Anomalous robustness of the ν=5/2 fractional quantum Hall state near a sharp phase boundary

We report magnetotransport measurements in wide GaAs quantum wells with a tunable density to probe the stability of the fractional quantum Hall effect at a filling factor of ν=5/2 in the vicinity of the crossing between Landau levels (LLs) belonging to the different (symmetric and antisymmetric) electric subbands. When the Fermi energy (E(F)) lies in the excited-state LL of the symmetric subband, the 5/2 quantum Hall state is surprisingly stable and gets even stronger near this crossing, and then suddenly disappears and turns into a metallic state once E(F) moves to the ground-state LL of the antisymmetric subband. The sharpness of this disappearance suggests a first-order transition.     

A Hanf number for saturation and omission: the superstable case

Suppose is a triple of two theories in vocabularies with cardinality λ, and a τ₁‐type p over the empty set that is consistent with T₁. We consider the Hanf number for the property “there is a model M₁ of T₁ which omits p, but is saturated”. In [2], we showed that this Hanf number is essentially equal to the Löwenheim number of second order logic. In this paper, we show that if T is superstable, then the Hanf number is less than .     

Electrochemical and microfabrication strategies for remotely operated smart chemical sensors: Application of anodic stripping coulometry to calibration-free measurements of copper and mercury

Remote unattended sensor networks are increasingly sought after to monitor the drinking water distribution grid, industrial wastewater effluents, and even rivers and lakes. One of the biggest challenges for application of such sensors is the issue of in-field device calibration. With this challenge in mind, we report here the use of anodic stripping coulometry (ASC) as the basis of a calibration-free micro-fabricated electrochemical sensor (CF-MES) for heavy metal determinations. The sensor platform consisted of a photo-lithographically patterned gold working electrode on SiO₂ substrate, which was housed within a custom stopped-flow thin-layer cell, with a total volume of 2–4 μL. The behavior of this platform was characterized by fluorescent particle microscopy and electrochemical studies utilizing Fe(CN)₆^3−/4− as a model analyte. The average charge obtained for oxidation of 500 μM ferrocyanide after 60 s over a 10 month period was 176 μC, corresponding to a volume of 3.65 μL (RSD = 2.4%). The response of the platform to copper concentrations ranging from 50 to 7500 ppb was evaluated, and the ASC results showed a linear dependence of charge on copper concentrations with excellent reproducibility (RSD ≤ 2.5%) and accuracy for most concentrations (≤5–10% error). The platform was also used to determine copper and mercury mixtures, where the total metallic content was measurable with excellent reproducibility (RSD ≤ 4%) and accuracy (≤6% error).