An extension of Purcell's vector method with applications to panel element equations

The classical Purcell's vector method, for the construction of solutions to dense systems of linear equations is extended to a flexible orthogonalisation procedure. Some properties are revealed of the orthogonalisation procedure in relation to the classical Gauss-Jordan elimination with or without pivoting. Additional properties that are not shared by the classical Gauss-Jordan elimination are exploited. Further properties related to distributed computing are discussed with applications to panel element equations in subsonic compressible aerodynamics. Using an orthogonalisation procedure within panel methods enables a functional decomposition of the sequential panel methods and leads to a two-level parallelism.

On a flexible elimination algorithm with applications to panel element equations

A flexible elimination algorithm is presented and is applied to the solution of dense systems of linear equations. Properties of the algorithm are exploited in relation to panel element methods for potential flow and subsonic compressible flow. Further properties in relation to distributed computing are also discussed.

[Book review] Barry Mazur, Imagining Numbers: (Particularly the Square Root of Minus Fifteen)

Tony Mann provides a review of the book: Barry Mazur, Imagining Numbers: (Particularly the Square Root of Minus Fifteen), London: Allen Lane, 2003, ISBN: 0713996307

Exploring the conditional performance of UK unit trusts

We evaluate the conditional performance of U.K. equity unit trusts using the approach of Lynch and Wachter (2007, 2008) relative to three conditional linear factor models. We find significant time variation in the conditional performance of some trust portfolios and individual trusts using the lag term spread as the information variable. The conditional performance of the trusts is countercyclical and larger trusts have more countercyclical performance than smaller trusts within certain investment sectors. These patterns in conditional trust performance cannot be fully explained by the underlying securities that the trusts hold.

Triterpenoid saponins from a cytotoxic root extract of Sideroxylon foetidissimum subsp. gaumeri

Evaluation of the cytotoxicity of an ethanolic root extract of Sideroxylonfoetidissimum subsp. gaumeri (Sapotaceae) revealed activity against the murine macrophage-like cell line RAW 264.7. Systematic bioassay-guided fractionation of this extract gave an active saponin-containing fraction from which four saponins were isolated. Use of 1D ((1)H, (13)C, DEPT135) and 2D (COSY, TOCSY, HSQC, and HMBC) NMR, mass spectrometry and sugar analysis gave their structures as 3-O-(beta-D-glucopyranosyl-(1-->6)-beta-D-glucopyranosyl)-28-O-(alpha-L-rhamnopyranosyl-(1-->3)[beta-D-xylopyranosyl-(1-->4)]-beta-D-xylopyranosyl-(1-->4)-alpha-L-rhamnopyranosyl-(1-->2)-alpha-L-arabinopyranosyl)-16alpha-hydroxyprotobassic acid, 3-O-beta-D-glucopyranosyl-28-O-(alpha-L-rhamnopyranosyl-(1-->3)[beta-D-xylopyranosyl-(1-->4)]-beta-D-xylopyranosyl-(1-->4)-alpha-L-rhamnopyranosyl-(1-->2)-alpha-L-arabinopyranosyl)-16alpha-hydroxyprotobassic acid, 3-O-(beta-D-glucopyranosyl-(1-->6)-beta-D-glucopyranosyl)-28-O-(alpha-L-rhamnopyranosyl-(1-->3)-beta-D-xylopyranosyl-(1-->4)[beta-D-apiofuranosyl-(1-->3)]-alpha-L-rhamnopyranosyl-(1-->2)-alpha-L-arabinopyranosyl)-16alpha-hydroxyprotobassic acid, and the known compound, 3-O-beta-D-glucopyranosyl-28-O-(alpha-L-rhamnopyranosyl-(1-->3)[beta-D-xylopyranosyl-(1-->4)]-beta-D-xylopyranosyl-(1-->4)-alpha-L-rhamnopyranosyl-(1-->2)-alpha-L-arabinopyranosyl)-protobassic acid. Two further saponins were obtained from the same fraction, but as a 5:4 mixture comprising 3-O-(beta-D-glucopyranosyl)-28-O-(alpha-L-rhamnopyranosyl-(1-->3)-beta-D-xylopyranosyl-(1-->4)[beta-D-apiofuranosyl-(1-->3)]-alpha-L-rhamnopyranosyl-(1-->2)-alpha-L-arabinopyranosyl)-16alpha-hydroxyprotobassic acid and 3-O-(beta-D-apiofuranosyl-(1-->3)-beta-D-glucopyranosyl)-28-O-(alpha-L-rhamnopyranosyl-(1-->3)[beta-D-xylopyranosyl-(1-->4)]-beta-D-xylopyranosyl-(1-->4)-alpha-L-rhamnopyranosyl-(1-->2)-alpha-L-arabinopyranosyl)-16alpha-hydroxyprotobassic acid, respectively. This showed greater cytotoxicity (IC(50)=11.9+/-1.5 microg/ml) towards RAW 264.7 cells than the original extract (IC(50)=39.5+/-4.1 microg/ml), and the saponin-containing fraction derived from it (IC(50)=33.7+/-6.2 microg/ml).

Triterpenoid saponins from the cytotoxic root extract of Sideroxylon foetidissimum, an endemic Yucatecan medicinal plant

The flora of the Yucatan peninsula (Mexico) includes approximately 3000 plant species. Sideroxylon foetidissimum Jacq. subsp. gaumeri (Sapotaceae) is an endemic plant to the Yucatan peninsula; its fruit is edible and local people use the plant for medicinal purposes, although no details on its preparation or application are available [1,2]. A preliminary cytotoxic evaluation of the ethanolic root extract of S. foetidissimum revealed a potent activity against murine macrophage like cell line RAW 264.7 (IC50=39.54±4.11µg/mL). The systematic bioassay-guided fractionation of the extract resulted in the identification of the active saponin-containing fraction (IC50=33.69±6.19µg/mL). Four new triterpenoid saponins and a 1:1 mixture of two saponins were isolated from the active saponin- containing fraction. The evaluation of their cytotoxic activity revealed no activity for the tested pure saponins; however, the 1:1 mixture of saponins showed a potent activity (IC50=11.91±1.49µg/mL). The isolation of the saponins was carried out using semi-preparative HPLC. The structural assignments of the pure saponins were based on 1D (1H and 13C and DEPT-135) and 2D (COSY, HMBC, HSQC and TOCSY) NMR and mass spectrometry analyses. In this presentation, the isolation, identification and cytotoxic activity of the isolated compounds is discussed in more detail.

Distress in children with learning disabilities at a respite unit: perspective on their experiences

Numerous studies have investigated the benefits of respite to families with a disabled child. Far fewer have examined the effects on the child and none have systematically compared information about this from different sources. Reports of behavioural reactions and views on distress were gathered from parents, teachers and respite staff. Children were also asked for their views. Over half the children (54%) were reported to show medium or strong negative reactions lasting for 1 or more days by a parent or teacher. Reported reactions varied widely between home and school and no concordance was found between parents, teachers and respite staff groups regarding distress. Some children's views differed from those of their parent or teacher. The findings highlight the extent of differences in perspectives and suggest the need for greater awareness of the possible distress to children attending respite. This is discussed in relation to factors such as the potential conflict of interests between parents and children, communication and behavioural difficulties, and the context in which the child is observed.