On the structure of complete simply connected embedded minimal surfaces

The helicoid and the plane are the only known complete simply connected minimal surfaces without self-intersections. In this paper we make an analytic study of this class of surfaces by first deforming them continuously into surfaces with self-intersections. Next, we study the (backward) time evolution of the set of self-intersections and see what geometric conditions must prevail in order for the self-intersections to rush off to infinity in finite time. As a result of this program it is shown that any surface of the type considered above has to satisfy at least one of five geometric possibilities. The first two of these alternatives are pathological, the third one is satisfied by the plane, and the next two are satisfied by the helicoid.     

A study of two-electron quantum dot spectrum using discrete variable representation method

A variational method called discrete variable representation is applied to study the energy spectra of two interacting electrons in a quantum dot with a three-dimensional anisotropic harmonic confinement potential. This method, applied originally to problems in molecular physics and theoretical chemistry, is here used to solve the eigenvalue equation to relative motion between the electrons. The two-electron quantum dot spectrum is determined then with a precision of at least six digits. Moreover, the electron correlation energies for various potential confinement parameters are investigated for singlet and triplet states. When possible, the present results are compared with the available theoretical values.     

Determination of siloxane-water partition coefficients by capillary extraction-high-resolution gas chromatography study of aromatic solvents

Partition coefficients of benzene, toluene, ethylbenzene and xylenes (BTEX), between crosslinked polydimethylsiloxane and water, were determined at room temperature by capillary extraction (a form of in-tube solid-phase microextraction, SPME) coupled to open tubular gas chromatography (in-tube SPME-high-resolution GC). A series of 7-9 repetitive extractions, performed on a 1-ml volume of diluted aqueous BTEX sample by the double-syringe squeeze method, gave exponential regression curves which fit very well with those predicted by partition theory. From the equations of the curves of relative FID response vs. extraction number, experimental Kd were easily calculated and the results compared with literature values. The whole measurement requires about 1 h from the start of the experiment to the final calculation of all BTEX partition coefficients. In-tube SPME resulted in a fast, clean, efficient, and cheaper alternative than the classic 1-cm, externally coated, SPME fiber-holder technique.     

Direct determination of selenium in urine samples by electrothermal atomic absorption spectrometry using a Zr plus Rh-treated graphite tube and co-injection of Rh as chemical modifier

Different chemical modifiers for use with electrothermal atomic absorption spectrometry (ET AAS) were investigated in relation to determining the selenium in human urine samples. The samples were diluted in a solution containing 1% v/v HNO₃ and 0.02% m/v cetyltrimethylammonium chloride (CTAC). Studying the modifiers showed that the use of either Ru or Ir as the permanent modifier gave low sensitivity to Se and the peak shape was very noisy, while Zr or Rh gave no peak at all. The same occurred when Zr was used in solution. For mixtures of permanent modifiers, Ir plus Rh or Zr plus Rh gave very low sensitivity, Zr plus Rh with co-injection of Ir in solution was also not efficient, Zr plus Rh in solution gave good sensitivity, but the best results were obtained with a mixture of Zr and Rh as the permanent modifier and co-injection of Rh in solution. Using this last modifier, the following dilutions with the HNO₃ and CTAC were studied: 1:1, 1:2, 1:3 and 1:4. The best dilution was 1:1, which promoted good sensitivity and a more defined peak shape and made it possible to correct for the background using a deuterium arc lamp. Under these conditions, a characteristic mass of 26±0.2 pg was obtained for Se in aqueous solution. Six certified urine samples were analyzed using matrix matching calibration and the measured concentrations were in agreement with the certified values, according to a t-test at the 95% confidence level. Recovery tests were carried out and the recoveries were in the range 100–103%, with relative standard deviation better than 9%. The limit of detection (LOD, 3 sd, n=10) was 3.0 μg L⁻¹ in the sample. The treated graphite tube could be used for at least 600 atomization cycles without significant alteration of the analytical signal.     

Probing the Catalytically Active Species in POM-Catalysed DNA-Model Hydrolysis**

Phosphoester hydrolysis is an important chemical step in DNA repair. One archetypal molecular model of phosphoesters is para-nitrophenylphosphate (pNPP). It has been shown previously that the presence of molecular metal oxide [Mo₇O₂₄]⁶⁻ may catalyse the hydrolysis of pNPP through the partial decomposition of polyoxomolybdate framework resulting in a [(PO₄)₂Mo₅O₁₅]⁶⁻ product. Real-time monitoring of the catalytic system using electrospray ionisation mass spectrometry (ESI-MS) provided a glance into the species present in the reaction mixture and identification of potential catalytic candidates. Following up on the obtained spectrometric data, Density Functional Theory (DFT) calculations were carried out to characterise the hypothetical intermediate [Mo₅O₁₅(pNPP)₂(H₂O)₆]⁶⁻ that would be required to form under the hypothesised transformation. Surprisingly, our results point to the dimeric [Mo₂O₈]⁴⁻ anion resulting from the decomposition of [Mo₇O₂₄]⁶⁻ as the active catalytic species involved in the hydrolysis of pNPP rather than the originally assumed {Mo₅O₁₅} species. A similar study was carried out involving the same species but substituting Mo by W. The mechanism involving W species showed a higher barrier and less stable products in agreement with the non-catalytic effect found in experimental results.