An approximation condition and extremal quasiconformal extensions

The possibility that the extremal dilatation of quasiconformal extensions from the circle is determined by quadrilaterals with vertices on the circle is related to an approximation question for holomorphic functions. This allows an alternative demonstration of a result of Anderson and Hinkkanen.

     

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.     

Relative homological algebra in the category of quasi-coherent sheaves

In this paper, we prove the existence of a flat cover and of a cotorsion envelope for any quasi-coherent sheaf over a scheme (X,O_X). Indeed we prove something more general. We define what it is understood by the category of quasi-coherent R-modules, where R is a representation by rings of a quiver Q, and we prove the existence of a flat cover and a cotorsion envelope for quasi-coherent R-modules. Then we use the fact that the category of quasi-coherent sheaves on (X,O_X) is equivalent to the category of quasi-coherent R-modules for some Q and R to get our result.     

Further Development and Validation of the Teaching Science as Inquiry (TSI) Instrument

The purpose of this study was to further develop and validate the Teaching Science as Inquiry (TSI) Instrument, an instrument designed to measure the self‐efficacy beliefs of preservice teachers in regards to the teaching of science as inquiry. Based on the validation processes and the associated data analysis, the TSI demonstrates continued content and construct validity with high internal reliability when used with prospective elementary science teachers.     

A photoelectron spectroscopic investigation of the electronic structure of trimethylsilylhaloacetylenes

The photoelectron spectra (He I excitation) of trimethylsilylacetylene M(H) and of the four trimethylsilylhaloacetylenes M(X) with X = F, Cl, Br, I hav