On the cube problem of Las Vergnas

We prove a conjecture of Las Vergnas in dimensions d7: The matroid of the d-dimensional cube C ^d has a unique reorientation class. This extends a result of Las Vergnas, Roudneff and Salaün in dimension 4. Moreover, we determine the automorphism group G ^d of the matroid of the d-cube C ^d for arbitrary dimension d, and we discuss its relation to the Coxeter group of C ^d . We introduce matroid facets of the matroid of the d-cube in order to evaluate the order of G ^d . These matroid facets turn out to be arbitrary pairs of parallel subfacets of the cube. We show that the Euclidean automorphism group W ^d is a proper subgroup of the group G ^d of all matroid symmetries of the d-cube by describing genuine matroid symmetries for each Euclidean facet. A main theorem asserts that any one of these matroid symmetries together with the Euclidean Coxeter symmetries generate the full automorphism group G ^d . For the proof of Las Vergnas' conjecture we use essentially these symmetry results together with the fact that the reorientation class of an oriented matroid is determined by the labeled lower rank contractions of the oriented matroid. We also describe the Folkman-Lawrence representation of the vertex figure of the d-cube and a contraction of it. Finally, we apply our method of proof to show a result of Las Vergnas, Roudneff, and Salaün that the matroid of the 24-cell has a unique reorientation class, too.     

Quality control of201TlCl solution obtained at IPEN-CNEN/SP

The radiopharmaceutical²⁰¹TlCl(thallium-201 chloride) is used in nuclear medicine for myocardial visualization. The solution of²⁰¹TlCl was prepared using²⁰¹Tl obtained by irradiating a natural mercury target with protons from the CV-28 cyclotron installed at IPEN-CNEN/SP. This solution was subjected to different quality control processes required for its use in medicine. Some of these controls concerned the determination of the radionuclidic impurities:²⁰⁰Tl,²⁰²Tl and²⁰³Hg; the chemical identification of²⁰¹Tl⁺; the hydrazine concentration, mercury contamination and the presence of phosphate. Furthermore. the biological distribution in Wistar rats and tests for sterility, pyrogenicity and toxicity were carried out. It was verified that the solution obtained was in the form of thallous chloride. This radiopharmaceutical gave good heart images in animals but due to the high levels of²⁰⁰Tl and²⁰²Tl its use in humans is not possible unless enriched²⁰²Hg is used as target in the irradiation.     

Amperometric detection of nitrite and nitrate at tetraruthenated porphyrin-modified electrodes in a continuous-flow assembly

The modification of a glassy carbon surface by coating with an electrostatically assembled film of tetraruthenated cobalt porphyrin/(meso-tetra(4-sulphonatephenyl)porphyrinate zinc(II) yields an indicator electrode that allows the determination of nitrite to be performed with a limit of detection of 0.1 μM in a flow injection configuration. The dynamic range extends up to 1000 μM and the repeatability of the measurements was evaluated to be 1.5% with a throughput of 50 samples per hour. The efficiency of the bilayered film to mediate the electron transfer allows the determinations to be performed at a less positive potential (+0.75 V) with enhanced sensitivity. The coating also prevents the surface poisoning and its stability is maintained over several weeks. The same detector was used for determination of nitrate after reduction to nitrite in a reductor column containing copperised cadmium. This method was used for the determination of nitrate and nitrite in mineral water, saliva and cured meats, the results being in agreement with certified values and those obtained by using recommended procedures.