The distribution of ITRM-recognizable reals

Infinite Time Register Machines (ITRM's) are a well-established machine model for infinitary computations. Their computational strength relative to oracles is understood, see e.g. ,  and . We consider the notion of recognizability, which was first formulated for Infinite Time Turing Machines in [6] and applied to ITRM's in [3]. A real x is ITRM-recognizable iff there is an ITRM-program P   such that P^y$P^y$ stops with output 1 iff y=x$y=x$, and otherwise stops with output 0. In [3], it is shown that the recognizable reals are not contained in the ITRM-computable reals. Here, we investigate in detail how the ITRM  -recognizable reals are distributed along the canonical well-ordering _<L${<}_L$ of Gödel's constructible hierarchy L  . In particular, we prove that the recognizable reals have gaps in _<L${<}_L$, that there is no universal ITRM in terms of recognizability and consider a relativized notion of recognizability.     

La3TaO7 derivatives with Weberite structure type: Possible electrolytes for solid oxide fuel cells and high temperature electrolysers

In this study, with the aim to enhance the ionic conduction of known structures by defect chemistry, the La₂O₃-Ta₂O₅ system was considered with a focus on the La₃TaO₇ phase whose structure is of Weberite type. In order to predict possible preferential substitution sites and substitution elements, atomistic simulation was used as a first approach. A solid solution La_3−xSr_xTaO_7−x/2 was confirmed by X-ray diffraction and Raman spectroscopy; it extends for a substitution ratio up to x = 0.15. Whereas La₃TaO₇ is a poor oxide ion conductor (σ_700 °C = 2 × 10⁻⁵S.cm⁻¹), at 700 °C, its ionic conductivity is increased by more than one order of magnitude when 3.3% molar strontium is introduced in the structure (σ_700 °C = 2 × 10⁻⁴S.cm⁻¹).     

Metal speciation in a complexing soft film layer: a theoretical dielectric relaxation study of coupled chemodynamic and electrodynamic interfacial processes

We report a comprehensive formalism for the dynamics of metal speciation across an interphase formed between a complexing soft film layer and an electrolyte solution containing indifferent ions and metal ions that form complexes with charged molecular ligands distributed throughout the film. The analysis integrates the intricate interplay between metal complexation kinetics and diffusive metal transfer from/toward the ligand film, together with the kinetics of metal electrostatic partitioning across the film/solution interphase. This partitioning is determined by the settling dynamics of the interfacial electric double layer (EDL), as governed by time-dependent conduction-diffusion transports of both indifferent and reactive metal ions. The coupling between such chemodynamic and electrodynamic processes is evaluated via derivation of the dielectric permittivity increment for the ligand film/electrolyte interphase that is perturbed upon application of an ac electric field (pulsation ω) between electrodes supporting the films. The dielectric response is obtained from the ω-dependent distributions of all ions across the ligand film, as ruled by coupled Poisson-Nernst-Planck equations amended for a chemical source term involving the intra-film complex formation and dissociation pulsations (ω(a) and ω(d) respectively). Dielectric spectra are discussed for bare and film coated-electrodes over a wide range of field pulsations and Deborah numbers De = ω(a,d)/ω(diff), where ω(diff) is the electric double layer relaxation pulsation. The frequency-dependent dynamic or inert character of the formed metal complexes is then addressed over a time window that ranges from transient to fully relaxed EDL. The shape and magnitude of the dielectric spectra are further shown to reflect the lability of dynamic complexes, i.e. whether the overall speciation process at a given pulsation ω is primarily rate-limited either by complexation kinetics or by ion-transport dynamics. The limits, strengths and extensions of the approach are further discussed within the context of metal speciation dynamics at soft planar and particulate complexing interphases.     

Chemistry of transition‐metal complexes containing functionalized phosphines: synthesis and structural analysis of rhodium(I) complexes containing allyl and cyanoalkylphosphines

A series of related acetylacetonate–carbonyl–rhodium compounds substituted by functionalized phosphines has been prepared in good to excellent yields by the reaction of [Rh(acac)(CO)₂] (acac is acetylacetonate) with the corresponding allyl‐, cyanomethyl‐ or cyanoethyl‐substituted phosphines. All compounds were fully characterized by ³¹P, ¹H, ¹³C NMR and IR spectroscopy. The X‐ray structures of (acetylacetonato‐κ²O,O′)(tert‐butylphosphanedicarbonitrile‐κP)carbonylrhodium(I), [Rh(C₅H₇O₂)(CO)(C₈H₁₃N₂)] or [Rh(acac)(CO)(^tBuP(CH₂CN)₂}] ( 2b ), (acetylacetonato‐κ²O,O′)carbonyl[3‐(diphenylphosphanyl)propanenitrile‐κP]rhodium(I), [Rh(C₅H₇O₂)(C₁₅H₁₄N)(CO)] or [Rh(acac)(CO){Ph₂P(CH₂CH₂CN)}] ( 2h ), and (acetylacetonato‐κ²O,O′)carbonyl[3‐(di‐tert‐butylphosphanyl)propanenitrile‐κP]rhodium(I), [Rh(C₅H₇O₂)(C₁₁H₂₂N)(CO)] or [Rh(acac)(CO){^tBu₂P(CH₂CH₂CN)}] ( 2i ), showed a square‐planar geometry around the Rh atom with a significant trans influence over the acetylacetonate moiety, evidenced by long Rh—O bond lengths as expected for poor π‐acceptor phosphines. The Rh—P distances displayed an inverse linear dependence with the coupling constants J_P‐Rh and the IR ν(C[triple‐bond]O) bands, which accounts for the Rh—P electronic bonding feature (poor π‐acceptors) of these complexes. A combined study from density functional theory (DFT) calculations and an evaluation of the intramolecular H…Rh contacts from X‐ray diffraction data allowed a comparison of the conformational preferences of these complexes in the solid state versus the isolated compounds in the gas phase. For 2b , 2h and 2i , an energy‐framework study evidenced that the crystal structures are mainly governed by dispersive energy. In fact, strong pairwise molecular dispersive interactions are responsible for the columnar arrangement observed in these complexes. A Hirshfeld surface analysis employing three‐dimensional molecular surface contours and two‐dimensional fingerprint plots indicated that the structures are stabilized by H…H, C…H, H…O, H…N and H…Rh intermolecular interactions.     

Comparing topologies on the Morse boundary and quasi-isometry invariance

Geometriae Dedicata - We compare several topologies on the Morse boundary $$\partial _{M} Y$$ of a $$\mathrm{CAT(0)}$$ cube complex Y. In particular, we show that the two topologies introduced by...     

Shape recovery behaviour of NiTi strips in bending: experiments and modelling

We present a theoretical and experimental investigation of the bending recovery performances for a commercial NiTi shape memory alloy strip. We evaluate the mechanical properties and the shape setting parameters and estimate the evolution of the curvature during heating in an Ethylene Glycol-based water solution. To model the strip bending response, we use a one-dimensional phenomenological constitutive equation for the shape memory material, based on the introduction of (twinned and detwinned) martensite and austenite volume fractions as internal variables. Under the assumption of uniform bending, we calculate a quasi-closed-form solution for the stress and martensite fraction distributions in a shape memory beam during bending and subsequent shape recovery. Using our characterisation data as input parameters of the model, we find that the theoretical curvature evolution is in good agreement with experimental data.     

Time‐resolved ion imaging at free‐electron lasers using TimepixCam

The application of a novel fast optical‐imaging camera, TimepixCam, to molecular photoionization experiments using the velocity‐map imaging technique at a free‐electron laser is described. TimepixCam is a 256 × 256 pixel CMOS camera that is able to detect and time‐stamp ion hits with 20 ns timing resolution, thus making it possible to record ion momentum images for all fragment ions simultaneously and avoiding the need to gate the detector on a single fragment. This allows the recording of significantly more data within a given amount of beam time and is particularly useful for pump–probe experiments, where drifts, for example, in the timing and pulse energy of the free‐electron laser, severely limit the comparability of pump–probe scans for different fragments taken consecutively. In principle, this also allows ion–ion covariance or coincidence techniques to be applied to determine angular correlations between fragments.     

Piscicidal constituents of pimelea species

Two fish toxins, linifolin a and linifolin b, which are both diterpene orthoesters, have been isolated from $\text{Pimelea}$$\text{linifolia}$.     

Space-charge layers in semi-insulating GaAs: Photoexcited two-dimensional electron systems

Resonant Raman spectra of photoexcited semi-insulating GaAs and Fe/GaAs show features characteristic of two-dimensional electron plasmas. The results are ascribed to the presence of a space-charge layer at the surface, originating in a slight mismatch of Fermi-level positions at the vacuum (or metal) interface and in the bulk. Calculations using values of intersubband transition energies from the data give an estimated shift of ～0.04 eV for the Fermi-level position at T = 85K.