Krull–Remak–Schmidt Fails for Artinian Modules over Local Rings

Let R be a ring. Any R-module M which is Artinian or Noetherian can be written as the direct sum of a finite number of indecomposable R-modules. The theorem of Krull–Remak–Schmidt asserts that in the case where M is of finite length, such a decomposition is unique up to isomorphism. On the other hand, examples of Noetherian R-modules which have essentially different decompositions have been known for a long time. The first examples of Artinian R-modules with essentially different decompositions were published only in 1995 by Facchini, Herbera, Levy and Vámos. In order to construct such examples, one needs to deal with suitable rings R. Note that for R Noetherian or commutative, all the Artinian modules have the Krull–Remak–Schmidt property. In 1998, Facchini raised the problem of whether the same is true in the case where R is a local ring. The aim of this note is to show that this is not so: we are going to present a local ring R and Artinian R-modules M with essentially different direct decompositions into indecomposables. The military importance of these results has been discussed during the NATO meeting at Constantia (August 2000) which was organized by K. W. Roggenkamp.     

In Situ Observation of Adiabatic Shear Band Formation in Aluminum Alloys

We used high-speed X-ray phase contrast imaging and infrared thermal imaging techniques to study the formation processes of adiabatic shear bands in aluminum 7075-T6 and 6061-T6 alloys. A modified compression Kolsky bar setup was used to apply the dynamic loading. A flat hat-shaped specimen design was adopted for generating the shear bands at the designated locations. Experimental results show that 7075-T6 exhibits less ductility and a narrower shear band than 6061-T6. Maximum temperatures of 720 K and 770 K were locally determined within the shear band zones for 7075-T6 and 6061-T6 respectively. This local high temperature zone and the resulting thermal instability were found to relate to the shear band formation in these aluminum alloys.

     

M-seminorms on spaces of continuous functions

Let U be a realcompact completely regular Hausdorff space, C(U) the vector lattice of all continuous functions on U. We consider representations of M-seminorms on C(U) and some subspaces) by semicontinuous functions on U.     

Phenomenological and Numerical Simulation of Shape Memory Alloys at Finite Strains

A phenomenological material law for pseudo elastic NiTi shape memory alloys (SMA) is presented. The model was derived from a thermodynamical framework and is well-suited to describe the thermomechanical coupled behaviour of the material. The material law, which was originally derived for small deformations, was extended to finite deformations using the Eulerian frame, in particular Hencky's logarithmic strain and the logarithmic rate. A first emphasis is on the physical interpretation of the material parameters and their identification. A second focus lies in the presentation of a structural example for the implementation of the material law into a commercial Finite Element code. Additionally a comparison of the numerical and experimental data of the presented example is performed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Expression and characterization of a recombinant Fusarium spp. galactose oxidase

The Fusarium spp. (Dactylium dendroides) galactose oxidase was expressed in Aspergillus oryzae and Fusarium venenatum hosts. Under the control of an A. niger α-amylase or a Fusarium trypsin promoter, high level galactose oxidase expression was achieved. The recombinant oxidase expressed in the A. oryzae host was purified and characterized. The purified enzyme had a molecular weight of 66 k Da on sodium dodecyl sulfate-polymerase gel electrophoresis (SDS-PAGE) and 0.4 mol copper atom per mole protein. The stoichiometry increased to 1.2 after a Cu saturation. Based on a peroxidase-coupled assay, the enzyme preparation showed an activity of 440 turnover per second toward d-galactose (0.1 M) at pH7 and 20°C. The enzyme had an optimal temperature of 60°C at pH 6.0 and an activation free Gibbs energy of 33 kJ/mol. A series of d-galactose derivatives was tested as the reducing substrate for the oxidase. The difference in activity was interpreted by the stereospecificity of the oxidase toward the substituents in the pyranose substrate, particularly on the C5 and the cyclic hemiacetal O sites. The recombinan toxidase could act on some galactose-containing polysaccharides, such as guar gum, but was not able to oxidize several common redox compounds that lacked a primary alcohol functional group.     

Hamiltonian evolution and quantization for extremal black holes

We present and contrast two distinct ways of including extremal black holes in a Lorentzian Hamiltonian quantization of spherically symmetric Einstein-Maxwell theory. First, we formulate the classical Hamiltonian dynamics with boundary conditions appropriate for extremal black holes only. The Hamiltonian contains no surface term at the internal infinity, for reasons related to the vanishing of the extremal hole surface gravity, and quantization yields a vanishing black hole entropy. Second, we give a Hamiltonian quantization that incorporates extremal black holes as a limiting case of nonextremal ones, and examine the classical limit in terms of wave packets. The spreading of the packets, even the ones centered about extremal black holes, is consistent with continuity of the entropy in the extremal limit, and thus with the Bekenstein-Hawking entropy even for the extremal holes. The discussion takes place throughout within Lorentz-signature spacetimes.     

Ruthenium Trichloride,Tricyclohexyl- phosphane, 1-Alkynes,Magnesium, Hydrogen,and Water—Ingredients of an Efficient One-Pot Synthesis of Ruthenium Catalysts for Olefin Metathesis

An active role is played by MgCl₂ during the conversion of the vinylidene precursor 2 into carbenes 3 (R=H, Ph; L=P(C₆H₁₁)₃). These complexes can be prepared in a convenient and very efficient one-pot synthesis and have a catalytic activity in metathesis comparable to that of Grubbs compound (Ph instead of CH₂R).     

Isocyanate-Based Dendritic Building Blocks: Combinatorial Tier Construction and Macromolecular-Property Modification

Used individually or combinatorially , unique isocyanate-based dendritic monomers generate homo- and heterofunctional materials (the sketch shows schematically a molecule with a heterofunctional surface). Tier construction by combinatorial monomer addition offers new avenues to macromolecular architectural design and the control of physical properties.