Thin equivalence relations in scaled pointclasses

For ordinals α beginning a Σ₁ gap in $\mathrm{L}(\mathbb {R})$, where $\Sigma _{1}^{\mathrm{J}_{\alpha }(\mathbb {R})}$ is closed under number quantification, we give an inner model‐theoretic proof that every thin $\Sigma _{1}^{\mathrm{J}_{\alpha }(\mathbb {R})}$ equivalence relation is $\Delta _{1}^{\mathrm{J}_{\alpha }(\mathbb {R})}$ in a real parameter from the (optimal) hypothesis $\mathsf {AD}^{\mathrm{J}_{\alpha }(\mathbb {R})}$.     

Parity-violating neutron spin rotation in hydrogen and deuterium

We calculate the (parity-violating) spin-rotation angle of a polarized neutron beam through hydrogen and deuterium targets, using pionless effective field theory up to next-to-leading order. Our result is part of a program to obtain the five leading independent low-energy parameters that characterize hadronic parity violation from few-body observables in one systematic and consistent framework. The two spin-rotation angles provide independent constraints on these parameters. Our result for np spin rotation is $\frac{1} {\rho }\frac{{d\varphi _{PV}^{np} }} {{dl}} = \left[ {4.5 \pm 0.5} \right] rad MeV^{ - \frac{1} {2}} \left( {2g^{\left( {^3 S_1 - ^3 P_1 } \right)} + g^{\left( {^3 S_1 - ^3 P_1 } \right)} } \right) - \left[ {18.5 \pm 1.9} \right] rad MeV^{ - \frac{1} {2}} \left( {g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 2} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right)$\frac{1} {\rho }\frac{{d\varphi _{PV}^{np} }} {{dl}} = \left[ {4.5 \pm 0.5} \right] rad MeV^{ - \frac{1} {2}} \left( {2g^{\left( {^3 S_1 - ^3 P_1 } \right)} + g^{\left( {^3 S_1 - ^3 P_1 } \right)} } \right) - \left[ {18.5 \pm 1.9} \right] rad MeV^{ - \frac{1} {2}} \left( {g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 2} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right), while for nd spin rotation we obtain $\frac{1} {\rho }\frac{{d\varphi _{PV}^{nd} }} {{dl}} = \left[ {8.0 \pm 0.8} \right] rad MeV^{ - \frac{1} {2}} g^{\left( {^3 S_1 - ^1 P_1 } \right)} + \left[ {17.0 \pm 1.7} \right] rad MeV^{ - \frac{1} {2}} g^{\left( {^3 S_1 - ^3 P_1 } \right)} + \left[ {2.3 \pm 0.5} \right] rad MeV^{ - \frac{1} {2}} \left( {3g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 1} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right)$\frac{1} {\rho }\frac{{d\varphi _{PV}^{nd} }} {{dl}} = \left[ {8.0 \pm 0.8} \right] rad MeV^{ - \frac{1} {2}} g^{\left( {^3 S_1 - ^1 P_1 } \right)} + \left[ {17.0 \pm 1.7} \right] rad MeV^{ - \frac{1} {2}} g^{\left( {^3 S_1 - ^3 P_1 } \right)} + \left[ {2.3 \pm 0.5} \right] rad MeV^{ - \frac{1} {2}} \left( {3g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 1} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right), where the g ^(X-Y), in units of $MeV^{ - \frac{3} {2}}$MeV^{ - \frac{3} {2}}, are the presently unknown parameters in the leading-order parity-violating Lagrangian. Using naıve dimensional analysis to estimate the typical size of the couplings, we expect the signal for standard target densities to be $\left| {\frac{{d\varphi _{PV} }} {{dl}}} \right| \approx \left[ {10^{ - 7} \ldots 10^{ - 6} } \right]\frac{{rad}} {m}$\left| {\frac{{d\varphi _{PV} }} {{dl}}} \right| \approx \left[ {10^{ - 7} \ldots 10^{ - 6} } \right]\frac{{rad}} {m} for both hydrogen and deuterium targets. We find no indication that the nd observable is enhanced compared to the np one. All results are properly renormalized. An estimate of the numerical and systematic uncertainties of our calculations indicates excellent convergence. An appendix contains the relevant partial-wave projectors of the three-nucleon system.     

A host-guest optical sensor for aliphatic amines based on lipophilic cyclodextrin

A host-guest optical sensor for the determination of aliphatic amines as exemplified by octylamine is proposed. It is based on the reversible fluorescence enhancement of heptakis(2,6-di-O-isobutyl)-β-cyclodextrin(DOB-β-CD) hosting tetraphenylporphyrin (TPP) immobilized in poly(vinyl chloride) (PVC) membrane by aliphatic amine extracted from aqueous phase into membrane phase. The optimum membrane contained 1.15 wt % TPP, 6.15 wt % DOB-β-CD as sensing reagent and other membrane materials. The fluorescence enhancement of the membrane resulted from the formation of a stable three-component complex among DOB-β-CD, TPP, and aliphatic amines. With the optimum conditions described, the fluorescence response of the sensor to octylamine shows a good correlation with the theoretically derived equation in the range 1.0 × 10^–6 to 8.0 × 10^–4 mol/L. The response characteristics including reversibility, response time, reproducibility and lifetime and selectivity of this optical device are also discussed in detail. This sensor has also been applied for the determination of octylamine in water samples containing interferents with satisfactory recovery.     

Electronic excitations induced by hydrogen surface chemical reactions on gold

Associated with chemical reactions at surfaces energy may be dissipated exciting surface electronic degrees of freedom. These excitations are detected using metal-insulator-metal (MIM) heterostructures (Ta-TaOx-Au) and the reactions of H with and on a Au surface are probed. A current corresponding to 5×10(-5) electrons per adsorbing H atom and a marked isotope effect are observed under steady-state conditions. Analysis of the current trace when the H atom flux is intermitted suggests that predominantly the recombination reaction creates electronic excitations. Biasing the front versus the back electrode of the MIM structure provides insights into the spectrum of electronic excitations. The observed spectra differ for the two isotopes H and D and are asymmetric when comparing negative and positive bias voltages. Modeling indicates that the excited electrons and the concurrently created holes differ in their energy distributions.     

Small time convergence of subordinators with regularly or slowly varying canonical measure

We consider subordinators $X_{\alpha }={\left(X_{\alpha }\left(t\right)\right)}_{t\ge 0}$ in the domain of attraction at 0 of a stable subordinator ${\left(S_{\alpha }\left(t\right)\right)}_{t\ge 0}$ (where $\alpha \in (0,1)$); thus, with the property that ${\overline{\Pi }}_{\alpha }$, the tail function of the canonical measure of $X_{\alpha }$, is regularly varying of index $?\alpha \in (?1,0)$ as $x\downarrow 0$. We also analyse the boundary case, $\alpha =0$, when ${\overline{\Pi }}_{\alpha }$ is slowly varying at 0. When $\alpha \in (0,1)$, we show that ${\left(t{\overline{\Pi }}_{\alpha }\left(X_{\alpha }\left(t\right)\right)\right)}^{?1}$ converges in distribution, as $t\downarrow 0$, to the random variable ${\left(S_{\alpha }\left(1\right)\right)}^{\alpha }$. This latter random variable, as a function of $\alpha$, converges in distribution as $\alpha \downarrow 0$ to the inverse of an exponential random variable. We prove these convergences, also generalised to functional versions (convergence in $\mathbb{D}[0,1]$), and to trimmed versions, whereby a fixed number of its largest jumps up to a specified time are subtracted from the process. The $\alpha =0$ case produces convergence to an extremal process constructed from ordered jumps of a Cauchy subordinator. Our results generalise random walk and stable process results of Darling, Cressie, Kasahara, Kotani and Watanabe.     

Coordination chemistry of [Cp*Fe(η5-P3C2tBu2)] (Cp* = η5-C5Me5) with copper(I) halides – Formation of oligomeric and polymeric compounds

The reaction of the 1,2,4-triphosphaferrocene [Cp*Fe(η⁵-P₃C₂tBu₂)] (1) with CuX (X = Cl, Br, I) in a 1:1 stoichiometric ratio leads to the formation of the oligomeric compounds [{Cu(μ-X)}₆(μ₆-X)Cu(MeCN)₃{μ,η²-(Cp*Fe(η⁵-P₃C₂tBu₂))}₂{μ₃,η³-(Cp*Fe(η⁵-P₃C₂tBu₂))}] (X = Cl (2), Br (3)) and [{Cu(μ-I)}₃{Cu(μ₃-I)}₃Cu(μ₆-I){μ,η²-(Cp*Fe(η⁵-P₃C₂tBu₂))}₃{η¹-(Cp*Fe(η⁵-P₃C₂tBu₂))}] (4) revealing Cu(I) halide cages surrounded by 1,2,4-triphosphaferrocene moieties. The reaction of [Cp*Fe(η⁵-P₃C₂tBu₂)] with CuI in a 1:4 stoichiometry leads to the formation of the two-dimensional polymer [{Cu(μ-I)}₄{Cu(μ₃-I)(MeCN)}₂{μ₃,η³-(Cp*Fe(P₃C₂tBu₂))}]_n (5). The oligomeric compounds show dynamic behavior in solution monitored by ³¹P NMR spectroscopy. All compounds are additionally characterized by single crystal X-ray diffraction.