Isomorphisms of Brin-Higman-Thompson groups

Let m, m′, r, r′, t, t′ be positive integers with r, r′ ? 2. Let \(\mathbb{L}_r \) denote the ring that is universal with an invertible 1×r matrix. Let \(M_m (\mathbb{L}_r^{ \otimes t} )\) denote the ring of m × m matrices over the tensor product of t copies of \(\mathbb{L}_r \) . In a natural way, \(M_m (\mathbb{L}_r^{ \otimes t} )\) is a partially ordered ring with involution. Let \(PU_m (\mathbb{L}_r^{ \otimes t} )\) denote the group of positive unitary elements. We show that \(PU_m (\mathbb{L}_r^{ \otimes t} )\) is isomorphic to the Brin-Higman-Thompson group tV _r,m ; the case t=1 was found by Pardo, that is, \(PU_m (\mathbb{L}_r )\) is isomorphic to the Higman-Thompson group V _r,m . We survey arguments of Abrams, Ánh, Bleak, Brin, Higman, Lanoue, Pardo and Thompson that prove that t′V _r′,m′ ≌ tV _r,m if and only if r′ =r, t′ =t and gcd(m′, r′?1) = gcd(m, r?1) (if and only if \(M_{m'} (\mathbb{L}_{r'}^{ \otimes t'} )\) and \(M_m (\mathbb{L}_r^{ \otimes t} )\) are isomorphic as partially ordered rings with involution).     

Die Anwendung des Magnesiums als Reagens

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New concepts for radiometric measurements of environmental samples

The Radiation Detection and Nuclear Sciences Group at Pacific Northwest National Laboratory has a long history in conducting measurements of radioisotopes for various applications. This experience includes ultra-low background measurements, arrays of germanium detectors, automated sampling and measurement systems and coincidence measurement systems. A recent lab-supported effort has been studying how these capabilities, both in terms of hardware and experience, can be leveraged to enable environmental sampling measurements. One area of interest is the release of fission products and actinides into the environment from a reactor incident. While the initial survey of this area is still under way, one isotope of interest that surfaced early in the study is ²³⁸Pu. Existing techniques to assay this isotope suffer from measurement challenges. In alpha counting, there can be significant interference with ²⁴¹Am, while in mass spectrometry, there can be interference with ²³⁸U. The authors are developing the concept for a detector that through coincidence counting techniques can distinguish ²³⁸Pu and ²⁴¹Am. In addition, we will design the system to conduct radiometric measurements of other plutonium isotopes to enable a direct comparison of those isotopes. We will present our concept of the detector system for ²³⁸Pu, as well as discuss other radiometric measurements of fission products and actinides with which we intend to advance the state of the art for environmental measurements.     

Investigation of the effect of drying and refining on the fiber–fiber shear bond strength measured using tensile fracture line analysis of sheets weakened by acid gas exposure

No reliable method exists for measuring the cellulose fiber–fiber shear bond strength in paper. This paper reports a simple method for measuring the fiber–fiber shear bond strength by weakening the fibers independently of the bonds in a sheet of paper, using acid vapor, until all the fibers break across the fracture line. The bond strength is then calculated from the fiber strength, as measured by the zero span test, at the point where the fibers first are weakened such that they all break. The method was used to calculate the average bond strength of handsheets made out of two different pulps. The first pulp was a never dried, 60% yield, unbleached radiata pine. The bond strength was 25.0 ± 3.3 MPa. Drying the fibers before reslushing and making sheets reduced the bond strength by up to 33%, with the reduction depending on the severity of the drying treatment. The second pulp was a bleached dried softwood kraft and was used to investigate the effect of low consistency refining on bond strength. The bond strength increased from 13.7 ± 1.0 MPa for the sheets made from the unrefined pulp to 37.0 ± 1.0 MPa, for the sheets made from the most heavily refined pulp. The bond strength measurements are considerably higher than previous literature estimates for the shear bond strength. The causes for the discrepancy include stress concentrations in tests of single fiber–fiber bonds.     

Ionothermal synthesis and crystal structures of metal phosphate chains

We have prepared isostructural aluminium and gallium phosphate chains by ionothermal reactions in 1-ethyl-3-methylimidazolium bromide and 1-ethylpyridinium bromide under a variety of conditions. The chains can be prepared as pure phases or along with three dimensional framework phases. The chains are favoured at shorter heating times and the crystallinity can be improved by addition of transition metal acetates and amines which are not included in the final structure. The chain can be prepared with or without the presence of hydrofluoric acid.     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-Betti numbers of one-relator groups

We determine the L ²-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the L ²-cohomology of left-orderable groups, and deduce the non-L ² result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free. Warren Dicks was Funded by the DGI (Spain) through Project BFM2003-06613.