Short and Sweet: D‐Glucose to L‐Glucose and L‐Glucuronic Acid

The scarcity and expense of access to L ‐sugars and other rare sugars have prevented the exploitation of their biological potential; for example D ‐psicose, only recently available, has been recognized as an important new food. Here we give the definitive and cheap synthesis of 99.4% pure L ‐glucose from D ‐glucose which requires purification of neither intermediates nor final product other than extraction into and removal of solvents; a simple crystallization will raise the purity to >99.8%.     

On Transfer Operators for Continued Fractions with Restricted Digits

For any non-empty subset I of the natural numbers, let _I denotethose numbers in the unit interval whose continued fractiondigits all lie in I. Define the corresponding transfer operator for , where Re (rß) = _I is the abscissa of convergence of the series . When acting on a certain Hilbert space H_I, rß, weshow that the operator L_I, rß is conjugate to an integraloperator K_I, rß. If furthermore rß is real,then K_I, rß is selfadjoint, so that L_I, rß: H_I, rß H_I, rß has purely real spectrum.It is proved that L_I, rß also has purely real spectrumwhen acting on various Hilbert or Banach spaces of holomorphicfunctions, on the nuclear space C [0, 1], and on the Fréchetspace C [0, 1]. The analytic properties of the map rß L_I, rßare investigated. For certain alphabets I of an arithmetic nature(for example, I = primes, I = squares, I an arithmetic progression,I the set of sums of two squares it is shown that rß L_I, rß admits an analytic continuation beyond thehalf-plane Re rß > _I. 2000 Mathematics SubjectClassification 37D35, 37D20, 30B70.     

Cosmetic Electrochemistry II: Rapid and Facile Production of Metallic Electrocatalytic Ensembles

We demonstrate a facile methodology for the production of metallic electrocatalytic microdomain ensembles for a range of analytical sensing challenges. A commercially available off‐the‐shelf cosmetic product can change the voltammetric characteristics of a metallic macro‐electrode created electrolytically into that of a random ensemble of metallic microelectrode domains. Proof‐of‐concept is shown for three examples: a palladium ensemble for hydrazine sensing, a gold ensemble for arsenic(III) detection via anodic stripping voltammetry and platinum ensembles for the direct oxidation of arsenic(III). Last we demonstrate that the fabrication of metallic microdomains can be simplified by sputter coating screen printed electrochemical sensing platforms which are beneficially constructed using this cosmetic methodology. Given the facile fabrication and low cost of the underlying electrode substrate and the cosmetic modifier, the widespread implementation of this novel fabrication methodology is expected.     

Looking-glass synergistic pharmacological chaperones: DGJ and L-DGJ from the enantiomers of tagatose

The enantiomers of tagatose are converted to L-DGJ [a noncompetitive inhibitor of human lysosome α-galactosidase A (α-Gal A), K(i) 38.5 μM] and DGJ [a competitive inhibitor of α-Gal A, K(i) 15.1 nM] in 66% yield. L-DGJ and DGJ provide the first examples of pharmacological chaperones that (a) are enantiomeric iminosugars and (b) have synergistic activity with implications for the treatment of lysosomal storage disorders and other protein deficiencies.     

Cohomology classes of dynamically non-negative Ck functions

Let T:x↦2x (mod 1) be the doubling map of the circle ?=ℝ/ℤ. We construct a trigonometric polynomial f:?→ℝ with the following property: ∫f  dμ≥0 for every T-invariant probability measure μ, so that f is cohomologous to a non-negative Lipschitz function, yet f is not cohomologous to any non-negative C ¹ function. Oblatum 28-VI-2001 & 4-X-2001?Published online: 18 January 2002     

On sums of powers of inverse complete quotients

For an irrational number , let denote its -th continued fraction inverse complete quotient, obtained by deleting the first partial quotients. For any positive real number , we establish the optimal linear bound on the sum of the -th powers of the first complete quotients. That is, we find the smallest constants such that for all and all irrationals .

     

Rigorous Computation of Diffusion Coefficients for Expanding Maps

For real analytic expanding interval maps, a novel method is given for rigorously approximating the diffusion coefficient of real analytic observables. As a theoretical algorithm, our approximation scheme is shown to give quadratic exponential convergence to the diffusion coefficient. The method for converting this rapid convergence into explicit high precision rigorous bounds is illustrated in the setting of Lanford’s map \(x\mapsto 2x +\frac{1}{2}x(1-x) \pmod 1 \).     

Metallic Free Carbon Nanotube Cluster Modified Screen Printed Electrodes for the Sensing of Nicotine in Artificial Saliva

We demonstrate that metallic free carbon nanotube cluster modified screen printed electrodes provide an advantageous sensing methodology for nicotine. The electrochemical oxidation of nicotine is possible at low potentials compared to other commercially available carbon electrodes. Using the carbon nanotube cluster modified screen printed electrodes a detection range of 10 to 1000 μM is possible with a limit of detection of 2 μM. The sensing protocol is shown to be viable in artificial saliva and is promising as a portable and rapid sensor for nicotine in oral fluid (saliva) in areas such as health/life insurance, instances where smoking is banned and also as a point of care test to help improve smoking quit rates.     

Temperature processing effects in proton-implantedn-type GaAs

Characterization of the effects of thermal processing on the optical and electronic properties of proton implantedn-type GaAs is reported in this paper. The thermal processing includes variations in the substrate temperature during implantation and postimplantation thermal annealing. Infrared reflectivity data indicate that the depths to which the optical changes extend in the as-implanted samples are greatest in the cryogenic implants. Carrier concentration profiles derived from capacitance-voltage measurements are shown to have significant differences depending upon processing history. Existence ofn-type surface layers are noted in high fluence level implants.     

Rotation, entropy, and equilibrium states

For a dynamical system and function we consider the corresponding generalised rotation set. This is the convex subset of consisting of all integrals of with respect to -invariant probability measures. We study the entropy of rotation vectors , and relate this to the directional entropy of Geller & Misiurewicz. For a mixing subshift of finite type, and of summable variation, we prove that if the rotation set is strictly convex then the functions and are in fact one and the same. For those rotation sets which are not strictly convex we prove that and can differ only at non-exposed boundary points .