On Genericity and Ershov's Hierarchy

It is natural to wish to study miniaturisations of Cohen forcing suitable to sets of low arithmetic complexity. We consider extensions of the work of Schaeffer [9] and Jockusch and Posner [6] by looking at genericity notions within the Δ₂ sets. Different equivalent characterisations of 1‐genericity suggest different ways in which the definition might be generalised. There are two natural ways of casting the notion of 1‐genericity: in terms of sets of strings and in terms of density functions, as we will see here. While these definitions coincide at the first level of the difference hierarchy, they turn out to differ at other levels. Furthermore, these differences remain when the remainder of the Δ⁰₂ sets are considered. While the string characterization of 1‐genericity collapses at the second level of the difference hierarchy to 2‐genericity, the density function definition gives a very interesting hierarchy at level w and above. Both of these results point towards the deep similarities exhibited by the n‐c.e. degrees for n ≥ 2.     

Interference from Trace Copper in Electrochemical Investigations Employing Carboxylic Acid Terminated Thiol Modified Gold Electrodes

Unexpectedly, electrochemistry at variable chain length carboxylic acid terminated alkylthiol self‐assembled monolayers (SAMs) on gold electrodes gives rise to a Faradaic process in buffered aqueous electrolyte solution. In particular, the three‐carbon chain length, 3‐mercaptopropionic acid (MPA), exhibits a chemically reversible process with a mid‐point potential of 175 mV vs. Ag/AgCl under conditions of cyclic voltammetry. This process is associated with the presence of trace (parts per billion) amounts of copper(II) ions present in the chemical reagents used to prepare the aqueous electrolyte and also from the gold electrode itself. The carboxylic acid moiety on the SAM concentrates Cu²⁺ ions by coordination and this surface confined layer is then reduced. Methods to minimize the interference of Cu²⁺ ions at carboxylic acid terminated SAM are discussed and caution with respect to the interpretation of protein electrochemistry is recommended when using carboxylic acid functionalized SAMs to provide biocompatible electrochemical transduction surfaces, unless a metal free environment can be obtained.     

Theoretical and experimental evaluation of screen-printed tubular carbon ink disposable sensor well electrodes by dc and Fourier transformed ac voltammetry

Mass-produced, screen-printed, carbon-ink-based microtubular band (well) electrodes, suitable for routine sensing applications, have been fabricated and evaluated with respect to their theoretical and analytical performance. Microscopic examination of the electrode surface reveals they are inherently rough and could easily suffer from high and variable resistance, capacitance and area, unless care is taken to minimise these problems. Simulation models have been applied to analyse cyclic voltammetric responses obtained at the well electrodes. Results of these theoretical calculations further demonstrate the care needed with electrode design and resistance in carbon ink electrodes. Substantial differences in voltammetry when wells are produced by mechanically punching or laser drilling are considered. The application of multi- and single-frequency Fourier Transform ac voltammetry, previously applied to planar carbon ink disc electrodes for quality control purposes, is now demonstrated with respect to the microtubular band electrode geometry. Theoretical and practical limitations are discussed, as is the analytical application to the reversible redox couple in the presence of oxygen in aqueous solution. Dedicated to Keith on his 80th birthday, a good friend and colleague.     

APN permutations on and Costas arrays

We study PN and APN functions over the integers modulo n. We give some construction techniques based on Costas arrays, which allow us to construct APN permutations on where p is a prime. Although PN permutations do not exist, one set of our functions is very close to being a set of PN permutations.     

Reading “A variant of the Hales–Jewett theorem” on its anniversary

In a recent paper “A variant of the Hales–Jewett theorem”, M. Beiglböck provides a version of the classic coloring result in which an instance of the variable in a word giving rise to a monochromatic combinatorial line can be moved around in a finite structure of specified type (for example, an arithmetic progression). We give an elementary proof and infinitary extensions.     

Experimental and theoretical investigations of the sulfite-based polyoxometalate cluster redox series: alpha- and beta-[Mo(18)O(54)(SO(3))(2)](4-/5-/6-)

The synthesis, isolation and structural characterization of the sulfite polyoxomolybdate clusters alpha-(D(3h))(C(20)H(44)N)(4){alpha-[Mo(18)O(54)(SO(3))(2)]}CH(3)CN and beta-(D(3d))(C(20)H(44)N)(4){beta-[Mo(18)O(54)(SO(3))(2)]}CH(3)CN is presented. Voltammetric studies in acetonitrile (0.1 M Hx(4)NClO(4), Hx(4)N=tetra-n-hexylammonium) reveal the presence of an extensive series of six one-electron reduction processes for both isomers. Under conditions of bulk electrolysis, the initial [Mo(18)O(54)(SO(3))(2)](4-/5-) and [Mo(18)O(54)(SO(3))(2)](5-/6-) processes produce stable [Mo(18)O(54)(SO(3))(2)](5-) and [Mo(18)O(54)(SO(3))(2)](6-) species, respectively, and the same reduced species may be produced by photochemical reduction. Spectroelectrochemical data imply that retention of structural form results upon reduction, so that both alpha and beta isomers are available at each of the 4-, 5-, and 6-redox levels. However, the alpha isomer is the thermodynamically favored species in both the one- and two-electron-reduced states, with beta-->alpha isomerization being detected in both cases on long time scales (days). EPR spectra also imply that increasing localization of the unpaired electron occurs over the alpha- and beta-[Mo(18)O(54)(SO(3))(2)](5-) frameworks as the temperature approaches 2 K where the EPR spectra show orthorhombic symmetry with different g and hyperfine values for the alpha and beta isomers. Theoretical studies support the observation that it is easier to reduce the alpha cluster than the beta form and also provide insight into the driving force for beta-->alpha isomerization in the reduced state. Data are compared with that obtained for the well studied alpha-[Mo(18)O(54)(SO(4))(2))](4-) sulfate cluster.     

Measurement of the viscosity-density product using multiple reflections of ultrasonic shear horizontal waves

We have developed an on-line computer-controlled sensor, based on ultrasound reflection measurements, to determine the product of the viscosity and density of a liquid or slurry for Newtonian fluids and the shear impedance of the liquid for non-Newtonian fluids. A 14 MHz shear wave transducer is bonded to one side of a 45-90 degrees fused silica wedge and the base is in contract with the liquid. Twenty-eight echoes were observed due to the multiple reflections of an ultrasonic shear horizontal (SH) wave within the wedge. The fast Fourier transform of each echo was obtained for a liquid and for water, which serves as the calibration fluid, and the reflection coefficient at the solid-liquid interface was obtained. Data were obtained for 11 sugar water solutions ranging in concentration from 10% to 66% by weight. The viscosity values are shown to be in good agreement with those obtained independently using a laboratory viscometer. The data acquisition time is 14s and this can be reduced by judicious selection of the echoes for determining the reflection coefficient. The measurement of the density results in a determination of the viscosity for Newtonian fluids or the shear wave velocity for non-Newtonian fluids. The sensor can be deployed for process control in a pipeline, with the base of the wedge as part of the pipeline wall, or immersed in a tank.     

Preferential synthesis of highly conducting Tl(TCNQ) phase II nanorod networks via electrochemically driven TCNQ/Tl(TCNQ) solid-solid phase transformation

Facile synthesis and characterization of the highly conducting, thermodynamically favored, Tl(TCNQ) phase II microrods/nanorods onto conducting (glassy carbon (GC)) and semiconducting (indium tin oxide (ITO)) surfaces have been accomplished via redox-based transformation of 7,7,8,8-tetracynoquinodimethane (TCNQ) microcrystals. This electrochemically irreversible process involves the one-electron reduction of surface-confined solid TCNQ into TCNQ·^? with concomitant incorporation of the Tl⁺ _(aq) cation, from the bulk solution, at the triple-phase boundary, GC or ITO│(TCNQ_(s)/TCNQ·^? _(s))│Tl⁺ _(aq), through a nucleation/growth mechanism. Consistent with the conceptually related M(TCNQ) systems (M⁺ = Li⁺, Na⁺, K⁺, Ag⁺, and Cu⁺), the TCNQ/Tl(TCNQ) interconversion is strongly dependent upon scan rate, Tl⁺ _(aq) electrolyte concentration, and the method of attaching solid TCNQ onto the electrode surface. Spectroscopic (infrared (IR) and Raman), microscopic (scanning electron microscopy (SEM)), and surface science (X-ray photoelectron spectroscopy (XPS), energy-dispersive X-ray (EDX), and X-ray diffraction (XRD)) characterization of the electrochemically synthesized material revealed formation of pure Tl(TCNQ) phase II. Importantly, the generic solid-state electrochemical approach used in this study not only offers facile protocol for controllable and preferential synthesis of Tl(TCNQ) phase II but also provides access to fabricate and tune the morphology to yield microrod/nanorod networks.

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Graphical abstract Controlled synthesis of the highly conducting Tl(TCNQ) phase II with either nanowire or rod-like morphologies is achieved via a redox-based solid-solid phase interconversion of TCNQ microcrystals in the presence of a Tl⁺ _(aq) electrolyte.

     

Use of CT scans and treatment planning software for validation of the dose component of food irradiation protocols

The challenging problem of estimating the dose delivered to heterogeneous products by radiation modalities of limited penetration can be readily handled by using technologies developed for, and widely used in, radiation therapy applications. In particular, combining CT scanning with radiation treatment planning programs can simulate radiation processing with either photons or electrons, and can provide detailed, high resolution and accurate dose maps for any arbitrary product and package configuration. Such dose maps are an essential part of process validation. Comparison of the simulated dose distributions with measured dose maps verifies the soundness of this approach. The present communication presents results obtained with the simulation technique for a variety of common food items which are likely candidates for radiation processing.     

Ionic-liquid-mediated active-site control of MoS2 for the electrocatalytic hydrogen evolution reaction

The layered crystal MoS(2) has been proposed as an alternative to noble metals as the electrocatalyst for the hydrogen evolution reaction (HER). However, the activity of this catalyst is limited by the number of available edge sites. It was previously shown that, by using an imidazolium ionic liquid as synthesis medium, nanometre-size crystal layers of MoS(2) can be prepared which exhibit a very high number of active edge sites as well as a de-layered morphology, both of which contribute to HER electrocatalytic activity. Herein, it is examined how to control these features synthetically by using a range of ionic liquids as synthesis media. Non-coordinating ILs with a planar heterocyclic cation produced MoS(2) with the de-layered morphology, which was subsequently shown to be highly advantageous for HER electrocatalytic activity. The results furthermore suggest that the crystallinity, and in turn the catalytic activity, of the MoS(2) layers can be improved by employing an IL with specific solvation properties. These results provide the basis for a synthetic strategy for increasing the HER electrocatalytic activity of MoS(2) by tuning its crystal properties, and thus improving its potential for use in hydrogen production technologies.