A Geometric Invariant for Metabelian Pro-p Groups

In [2] Bieri and Strebel introduced a geometric invariant forfinitely generated abstract metabelian groups that determineswhich groups are finitely presented. For a valuable survey oftheir results, see [6]; we recall the definition briefly inSection 4. We shall introduce a similar invariant for pro-pgroups. Let F be the algebraic closure of F_p and U be the formal powerseries algebra F[T], with group of units U^x. Let Q be a finitelygenerated abelian pro-p group. We write Z_p[Q] for the completedgroup algebra of Q over Z_p. Let T(Q) be the abelian group Hom(Q,U^x) of continuous homomorphisms from Q to U^x. We write 1 forthe trivial homomorphism. Each vT(Q) extends to a unique continuousalgebra homomorphism from Z_p[Q]to U.     

Heterogeneous reactions of sulfur dioxide with carbonaceous particles

The rate of adsorption of SO₂ on a prototype carbonaceous surface was measured at low pressure in a flow reactor. The measured rate indicates a maximum atmospheric loss of SO₂ by heterogeneous reaction of 1%/h for a particle density of 100 μg/m³. The capacity of carbon particles to adsorb SO₂ is limited at ～1 mg SO₂ g^?1 C. NO₂ has no effect on the rate of SO₂ adsorption or the saturation behavior.     

Approaches to the regiospecific synthesis of Anthracycline antibiotics

Synthetic approaches to anthracycline antibiotics were studied through the use of Claisen rearrangements on 1-methallyloxy-5-methoxyantraquinone (9) which required reducing conditions to proceed through a hydroquinone intermediate in situ. 1-(2′-Methylene-4′-pentenoxy)-5-methoxyanthraquinone (13) underwent a similar reductive rearrangement but also produced a spiro compound 16 as a result of an ene reaction between the phenol and side chain double bond. 1-Hydroxy-2-methally-5-methoxyanthraquinone (11) could not be oxidized to quinizarin 17. 1-Hydroxy-2-methally-5,9,10-trimethoxyanthracene (21) was oxidatively coupled to the dimer at C-2. Dimer 23 reacted with diazomethane to form a 1,3-dipolar adduct 24.     

The stereochemistry of cyclisation of n-t-butyldihydrocinnamamide to a β-lactam

Using a stereospecifically labelled precursor, the peroxide catalysed cyclisation of N-$\text{t}$-butyldihydrocinnamamide to the corresponding β-lactam was shown to proceed with complete loss of stereochemistry at the benzylic carbon atom.     

Crystal and molecular structure of diaquobis(1,1′-dimethyl-2,2′-diimidazolylsulfide)copper(II) methylsulfate, (C8H10N4S)2Cu(II)(OH2)2(CH3OS03)2

The crystal and molecular structure of the title complex has been determined. The space group isP2₁/n, witha=8.460(3),b=8.503(3),c=20.341 (8) Å,=98.41(3) andZ=2. The ligand molecules chelate the Cu^II such that the metal has a tetragonally distorted octahedral geometry; four N atoms occupy the equatorial plane and two H₂O molecules occupy the axial positions. The average Cu-N and Cu-O distances are 2.005(6) and 2.47(1) Å, respectively. The novel ligand, 1,1-dimethyl-2,2-diimidazolylsulfide was formedin situ from a methanolic solution of copper(II) sulfate pentahydrate and 1-methylimidazole-2-thiol. The measured spectral parameters (visible, EPR, and photoelectron spectroscopy) correlate well with the molecular structure.     

Viscoelastic shear properties of in vivo breast lesions measured by MR elastography

Elastography is a technique to assess the viscoelastic properties of tissue by measuring an acoustic wave propagating though the object. Here, the technique is applied in the course of standard MR mammography to 15 patients with different pathologies (six breast cancer cases, six fibroadenoma cases and three mastopathy cases). Low-frequency mechanical waves are coupled longitudinally into the tissue in order to obtain sufficient wave amplitude throughout the entire breast. This leads to the presence of a substantial fraction of compressional waves, which contribute to the total displacement field. It is shown theoretically that the correct evaluation of these contributions from the compressional wave is rather difficult due to the almost incompressible nature of tissue. To overcome this problem, it is proposed to apply the curl-operator to the measured displacement field in order to completely remove contributions from the compressional wave. Results from simulations and a breast phantom demonstrate the feasibility of the technique. The in vivo results show a good separation between breast cancer and benign fibroadenoma utilizing the shear modulus. Breast cancer appears on average 2.2 (P<.001) times stiffer. All breast cancer cases showed a good delineation to the surrounding breast tissue with an average elevation of a factor of 3.3 (P< 1.4 x 10(-6)). The results as obtained for the shear viscosity do not indicate to be useful for separating benign from malignant lesions.     

A novel oxidative rearrangement of 6-methoxypyran-2-ones

As part of our continuing studies of pyrone-containing natural products, a series 6-methoxypyran-2-ones were synthesized. These were found to react with molecular oxygen at 20 degrees C, and this novel reaction yielded a series of highly functionalized alpha,beta-butenolides. [reaction: see text]