LETTER: BTZ Black Hole from (3+1) Gravity

We propose an approach for constructing spatial slices of (3+1) spacetimes with cosmological constant but without a matter content, which yields (2+1) vacuum with solutions. The reduction mechanism from (3+1) to (2+1) gravity is supported on a criterion in which the Weyl tensor components are required to vanish together with a dimensional reduction via an appropriate foliation. By using an adequate reduction mechanism from the Plebaski–Carter[A] solution in (3+1) gravity, the (2+1) BTZ solution can be obtained.     

Gross alpha and gross beta radioactivity in drinking water from Zacatecas and Guadalupe cities, Mexico

The conditions to measure the gross alpha and gross beta radioactivity in water samples from Zacatecas and Guadalupe cities in the State of Zacatecas, Mexico were established. The gross alpha and beta radioactivity of water samples were measured using a liquid scintillation detector. The results show that the gross beta radioactivity in all cases is lower than the maximum contaminant level and the gross alpha radioactivity is higher in the samples collected from Guadalupe City and in the samples collected from the Southwest of Zacatecas City.     

Improvement of the analysis of dansylated derivatives of polyamines and their conjugates by high-performance liquid chromatography.

The paper described a method for improving the hydrolysis of conjugated polyamines in PH fraction, isolated from the lichen Evernia prunastri, as well as the optimization of dansylation procedure of these polyamines on the basis of the pH value to which derivatization is achieved. Dansylated polyamines have been later separated by high-performance liquid chromatography (HPLC) using a gradient elution. Hydrolysis of conjugates requires acid treatment at room temperature rather than at 110 degrees C, as usually described. Dansylation is improved at high pH values, whereas removal of phenolics (mainly evernic acid), from the conjugates requires low pH values.     

Realisation of special Kähler manifolds as parabolic spheres

We prove that any simply connected special Kähler manifold admits a canonical immersion as a parabolic affine hypersphere. As an application, we associate a parabolic affine hypersphere to any nondegenerate holomorphic function. We also show that a classical result of Calabi and Pogorelov on parabolic spheres implies Lu's theorem on complete special Kähler manifolds with a positive definite metric.

     

Nitrogen‐doped zirconia single crystals

The aim of this work is the preparation of nitrogen‐doped single crystals of cation‐stabilized zirconia. Thin plates of these crystals were nitrided in a graphite heated resistance furnace with nitrogen as reaction gas. Several dwell times and reaction temperatures were tested and their effect on the amount of incorporated nitrogen is investigated. During nitridation at high temperatures a rock salt‐type ‘ZrN’ layer grows on the surface, leading to the destruction of the crystal. In contrast to the fluorite‐type bulk material, which can be described as a fast anion conductor, the surface layer shows electronic conductivity. For possible applications of the bulk material (solid electrolyte) the formation of the surface layer must be avoided. Therefore, the interface between surface epilayer and bulk material was investigated in detail by electron microscopy methods. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reciprocal Polynomial Extrapolation

An alternative to the classical extrapolations is proposed. The stability and the accuracy are studied. The new extrapolation behaves better than the classical ones when there are problems of stability. This technique will be useful in those problems where the region of stability is very small and it forces to work with too fine scales.     

Differential-pulse voltammetric determination of low μg l cyanide levels using EDTA, Cu(II) and a hanging mercury drop electrode

The proposed method for cyanide determination at the ultratrace level by differential pulse voltammetry is based in the sensitivity enhancement obtained when both Cu(II) and EDTA are present in the background electrolyte. Comparison of the detection limits and linear dynamic ranges using the conventional borate (pH 9.75), and the proposed borate-EDTA–Cu(II) background electrolytes was carried out. Best results have been obtained with the addition of 0.5 mmol l⁻¹ EDTA and 0.02 mmol l⁻¹ of Cu(II), which allow a detection limit of 1.7 μg l⁻¹ CN⁻ (65 nmol l⁻¹ — absolute detection limit 34 ng) with a precision better than ±2% for a 40 μg l⁻¹ level. Calibration range extended from detection limit up to 100 μg l⁻¹. Cyclic voltammetry indicates that the measured cyanide peak is obtained when the electrogenerated CuCN adsorbed onto the hanging mercury drop electrode surface, is oxidised at positive going potential scan. The method has been successfully applied to various industrial waste waters such as metal-finishing waste waters, water/sand mixtures from cleaning processes of coke production, leachates from wastes obtained from electrolytic cells of aluminium production, and liquors from gold extraction industry. Results obtained by the proposed method showed good agreement with those obtained by the standard methods (ion-selective potentiometry and the spectrophotometric pyridine method).     

Inflection points and topology of surfaces in 4-space

We consider asymptotic line fields on generic surfaces in 4-space and show that they are globally defined on locally convex surfaces, and their singularities are the inflection points of the surface. As a consequence of the generalized Poincaré-Hopf formula, we obtain some relations between the number of inflection points in a generic surface and its Euler number. In particular, it follows that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.

     

Boundary Concentration for Eigenvalue Problems Related to the Onset of Superconductivity

We examine the asymptotic behavior of the eigenvalue w(h) and corresponding eigenfunction associated with the variational problem m(h) o inf_{y ? H¹(W;C )} \fracò_W \abs(i?+hA)y² dx dy ò_W\absy² dx dy \mu(h)\equiv\inf_{\psi\in H^{1}(\Omega;{\bf C} )} \frac{\int_{\Omega } \abs{(i\nabla+h{\bf A})\psi}^{2}\,dx\,dy} {\int_{\Omega }\abs{\psi}^{2}\,dx\,dy} in the regime h>>1. Here A is any vector field with curl equal to 1. The problem arises within the Ginzburg-Landau model for superconductivity with the function w(h) yielding the relationship between the critical temperature vs. applied magnetic field strength in the transition from normal to superconducting state in a thin mesoscopic sample with cross-section W ì \R²\Omega\subset\R^{2}. We first carry out a rigorous analysis of the associated problem on a half-plane and then rigorously justify some of the formal arguments of [BS], obtaining an expansion for w while also proving that the first eigenfunction decays to zero somewhere along the sample boundary ?W\partial \Omega when z is not a disc. For interior decay, we demonstrate that the rate is exponential.