demonstrated in sequential dynamic susceptibility contrast MR experiments. While these residual effects quickly reach a saturation steady state, their etiology is uncertain, and they can lead to spurious estimates of hemodynamic parameters in activation experiments. The possible influence ofT₁effects is now investigated with experiments in whichT₁weighting is varied as well as with serial regionalT₁measurements. Little evidence for significant residualT₁effects is found, suggesting instead that susceptibility effects underlie these observations. An initial saturation dose of contrast agent minimizes this effect.     

Laser spectroscopy of the 1s HFS of H-like ions at a bunched beam in the storage ring ESR

The investigation of the 1s HFS provides a good possibility for testing QED effects in a combination of a strong electric and magnetic field. Here, we report about the laserspectroscopic measurements of the ground state hyperfine splitting in ²⁰⁷Pb⁸¹⁺. To handle this M1-transition in the infrared optical regime with its long lifetime, we developed a new detection technique using a bunched ion beam. For the observation of fluorescence light, a new mirror system is adapted to the emission characteristics from an ion beam at relativistic velocities. This revised version was published online in July 2006 with corrections to the Cover Date.     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

Interactions between the components in isotactic polypropylene blended with EPDM

The interaction of isotactic polypropylene with ethylene propylene diene terpolymer in their blends has been investigated by use of differential scanning calorimetry, dynamic mechanical analysis, wide- and small-angle x-ray scattering, and by investigating the nucleation and kinetics of crystallization of the iPP component under the polarization microscope. It is found, that the dispersion of the EPDM component in the iPP matrix is dependent on blend composition and is maximal at 10% EPDM content. An interface layer between the two components is formed by migration of iPP molecules into the EPDM phase. A model for this interface is proposed.     

FORECASTING MINERAL SUPPLY FROM MINERAL RENT DATA

An optimal control model of exhaustible resources is used to clarify the long run relationship between mineral rent and depletion cost at the industry level. A standard first order condition of the time rate of change of rents is reformulated to reveal that rent data may be used to help forecast the rise in extraction costs resulting from resource depletion. This application of the theory of exhaustible resources is illustrated using historical mineral industry rent and extraction cost data. A forecast of U.S. coal extraction costs, following the method proposed in this paper, suggests that future rates of extraction cost increases will be similar to rates experienced in the past.