Mediated amperometric biosensors for d-galactose,glycolate and l-amino acids based on a ferrocene-modified carbon paste electrode

Direct-current cyclic voltammetry is used to investigate the suitability of a ferrocene derivative as a mediator with galactose, glycolate and l-amino acid oxidases. The three enzymes coupled catalytically to ferrocene monocarboxylic acid exhibiting homogeneous second-order rate constants in the range 0.4 × 10⁵ to 8.5 × 10⁵ l mol^?1 s^?1. Enzyme electrodes which responded to d-galactose, glycolate or l-amino acids were constructed. The appropriate oxidase was retained behind a dialysis membrane at a carbon paste electrode containing the poorly soluble derivative 1,1′-dimethylferrocene. All the electrodes responded rapidly to millimolar concentrations of their respective substrates producing 95% of the steady-state current response in <2 min. This general method of biosensor construction should be widely applicable to oxidases and other oxidoreductase enzymes.     

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).     

<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.     

On hyperbolic once-punctured-torus bundles II: fractal tessellations of the plane

We describe fractal tessellations of the complex plane that arise naturally from Cannon–Thurston maps associated to complete, hyperbolic, once-punctured-torus bundles. We determine the symmetry groups of these tessellations. To our wives, Ardyth and Elena.     

Free algebras over Bezout domains are Sylvester domains

Let λ be a finitary geometric theory and δ its classifying topos. We prove that δ is Boolean if and only if (1) every first-order formula in the language of λ is ?-provably equivalent to a geometric formula and (2) for any finite list of varibles, x, there are, up to ?-provable equivalence, only finitely many formulas, in the language of λ with free variables among x. We use this characterization to show that, when δ is Boolean, it is an atomic topos and can be viewed as a finite coproduct of topoi of continuous G-sets for topological groups G satisfying a certain finiteness condition.     

Coherent control of ultracold molecule dynamics in a magneto-optical trap by use of chirped femtosecond laser pulses

We have studied the effects of chirped femtosecond laser pulses on the formation of ultracold molecules in a Rb magneto-optical trap. We have found that application of chirped femtosecond pulses suppressed the formation of (85)Rb and (87)Rb(2) a(3)sigma(+)(u) molecules in contrast to comparable nonchirped pulses, cw illumination, and background formation rates. Variation of the amount of chirp indicated that this suppression is coherent in nature, suggesting that coherent control is likely to be useful for manipulating the dynamics of ultracold quantum molecular gases.     

Weight 2 CM newforms as p-adic limits

The Ramanujan Journal - Previous works have shown that certain weight 2 newforms are p-adic limits of weakly holomorphic modular forms under repeated application of the U-operator. The proofs of...     

The EcoScale as a framework for undergraduate green chemistry teaching and assessment

An upper-year undergraduate practical examination is presented that utilizes the EcoScale (a semi-quantitative tool) and several established mass metrics to assess student understanding of green chemistry principles. This activity focuses on the straightforward preparation of a benzodiazepine via three different catalytic methods, and the analysis of individual experimental data during laboratory time. Students learn about the structure of the EcoScale, apply it as a simplistic life cycle assessment, and critique it as a scientific model. The examination complements more traditional expository and self-design experiments within a synthetic course where green chemistry and sustainability are central themes.