The GHP Formalism and a Type N Twisting Vacuum Metric with Killing Vector

It is shown that the formalism introduced byGeroch, Held and Penrose has a geometrical basis. Withthe help of the resulting insight a canonical splittingof the complex function which appears in the standard form of the Algebraically Special metrics isrealized. The results of this splitting are applied tothe problem of a (special) Type N vacuum metric with atwisting principle null direction. It is demonstrated that it is possible (but not feasable) to findthe metric without the use of differential equations. Anestimate of the size of the metric is given.     

Integration in the GHP Formalism IV: A New Lie Derivative Operator Leading to an Efficient Treatment of Killing Vectors

In order to achieve efficient calculations and easy interpretations of symmetries, a strategy for investigations in tetrad formalisms is outlined: work in an intrinsic tetrad using intrinsic coordinates. The key result is that a vector field is a Killing vector field if and only if there exists a tetrad which is Lie derived with respect to ; this result is translated into the GHP formalism using a new generalised Lie derivative operator with respect to a vector field . We identify a class of it intrinsic GHP tetrads, which belongs to the class of GHP tetrads which is generalised Lie derived by this new generalised Lie derivative operator in the presence of a Killing vector field . This new operator also has the important property that, with respect to an intrinsic GHP tetrad, it commutes with the usual GHP operators if and only if is a Killing vector field. Practically, this means, for any spacetime obtained by integration in the GHP formalism using an intrinsic GHP tetrad, that the Killing vector properties can be deduced from the tetrad or metric using the Lie-GHP commutator equations, without a detailed additional analysis. Killing vectors are found in this manner for a number of special spaces.     

Integration in the GHP formalism I: A coordinate approach with applications to twisting type N spaces

The compacted spin coefficient (ghp) formalism is clearly more concise and efficient than the older Newman-Penrose formalism. Yet few people use it when integration of the field equations is involved, Held being the notable exception. However, to most workers in the field, Held's approach seems far removed from the usual Newman-Unti (nu) type integration procedure. This paper and a subsequent one are concerned with integration within theghp formalism. In this first paper we develop aghp coordinate-style integration procedure modelled closely on thenu procedure whereas in the second paper we present aghp operator-style integration procedure along the lines suggested by Held. For simplicity of illustration we restrict the discussion to algebraically special vacuum spacetimes. We show clearly the similarities and differences between the two approaches, and compare their respective efficiencies. To deal with a concrete example, we illustrate the two methods by once more considering the problem of twisting typeN vacuum solutions to Einstein's field equations. TheGhp approach enables us to have a comprehensive overview of this much discussed problem and gain new insight into the relationship between various results derived in a number of different formalisms.     

Calibration Curve with Improved Limit of Detection for Cadmium in Soil: An Approach to Minimize the Matrix Effect in Laser-Induced Breakdown Spectroscopic Analysis

The present article describes a working or combined calibration curve in laser-induced breakdown spectroscopic analysis, which is the cumulative result of the calibration curves obtained from neutral and singly ionized atomic emission spectral lines. This working calibration curve reduces the effect of change in matrix between different zone soils and certified soil samples because it includes both the species' (neutral and singly ionized) concentration of the element of interest. The limit of detection using a working calibration curve is found better as compared to its constituent calibration curves (i.e., individual calibration curves). The quantitative results obtained using the working calibration curve is in better agreement with the result of inductively coupled plasma–atomic emission spectroscopy as compared to the result obtained using its constituent calibration curves.     

Second-order contributions to the structure functions in deep inelastic scattering: (II) Comparison with experiment for the non-singlet contributions to e, μ-nucleon scattering

Quantum chromodynamics predictions for the non-singlet structure functions of ep and μp inclusive scattering are tested against experiment. Target mass corrections and leading and next-to-leading terms α_c are taken into account. The fits to experimental data are very good; they improve systematically when including second-order corrections. The preferred value for the invariant parameter Λ entering α_c is Λ=0.20 ± 0.06 GeV, when second-order and target mass corrections are taken into account.     

Aqueous flat-cells perpendicular to the electric field for use in electron paramagnetic resonance spectroscopy, II: design

This paper builds on the work of Mett and Hyde [J. Magn. Reson. 165 (2003) 137]. Various aqueous flat-cell geometries in the perpendicular orientation have been studied using Ansoft High Frequency Structure Simulator (version 9.0, Pittsburgh, PA) and Computer Simulation Technology Microwave Studio (version 5.0, Wellesley Hills, MA). The analytic theory of Mett and Hyde has been refined to predict optimum dimensions of multiple sample cell structures including the effect of the sample holder dielectric properties and the interaction of the cells with each other on EPR signal strength. From these calculations and simulations we propose a practical multiple cell sample structure for use in commercial rectangular TE102 cavities that yields 2.0-2.3 times higher sensitivity relative to a single flat-cell in the nodal orientation. We also describe a modified TE102 resonator design with square rather than cylindrical sample-access stacks that is predicted to give a factor of 2.2-2.7 enhancement in EPR signal strength of a single flat-cell in the nodal orientation. These signal enhancements are predicted with sample holders fabricated from polytetrafluoroethylene. Additional improvement in EPR signal of up to 75% can be achieved by using sample holder materials with lower dielectric constants.