On the numerical radius of matrices and its application to iterative solution methods

Uses of the numerical radius in the analysis of basic iterative solution methods, of the SOR method for quasi-Hermitian positive definite matrices (not being consistently ordered) and of maximal eigenvalues of symmetric positive definite matrices using incomplete block-matrix factorizations are presented.     

Determination of trace amounts of calcium and barium in caustic soda

Zusammenfassung Es wird gezeigt, daß bei der komplexometrischen Titration von Calcium bei pH 12,2 zum visuellen Endpunkt des Mischindicators von Calcein und Thymolphthalein [4] das Barium quantitativ mittitriert wird. Eine verbesserte Methode wird nun für die Bestimmung von sowohl Calcium als auch Barium in 50% igen Ätznatronlösungen beschrieben. Nach einer Vortrennung und Anreicherung durch Ionenaustausch wird die Summe von Calcium und Barium durch Titration mit ÄDTA-Lösung bei pH 12,2 bestimmt. Barium wird dann durch Sulfat aus dem ÄDTA-Komplex freigesetzt und die äquivalente Menge ÄDTA durch Zugabe einer bekannten Menge Calcium im Überschuß und Titration des Überschusses mit ÄDTA bestimmt.     

Biologically derived value-added products from coal

The Idaho National Engineering Laboratory (INEL) has for several years conducted research in the area of coal bioprocessing. Fundamental and exploratory research has been directed toward the conversion of coal to cleaner fuels and the remediation of harmful byproducts of coal utilization. Specific research projects have involved coal depolymerization, coal solubilization, removal of organosulfur and pyritic sulfur from coal, the molecular biology of coal-modifying microorganisms, removal of ash-forming minerals from coal, conversion of coal combustion gases, and the development of novel coal bioreactors. Notable research accomplishments include elucidation of mechanisms by which microorganisms solubilize different portions of coal, discovery and characterization of microorganisms capable of depolymerizing macromolecular coal, discovery of microorganisms capable of removing organosulfur from coal, development of technologies critical to analyzing biologically mediated depolymerization and organosulfur removal, novel methods of pyritic sulfur removal, novel methods of removal (and conversion) of CO₂, SO_x, and NO_x from combustion gases, and new technologies for bioconversion of waste gypsum generated in coal combustion gas scrubbers.     

Experimental comparison of three-dimensional point and line modified incomplete factorizations

We examine how the variations of the coefficients of 3-dimensional (3D) partial differential equations (PDEs) influence the convergence of the conjugate gradient method, preconditioned by standard pointwise and linewise modified incomplete factorizations. General analytical spectral bounds obtained previously are applied, which displays the conditions under which good performances could be expected. The arguments also reveal that, if the total number of unknowns is very large or the number of unknowns in one direction is much larger than in both other ones, or if there are strong jumps in the variation of the PDE coefficients or fewer Dirichlet boundary conditions, then linewise preconditionings could be significantly more efficient than the corresponding pointwise ones. We also discuss reasons to explain why in the case of constant PDE coefficients, the advantage of preferring linewise methods to pointwise ones is not as pronounced as in 2D problems. Results of numerical experiments are reported. This revised version was published online in June 2006 with corrections to the Cover Date.