An isomorphism between group C*-algebras of ax + b-like groups

We give a necessary and sufficient condition for two ax+b-like groups to have isomorphic C*-algebras. In particular, we show that there are many non-isomorphic ax+b -like Lie groups having isomorphic group C*-algebras.

The C*-algebra of ax+b-like groups

We describe the C*-algebras of " ax+b" -like groups in terms of algebras of operator fields defined over their dual spaces.

Exchange systems and style in the Central Mediterranean. 4500-1700 b.c..:Unpublished PhD. Cambridge University Library

Malone, C.A.T., 1986, Unpublished PhD, Cambridge University, Cambridge.

Human B cell colony growth from pre-B cells in vitro

We describe a simple one-step technique for the growth of human B cell colonies in semi-solid agar in vitro. This method used conditioned medium from the human plasmacytoma cell line LICR-LON-H My 2 as a source of stimulating activity. A linear relationship exists between the number of B cells seeded and the number of colonies formed (r = 0.95). Most colony forming cells, approximately 1 in 500 of B cells seeded, lack surface immunoglobulin, possess Fc receptors and mark with the Leu 12 monoclonal antibody. Cells within developing colonies are found to have cytoplasmic IgM, IgA and IgG depending on the length of time in culture.

Regulation of TGF-β1-Driven Differentiation of Human Lung Fibroblasts: Emerging Roles of Cathepsin B and Cystatin C

Lung matrix homeostasis partly depends on the fine regulation of proteolytic activities. We examined the expression of human cysteine cathepsins (Cats) and their relative contribution to TGF-β1-induced fibroblast differentiation into myofibroblasts. Assays were conducted using both primary fibroblasts obtained from patients with idiopathic pulmonary fibrosis (IPF) and human lung CCD-19Lu fibroblasts. Pharmacological inhibition and genetic silencing of Cat B diminished α-smooth muscle actin expression, delayed fibroblast differentiation and led to an accumulation of intracellular 50-kDa TGF-β1. Moreover addition of Cat B generated 25-kDa mature form of TGF-β1 in Cat B siRNA-pretreated lysates. Inhibition of Cat B decreased Smad 2/3 phosphorylation, but had no effect on p38 MAPK and JNK phosphorylation indicating that Cat B mostly disturbs TGF-β1-driven canonical Smad signaling pathway. While mRNA expression of cystatin C was stable, its secretion, which was inhibited by brefeldin A, increased during TGF-β1-induced differentiation of IPF and CCD-19Lu fibroblasts. In addition cystatin C participated in the control of extracellular Cats, since its gene silencing restored their proteolytic activities. These data support the notion that Cat B participates in lung myofibrogenesis as suggested for stellate cells during liver fibrosis. Moreover, we propose that TGF-β1 promotes fibrosis by driving the effective cystatin C-dependent inhibition of extracellular matrix-degrading Cats.

Interpreting A-level Mathematics grades – as easy as A, B, C?

Many concerns have been expressed that students’ basic mathematical skills have deteriorated during the 1990s and there has been disquiet that current A-level grading does not distinguish adequately between the more able students. This study reports the author’s experiences of teaching maths to large classes of first-year engineering students and aims to enhance understanding of levels of mathematical competence in more recent years. Over the last four years, the classes have consisted of a very large proportion of highly qualified students – about 91% of them had at least grade B in A-level Mathematics. With a small group of students having followed a non-traditional route to university (no A-level maths) and another group having benefitted through taking A-level Further Mathematics at school, the classes have contained a very wide range of mathematical backgrounds. Despite the introductory maths course at university involving mainly repetition of A-level material, students’ marks were spread over a very wide range – for example, A-level Mathematics grade B students have scored across the range 16 – 97%. Analytical integration is the topic which produced the largest variation in performance across the class but, in contrast, the A-level students generally performed well in differentiation. Initial analysis suggests some stability in recent years in the mathematical proficiency of students with a particular A-level Mathematics grade. Allowing choice of applied maths modules as part of the A-level maths qualification increases the variety of students’ mathematical backgrounds and their selection from mechanics, statistics or decision maths is not clear from the final qualification.

Asymmetric Total Synthesis of (+)-Inthomycin C Via O-Directed Free Radical Alkyne Hydrostannation with Ph3SnH and Catalytic Et3B: Reinstatement of the Zeeck-Taylor (3R)-Structure for (+)-Inthomycin C

A new pathway to (+)-inthomycin C is reported that exploits an O-directed free radical hydrostannation reaction on (−)-12 and a Stille cross-coupling as key steps. Significantly, the latter process was effected on 19 where a gauche-pentane repulsive interaction could interfere. Our stereochemical studies on the alkynol (−)-12 and the enyne (+)-7 confirm that Ryu and Hatakeyama’s (3S)-stereochemical revision of (+)-inthomycin C is invalid and that Zeeck and Taylor’s original (3R)-stereostructure for (+)-inthomycin C is correct.

Synthesis of the C(7)-C(22)-Sector of (+)-Acutiphycin Via O-Directed Double Free Radical Alkyne Hydrostannation with Ph3SnH/Et3B, Double I-Sn Exchange and Double Stille Coupling

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Herein a new double O-directed free radical hydrostannation reaction is reported on the structurally complex dialkyldiyne 11. Through our use of a conformation-restraining acetal to help prevent stereocenter-compromising 1,5-H-atom abstraction reactions by vinyl radical intermediates, the two vinylstannanes of 10 were concurrently constructed with high stereocontrol using Ph3SnH/Et3B/O2. Distannane 10 was thereafter elaborated into the bis-vinyl iodide 9 via O-silylation and double I–Sn exchange; double Stille coupling of 9, O-desilylation, and oxidation thereafter furnished 8.