Field-of-values analysis of preconditioned iterative methods for nonsymmetric elliptic problems

Summary. The convergence rate of Krylov subspace methods for the solution of nonsymmetric systems of linear equations, such as GMRES or FOM, is studied. Bounds on the convergence rate are presented which are based on the smallest real part of the field of values of the coefficient matrix and of its inverse. Estimates for these quantities are available during the iteration from the underlying Arnoldi process. It is shown how these bounds can be used to study the convergence properties, in particular, the dependence on the mesh-size and on the size of the skew-symmetric part, for preconditioners for finite element discretizations of nonsymmetric elliptic boundary value problems. This is illustrated for the hierarchical basis and multilevel preconditioners which constitute popular preconditioning strategies for such problems. Received May 3, 1996     

Quecksilber(II)‐chlorid‐ und ‐iodid‐Komplexe von Dithia‐ und Tetrathiakronenethern

Mercury(II) Chloride and Iodide Complexes of Dithia‐ and Tetrathiacrown Ethers The complexes [(HgCl₂)₂((ch)₂30S₄O₆)] ( 1 ), [HgCl₂(mn21S₂O₅)] ( 2 ), [HgCl₂(ch18S₂O₄)] ( 3 ) and [HgI(meb12S₂O₂)]₂[Hg₂I₆] ( 4 ) have been synthesized, characterized and their crystal structures were determined. In [(HgCl₂)₂((ch)₂30S₄O₆)] two HgCl₂ units are discretely bonded within the ligand cavity of the 30‐membered dichinoxaline‐tetrathia‐30‐crown‐10 ((ch)₂30S₄O₆) forming a binuclear complex. HgCl₂ forms 1 : 1 “in‐cavity” complexes with the 21‐membered maleonitrile‐dithia‐21‐crown‐7 (mn21S₂O₅) ligand and the 18‐membered chinoxaline‐dithia‐18‐crown‐6 (ch18S₂O₄) ligand, respectively. The 12‐membered 4‐methyl‐benzo‐dithia‐12‐crown‐4 (meb12S₂O₂) ligand gave with two equivalents HgI₂ the compound [HgI(meb12S₂O₂)]₂[Hg₂I₆]. In the cation [HgI(meb12S₂O₂)]⁺ meb12S₂O₂ forms with the cation HgI⁺ a half‐sandwich complex.     

In situ observations of water production and distribution in an operating H2/O2 PEM fuel cell assembly using 1H NMR microscopy

Proton NMR imaging was used to investigate in situ the distribution of water in a polymer electrolyte membrane fuel cell operating on H2 and O2. In a single experiment, water was monitored in the gas flow channels, the membrane electrode assembly, and in the membrane surrounding the catalysts. Radial gradient diffusion removes water from the catalysts into the surrounding membrane. This research demonstrates the strength of 1H NMR microscopy as an aid for designing fuel cells to optimize water management.     

A hybrid Arnoldi-Faber iterative method for nonsymmetric systems of linear equations

Summary We present here a new hybrid method for the iterative solution of large sparse nonsymmetric systems of linear equations, say of the formAx=b, whereA ^{N, N} , withA nonsingular, andb ^N are given. This hybrid method begins with a limited number of steps of the Arnoldi method to obtain some information on the location of the spectrum ofA, and then switches to a Richardson iterative method based on Faber polynomials. For a polygonal domain, the Faber polynomials can be constructed recursively from the parameters in the Schwarz-Christoffel mapping function. In four specific numerical examples of non-normal matrices, we show that this hybrid algorithm converges quite well and is approximately as fast or faster than the hybrid GMRES or restarted versions of the GMRES algorithm. It is, however, sensitive (as other hybrid methods also are) to the amount of information on the spectrum ofA acquired during the first (Arnoldi) phase of this procedure.     

Qualitative and quantitative analysis of carbohydrates in green juices (wild mix grass and alfalfa) from a green biorefinery by gas chromatography/mass spectrometry

Green juices from biorefinery original raw material (wild mix grass and alfalfa after wet fractionation and protein separation) have been investigated by gas chromatography/mass spectrometry. The carbohydrates, involved in the green juices, were derivatized and identified by both their retention times in the gas chromatogram and EI mass spectra compared to those of pure reference compounds. Additionally, chemical ionization mass spectra were recorded for better characterizing the carbohydrates present. The carbohydrates which could thus be identified, were quantified by response signals with respect to that of the internal standard beta-phenyl-D-glucopyranoside.     

Monodentate sigma-N and Bidentate sigma-N,sigma-N' Coordination of 1,1-Bis((N-p-tolylimino)diphenylphosphoranyl)ethane, CHCH(3)(PPh(2)=NC(6)H(4)-4-CH(3))(2), to Platinum(II)

The new ligand, 1,1-bis((N-p-tolylimino)diphenylphosphoranyl)ethane (1,1-BIPE), 1, has been synthesized by means of a Staudinger reaction of 1,1-bis(diphenylphosphino)ethane (1,1-dppe) with 2 equiv of p-tolylazide. Bridge-splitting reactions of Pt(2)Cl(4)(PR(3))(2) with 1 readily afforded sigma-N monodentate complexes, [PtCl(2)(PR(3)){1,1-BIPE-sigmaN}] (2a, PR(3) = PEt(3); 2b, PR(3) = PMe(2)Ph). Conversion of 2 into the six-membered platinacycle [PtCl(PR(3)){1,1-BIPE-sigmaN,sigmaN'}](+)[X](-) (3) (X = Cl, PtCl(3)(PR(3)), BF(4)) took place after prolonged stirring, its reaction rate being strongly dependent on the type of phosphine (>5 days for 2ain the presence of NaBF(4), 1 h for 2b) and the metal-to-ligand ratio. The compounds 1, 2, and 3 have been fully characterized by (1)H, (31)P{(1)H}, and (13)C{(1)H} NMR and IR spectroscopy, elemental analysis, or FAB mass spectroscopy. The molecular structures of CHCH(3)(PPh(2)=NC(6)H(4)-4-CH(3))(2) (1) and [PtCl(PMe(2)Ph){(N(pTol)=PPh(2))(2)CHCH(3)}](+)[Cl](-) (3b) have been determined by X-ray crystallography. Crystal data for 1: space group P2(1)/c with a = 8.9591(5) ?, b = 19.1961(12) ?, c = 21.9740(9) ?, beta = 105.069(4) degrees, V = 3649.1(3) ?(3), and Z = 4. The structure refinement converged to R = 0.080 and R(w) = 0.109. Crystal data for 3b: monoclinic, space group P2(1)/c with a = 12.4021(7) ?, b = 16.9705(11) ?, c = 23.760(2) ?, beta = 109.544(5) degrees, V = 4712.7(5) ?(3), and Z = 4. The structure refinement converged to R1 = 0.057, wR2 = 0.122. Variable temperature NMR spectroscopy has revealed that complexes 3 exclusively adopt a twisted boat conformation with the methyl group in equatorial position at low temperature, in agreement with the solid state structure of 3b as determined by X-ray crystallography. Boat-to-boat inversion is assumed to take place at temperatures above 293 K. Furthermore, for 3, hindered rotation of one of the p-tolyl substituents on nitrogen has been established at low temperatures.     

Formation of Iron-Carbon Nanoparticles behind Shock Waves

An attempt was made to obtain iron-carbon nanoparticles by two-step pyrolysis of Fe(CO)₅- and C₃O₂-containing mixtures behind incident and reflected shock waves in a shock tube. The formation of binary particles was monitored by recording the extinction of He-Ne laser radiation and laser-induced incandescence (LII). The LII method provides particle size estimates if the thermal and optical properties of the constituting material are known. Behind an incident shock wave, at temperatures of 700–1500 K, Fe(CO)₅ decomposes within a short period of time (∼50 µs). The resulting iron atoms combine into particles, which serve as condensation nuclei for carbon vapor resulting from C₃O₂ pyrolysis at 1500–3000 K behind the reflected shock wave. The binary particles thus produced are considerably larger than pure carbon or iron particles. As the mixture temperature behind the reflected shock wave is raised, the diameter of these binary particles decreases.__________Translated from Kinetika i Kataliz, Vol. 46, No. 3, 2005, pp. 333–343.Original Russian Text Copyright © 2005 by Gurentsov, Eremin, Roth, Starke.Based on a report at the VI Russian Conference on Mechanisms of Catalytic Reactions (Moscow, October 1–5, 2002).     

Sensitivities and detection limits of X-ray fluorescence analysis with a 10 mCi<Superscript>241</Superscript>Am source

A method is discussed, which is preferentially used for rapid analyses. After fusion of the sample with dipotassium disulphate and dissolution of the molten mass in water, antimony is titrated with potassium bromate in hydrochloric solution without separating the matrix. 5–7% of Sb can be determined with a standard deviation of 0.04%.