Algorithms for the matrix <Emphasis Type="Italic">p</Emphasis>th root

New theoretical results are presented about the principal matrix pth root. In particular, we show that the pth root is related to the matrix sign function and to the Wiener–Hopf factorization, and that it can be expressed as an integral over the unit circle. These results are used in the design and analysis of several new algorithms for the numerical computation of the pth root. We also analyze the convergence and numerical stability properties of Newtons method for the inverse pth root. Preliminary computational experiments are presented to compare the methods. AMS subject classification 15A24, 65H10, 65F30Numerical Analysis Report 454, Manchester Centre for Computational Mathematics, July 2004.Dario A. Bini: This work was supported by MIUR, grant number 2002014121.Nicholas J. Higham: This work was supported by Engineering and Physical Sciences Research Council grant GR/R22612 and by a Royal Society – Wolfson Research Merit Award.     

Hartmagnetische Legierungen der Seltenen Erdmetalle mit 3d-Metallen

The phase relations obtained from alloys of the rare-earth metals (RE) with 3d-metals are initially discussed, as well as the crystal structures and the general physical properties of the corresponding intermetallic compounds. The magnetic properties of RE-3d-compounds and the essential data of a hard-magnetic material are then summarized. The different steps in the production of RE-Co-permanent magnets are reviewed in relation to the underlying basic physical mechanisms. Finally, other possible hard-magnetic RE-3d-alloys and some general trends of physical and metallurgical investigations, necessary for the improvement of the RECo₅-magnets, are outlined.

     

Chromatic uniqueness of the generalized θ-graph

A generalized θ-graph in a connected graph with 3 paths between a pair of vertices of degree 3. It is shown that any graph having the same chromatic polynomial as a generalized θ-graph, must be isomorphic to the generalized θ-graph.     

Beta-D-galactopyranosyl azide: its one-step quantitative synthesis using E461G-beta-galactosidase (Escherichia coli) and a demonstration of its potential as a reagent for molecular biology

A simple one-step synthesis of β-d-galactopyranosyl azide from 0-nitrophenyl-β-d-galactopyranoside and azide catalyzed by E461G-β-galactosidase is described. The synthesis is quantitative in the presence of excess azide and only the β anomer is produced. The product was purified (71% yield) from the other reaction components by extraction with ethyl acetate, silica gel chromatography, and crystallization. The purity was verified by GLC, TLC, and NMR. Thus, E461G-β-galactosidase is able to specifically and quantitatively from β-d-galactopyranosyl-azide. The purified β-d-galactopyranosylazide inhibited the growth of Escherichia coli that express β-galactosidase but not of E. coli that do not. Growth is stopped because β-galactosidase catalyzes the hydrolysis of the β-galactopyranosyl-azide, and the azide that is produced inhibits cell growth. This selective inhibition of growth has potential application in molecular biology screening.     

Mass spectrometry and chemical synthesis. The case of some substituted Spiro[1,3-benzodioxole-2,1′-cyclohexanes]

The electron impact mass spectrometric behaviour of some substituted spiro[1,3-benzodioxole-2,1′-cyclohexanes] has been studied in detail with the aid of linked scans and exact mass measurements. Mass spectrometry has proved to be a valid tool in the structural characterization of the different couples of isomers.     

CIDNP.-Investigation of Photoinduced Polymerization

The photochemistry and some initiator characteristics of the polymerization initiators ω,ω-dimethoxy-ω-phenyl-acetophenone ( A ), ω,ω-diethoxy-acetophenone ( B ) and ω,ω-diisopropoxy-acetophenone ( C ) have been studied by ¹H- and ¹³C-chemically-induced nuclear polarization (CIDNP.) experiments. The primary reaction of initiator A is a Norrish-type I cleavage, while for B and C Norrish-type I and Norrish-type II cleavages are of comparable importance. Three different recombination products could be detected for initiator A which correspond to the three canonical resonance forms of the substituted benzyl radical. In a number of polymerization experiments the competition between reactions among initiator radicals and reactions of initiator radicals with the monomer acrylic acid methyl ester was studied at low concentrations of the monomer. These experiments give insight into the first steps of the polymerization process. The positive sign of the α-hydrogen hyperfine couplings of the dimethoxy-methyl- and the diisoproproxymethyl-radicals could be established, in agreement with the deviation of these radicals from planarity. A slow square-wave light-modulation technique has been employed in ¹³C-FT.-experiments to measure absolute CIDNP.-intensities.     

Structural approach to the permeability aftereffect in zero- magnetostrictive amorphous alloys

Magnetic aftereffects are a general feature of both magnetostrictive and zero-magnetostriction amorphous ferromagnetic materials. It is shown, that the existence of magnetic relaxation effects in zeromagnetostrictive amorphous ferromagnets can be explained within a recently proposed structural approach, by taking into account the nonisotropic character of the local magnetostrictive strain.     

Significance of the Geminal Dimethyl Group in the Odor Principle of Ambrox®

The diastereoisomeric 18-nor- and 19-norambrox ((6α)- and (6β)-dodecahydro-3a,6,9a-trimethylnaphtho[2,1-b]furans resp.) as well as the corresponding 18,19-dinor-derivatives (dodecahydro-3a,9a-dimethylnaphtho[2,1-b]furans) have been synthesized and subjected to sensory evaluation. Threshold data and odor determination give an enlarged insight into the structure-activity relationship (SAR) in ambrox-type ambergris fragrances. As a general conclusion, the accumulation of axial CH₃ groups in the tricyclic ethers 1 – 12 leads to the strongest receptor affinity.     

Transport properties in the pseudobinary (Gd,Y) Al2 series

The temperature dependence of the electrical resistivity, the thermal conductivity and the thermopower of the cubic isostructural (Gd_xY_1–x)Al₂ series will be presented. The magnetic properties of this system are characterized by the existence of ferromagnetism for Gd concentrations x>0.3 while for low Gd contents cluster and spinglass behaviour is observed. The spin dependent scattering contribution to the transport phenomena has been obtained by comparing the experimental data of the magnetic compounds with those of the isostructural nonmagnetic YAl₂. For the ferromagnetic concentration range and forT>T _c (T _c =Curie temperature) we revealed a temperature independent contribution to the electrical resistivity, a contribution with a temperature variation of 1/T to the thermal resistivity and a linear temperature dependence of this part to the thermopower. These results are in good agreement with the temperature dependence calculated by solving the linearized Boltzmann equation for this type of scattering processes.