Coring Categories and Villamayor–Zelinsky Sequence for Symmetric Finite Tensor Categories

Applied Categorical Structures - In the preceeding paper we constructed an infinite exact sequence a la Villamayor–Zelinsky for a symmetric finite tensor category. It consists of cohomology...     

Rapid and robust spin state amplification

Electron and nuclear spins have been employed in many of the early demonstrations of quantum technology. However, applications in real world quantum technology are limited by the difficulty of measuring single spins. Here we show that it is possible to rapidly and robustly amplify a spin state using a lattice of ancillary spins. The model we employ corresponds to an extremely simple experimental system: a homogenous Ising-coupled spin lattice in one, two, or three dimensions, driven by a continuous microwave field. We establish that the process can operate at finite temperature (imperfect initial polarization) and under the effects of various forms of decoherence.     

Electron transfer at tetrahedral cobalt(II). Part 1. Kinetics of bromate ion reduction

Summary The bromate ion reduction by 12-tungstocobaltate(II) anion has been investigated. The reaction obeys the empirical rate law:-d[reductant]/dt=5(a+b[H⁺]²)[BrO ₃ ^– ][reductant]: where a=(2.49±0.18)×10^–4M^–1 s^–1, b=(4.65±0.20)×10^–5M^–3s^–1 at 24.5±0.1°C [H⁺]=0.05–1.50M and I=2.0M (NaClO₄). This rate law is interpreted in terms of parallel reactions of BrO ₃ ^– and H₂BrO ₃ ⁺ . On the basis of the observed anion catalysis, substitution intertness of the reductant and Marcus type linear free energy relations, the outer sphere mechanism is proposed for both pathways.     

Invertible bimodule categories over the representation category of a Hopf algebra

For any finite-dimensional Hopf algebra H   we construct a group homomorphism BiGal(H)→BrPic(Rep(H))$\mathrm{BiGal}(H)\to \text{BrPic}(\mathrm{Rep}(H))$, from the group of equivalence classes of H  -biGalois objects to the group of equivalence classes of invertible exact Rep(H)$\mathrm{Rep}(H)$-bimodule categories. We discuss the injectivity of this map. We exemplify in the case H=_Tq$H=T_q$ is a Taft Hopf algebra and for this we classify all exact indecomposable Rep(_Tq)$\mathrm{Rep}(T_q)$-bimodule categories.     

A Sequence to Compute the Brauer Group of Certain Quasi-Triangular Hopf Algebras

A deeper understanding of recent computations of the Brauer group of Hopf algebras is attained by explaining why a direct product decomposition for this group holds and describing the non-interpreted factor occurring in it. For a Hopf algebra B in a braided monoidal category ${{\mathcal C}}$ , and under certain assumptions on the braiding (fulfilled if ${{\mathcal C}}$ is symmetric), we construct a sequence for the Brauer group ${{\rm{BM}}}({{\mathcal C}};B)$ of B-module algebras, generalizing Beattie’s one. It allows one to prove that ${{\rm{BM}}}({{\mathcal C}};B) \cong {{\rm{Br}}}({{\mathcal C}}) \times {\operatorname{Gal}}({{\mathcal C}};B)$ , where ${{\rm{Br}}}({{\mathcal C}})$ is the Brauer group of ${{\mathcal C}}$ and ${\operatorname{Gal}}({{\mathcal C}};B)$ the group of B-Galois objects. We also show that ${{\rm{BM}}}({{\mathcal C}};B)$ contains a subgroup isomorphic to ${{\rm{Br}}}({{\mathcal C}}) \times {\operatorname{H^2}}({{\mathcal C}};B,I),$ where ${\operatorname{H^2}}({{\mathcal C}};B,I)$ is the second Sweedler cohomology group of B with values in the unit object I of ${{\mathcal C}}$ . These results are applied to the Brauer group ${{\rm{BM}}}(K,B \times H,{{\mathcal R}})$ of a quasi-triangular Hopf algebra that is a Radford biproduct B × H, where H is a usual Hopf algebra over a field K, the Hopf subalgebra generated by the quasi-triangular structure ${{\mathcal R}}$ is contained in H and B is a Hopf algebra in the category ${}_H{{\mathcal M}}$ of left H-modules. The Hopf algebras whose Brauer group was recently computed fit this framework. We finally show that ${{\rm{BM}}}(K,H,{{\mathcal R}}) \times {\operatorname{H^2}}({}_H{{\mathcal M}};B,K)$ is a subgroup of ${{\rm{BM}}}(K,B \times H,{{\mathcal R}})$ , confirming the suspicion that a certain cohomology group of B × H (second lazy cohomology group was conjectured) embeds into it. New examples of Brauer groups of quasi-triangular Hopf algebras are computed using this sequence.     

Eluent-Induced Separation of Inorganic Cations in Capillary Liquid Chromatography with Contactless Conductivity Detector

A non-suppressed contactless conductivity detector has been used as a capillary detector in a capillary ion chromatograph, combining a reversed-phase C30 column permanently modified with ionic surfactant. The C30 column (100 × 0.32 mm. id) was modified with sodium dodecyl sulfate (SDS) for the separation of inorganic cations. Monovalent cations could be separated by the proposed system, in which methanesulfonic acid (MSA) and SDS were employed as the mobile phase component, but divalent cations could not be eluted under this condition. As for the case of SDS used as the eluent, an H⁺-cation-exchange column was placed before the sample injector to convert the Na⁺ from the eluent into H⁺, and when the mixture of MSA and dodecyl sulfuric acid was used as the eluent, the retention of cations was improved and baseline separation of the cations was achieved within 23 min. The effect of the eluent composition on the retention behavior of inorganic cations was investigated. The repeatability of retention time and peak height varied from 0.39 to 0.58 and 2.21 to 3.25 % as relative standard deviation, respectively.     

Oxidation of glutathione by diaquatetrakis(2,2′-bipyridine)-μ-oxo diruthenium(III) ion in aqueous acidic solutions

Summary The kinetics of the oxidation of glutathione by diaquatetrakis(2,2-bipyridine)--oxo diruthenium(III) ion in aqueous HClO₄ have been investigated. The reaction obeys the empirical rate law:-2d[oxidant]/dt = k[oxidant][reductant]/[H⁺] where k = 7.42 ± 0.40 × 10^-3 s^-1 at 25.5 °C, [H⁺] = 0.005–0.05 M and I = 1.0 M (LiClO₄). Free radicals are important in the reaction and a mechanism consistent with the experimental results has been postulated.     

Kinetics and mechanism of the reduction of diaquatetrakis (2,2′-bipyridine)-μ-oxo diruthenium(III) by ascorbic acid

Summary The kinetics of the oxidation of ascorbic acid by diaquatetrakis (2,2-bipyridine)--oxo diruthenium(III) in aqueous HClO₄ were investigated. The dependence of the second order rate constantk ₂ on [H⁺] is given by k ₂=a+b[H⁺]^–, indicating that both the undissociated form and the monoanion of ascorbic acid are reactive. Marcus theory was used to estimate the redox potential for the Ru^III-O-Ru^III/Ru^III-O-Ru^II couple and a feasible mechanism has been proposed to explain the results.     

Kinetics and mechanism of the oxidation of iodide by diaquote- trakis(2,2′-bipyridine)-μ-oxodiruthenium(III) ion in acid medium

Transition Metal Chemistry - The kinetics of the oxidation of iodide by diaquotetrakis-(2,2-bipyridine)-μ-oxodiruthenium(III), [Ru2O]4+, were studied in aqueous perchloric acid at...