Charged axially symmetric solution and energy in teleparallel theory equivalent to general relativity

An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity. The associated metric has the structure function G(ξ)=1-ξ²-2mAξ³-q²A²ξ⁴. The fourth order nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad whose metric has the structure function in a factorizable form (1-ξ²)(1+r₊Aξ)(1+r_-Aξ) with r_± as the horizons of Reissner–Nordström space-time. This new form has the advantage that its roots are now trivial to write down. Then, we study the singularities of this space-time. Using another coordinate transformation, we obtain a tetrad field. Its associated metric yields the Reissner–Nordström black hole. In calculating the energy content of this tetrad field using the gravitational energy-momentum, we find that the resulting form depends on the radial coordinate! Using the regularized expression of the gravitational energy-momentum in the teleparallel equivalent of general relativity we get a consistent value for the energy.     

Spectrophotometric determination of aromatic amines by reaction with p-benzoquinone

A comprehensive study is made of the application of the p-benzoquinone spectrophotometric technique to the aromatic amines. The technique involves a reaction with excess p-benzoquinone; the colored products display maximum absorption at 490–510 nm (varying according to the type of the amine used) and E_{1 cm}^1% in the range of 90–380. On the basis of an IR investigation, ethyl alcohol has been selected as a suitable solvent medium for aromatic amine determination. Electron-donating groups react faster and give more intense color than do electron-withdrawing groups. Results with an average recovery of 95% and mean standard deviation of 3.4% are obtained with seven aromatic amines.     

Energy and Momentum of Robinson-Trautman Space-Times

Robinson and Trautman space-times are studied in the context of teleparallel equivalent of general relativity (TEGR). These space-times are the simplest class of asymptotically flat geometries admitting gravitational waves. We calculate the total energy for such space-times using two methods, the gravitational energy-momentum and the translational momentum 2-form. The two methods give equal results of these calculations. We show that the value of energy depends on the gravitational mass M, the Gaussian curvature of the surfaces λ(u,θ) and on the function K(u,θ). The total energy reduces to the energies of Schwarzschild’s and Bondi’s space-times under specific forms of the function K(u,θ).     

Characterizations of optimality in convex programming: the nondifferentiable case

Primal, dual and saddle-point characterizations of optimality are given for convex programming in the general case (nondifferentiable functions and no constraint qualification).     

A new liquid membrane electrode for determination of vitamin B1 in multivitamin preparations

Summary A new liquid membrane electrode was developed which is highly selective and sensitive for vitamin B₁. It is based on the thiamine-picrolonate ion-pair complex as an electroactive material in nitrobenzene solvent. The electrode has a remarkable selectivity for vitamin B₁ in the presence of vitamins B₂, B₆, B₁₂ and nicotinamide. The results obtained for the determination of vitamin B₁ in various multivitamin preparations at levels as low as 1 g/ml show an average recovery of 98% (mean standard deviation 1.8%) and are favourably compared with those obtained by the official methods.

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Neue Flüssig-Membranelektrode zur Bestimmung von Vitamin B₁ in Multivitaminpräparaten

Zusammenfassung Eine neue, für Vitamin B₁ hochselektive Flüssig-Membranelektrode wurde entwickelt. Sie beruht auf dem Thiamin-Picrolonat-Ionenpaarkomplex als elektroaktives Material im Lösungsmittel Nitrobenzol. Die Elektrode besitzt eine beachtliche Selektivität für Vitamin B₁ in Gegenwart der Vitamine B₂, B₆, B₁₂ und Nicotinamid. Bei Bestimmungen in verschiedenen Multivitaminpräparaten mit Konzentrationen bis herab zu 1 g/ml erhielt man eine durchschnittliche Wiederfindung von 98% (mittlere Standardabweichung 1,8%). Die erhaltenen Resultate zeigen gute Übereinstimmung mit den nach amtlichen Methoden erhaltenen Werten.

     

Some exponentially decreasing error bounds for a numerical inversion of the Laplace transform

Convergence properties of a class of least-squares methods for finding approximate inverses of the Laplace transform are obtained by using reproducing kernel Hilbert space techniques (or, alternatively, related minimization techniques) and some classical interpolation results.     

On moment-discretization and least-squares solutions of linear integral equations of the first kind

Let K(s, t) be a continuous function on [0, 1] × [0, 1], and let $\text{K}$ be the linear integral operator induced by the kernel K(s, t) on the space $\text{L}$₂[0, 1]. This note is concerned with moment-discretization of the problem of minimizing 6K_x?y6 in the $\text{L}$₂-norm, where y is a given continuous function. This is contrasted with the problem of least-squares solutions of the moment-discretized equation: ∝₀¹K(s_i, t) x(t) dt = y(s_i), i = 1, 2,h., n. A simple commutativity result between the operations of “moment-discretization” and “least-squares” is established. This suggests a procedure for approximating $\text{K2y}$ (where $\text{K}$² is the generalized inverse of $\text{K}$), without recourse to the normal equation $\text{K1Kx = K1y}$, that may be used in conjunction with simple numerical quadrature formulas plus collocation, or related numerical and regularization methods for least-squares solutions of linear integral equations of the first kind.     

Stability of the vacuum non-singular black hole

The singularity of the black hole solutions obtained before in Møller’s theory are studied. It is found that although the two solutions reproduce the same associated metric the asymptotic behavior of the scalars of torsion tensor and basic vector are quite different. The stability of the associated metric of those solutions which is spherically symmetric non-singular black hole is studied using the equations of geodesic deviation. The condition for the stability is obtained. From this condition the stability of the Schwarzschild solution and di Sitter solution can be obtained.     

On the cones of tangents with applications to mathematical programming

In this study, we present a unifying framework for the cones of tangents to an arbitrary set and some of its applications. We highlight the significance of these cones and their polars both from the point of view of differentiability and subdifferentiability theory and the point of view of mathematical programming. This leads to a generalized definition of a subgradient which extends the well-known definition of a subgradient of a convex function to the nonconvex case. As an application, we develop necessary optimality conditions for a min-max problem and show that these conditions are also sufficient under moderate convexity assumptions.