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.     

Helicity amplitudes for matter-coupled gravity

The great simplicity attained by the Weyl-van der Waerden spinor technique in the evaluation of helicity invariant amplitudes is shown to apply in the cumbersome calculations within the framework of linearized gravitation. Once the graviton couplings to spin-0, 1/2, 1, and 3/2 particles are given, we exhibit the reach of this method by evaluating, as an example, the helicity amplitudes for the process electron + positron photon + graviton in a very straightforward way.     

Preconcentration Systems Using Polyurethane Foam/Me-BDBD for Determination of Copper in Food Samples

A new reagent, 6-[2′-(6′-methyl-benzothiazolylazo)]-1,2-dihydroxy-3,5-benzenedisulfonic acid (Me-BDBD), was synthesised and used in on-line and off-line systems for copper preconcentration by solid-phase extraction. Spectrophotometry and Flame Atomic Absorption Spectrometry (FAAS) were the detection techniques. Polyurethane foam loaded with Me-BDBD packed in a minicolumn was used as sorbent in both systems. The spectral characteristics of Me-BDBD were investigated. The optimum pH values for maximum sorption of the metal are between 7.0 and 8.5. Copper was desorbed with 0.05 and 0.50 mol L⁻¹ hydrochloric acid solutions, for on-line and off-line systems, respectively. The effects of several foreign substances on the adsorption of copper are reported. The enrichment factors obtained were 7 (on-line) and 26 (off-line) for the systems. The proposed procedures allowed the determination of copper with detection limits of 3.4 and 1.4 μg L⁻¹ (0.85 and 0.35 μg per gram of sample) for on-line and off-line systems, respectively. The precision of the procedures was also calculated: 3.2 (on-line) and 1.9% (off-line). The validation of the procedures was carried out by analysis of certified reference material. The copper contents in corn and rice flour and black tea samples were determined by applying the proposed procedures.     

Synthesis of amberlite XAD-2-PC resin for preconcentration and determination of trace elements in food samples by flame atomic absorption spectrometry

A new chelating sorbent has been developed using Amberlite XAD-2 resin anchored with pyrocatechol through –N=C– group. This sorbent, characterised by elemental analysis and infrared (IR) spectra, was used as packing for the minicolumn in an on-line system preconcentration system for cadmium, cobalt, copper and nickel determination. Metal ions were sorbed in the minicolumn, from which it could be eluted directly to the nebulizer–burner system of the flame atomic absorption spectrometer (FAAS). Elution of all metals from minicolumn can be made with 0.50 mol L^− 1 HCl or HNO₃. The enrichment factors obtained were 16 (Cd), 24 (Co), 15 (Cu) and 19 (Ni), for 60 s preconcentration time, and 39 (Cd), 69 (Co), 36 (Cu) and 41 (Ni), if used 180 s preconcentration time. Under the optimum conditions, the proposed procedure allowed the determination of cadmium, cobalt, copper and nickel with detection limits of 0.31, 0.32, 0.39 and 1.64 μg L^− 1, respectively, when used preconcentration periods of 180 s. The accuracy of the developed procedure was sufficient and evaluated by the analysis of the certified reference materials NIST 1515 apple leaves and NIST 1570a spinach leaves. The method was applied to the analysis of food samples (spinach, black tea and rice flour).     

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.