Graded Lie algebras of maximal class IV

We describe the isomorphism classes of certain infinite-dimensional graded Lie algebras of maximal class, generated by an element of weight one and an element of weight two, over fields of odd characteristic.Comment: 38 pages. See also http://www-math.science.unitn.it/~caranti/ and http://users.ox.ac.uk/~vlee

An analogue of Ryser's Theorem for partial Sudoku squares

In 1956 Ryser gave a necessary and sufficient condition for a partial latin rectangle to be completable to a latin square. In 1990 Hilton and Johnson showed that Ryser's condition could be reformulated in terms of Hall's Condition for partial latin squares. Thus Ryser's Theorem can be interpreted as saying that any partial latin rectangle $R$ can be completed if and only if $R$ satisfies Hall's Condition for partial latin squares. We define Hall's Condition for partial Sudoku squares and show that Hall's Condition for partial Sudoku squares gives a criterion for the completion of partial Sudoku rectangles that is both necessary and sufficient. In the particular case where $n=pq$, $p|r$, $q|s$, the result is especially simple, as we show that any $r \times s$ partial $(p,q)$-Sudoku rectangle can be completed (no further condition being necessary).Comment: 19 pages, 10 figure

A complete sample of Seyfert galaxies selected at 1/4 keV

We have used the ROSAT Bright Source Catalogue to extract a complete sample of sources selected in the band from 0.1-0.4 keV. This 1/4 keV-selected sample is comprised of 54 Seyfert galaxies, 25 BL Lacertae objects, 4 clusters and 27 Galactic stars or binaries. Seyfert-type galaxies with ``ultrasoft'' X-ray spectra can very often be classed optically as Narrow-line Seyfert 1s (NLS1s). Such objects are readily detected in 1/4 keV surveys; the sample reported here contains 20 NLS1s, corresponding to a 40% fraction of the Seyferts. Optical spectra of the Seyfert galaxies were gathered for correlative analysis, which confirmed the well-known relations between X-ray slope and optical spectral properties (e.g., [O III]/H-beta ratio; Fe II strength, H-beta width). The various intercorrelations are most likely driven, fundamentally, by the shape of the photoionising continuum in Seyfert nuclei. We argue that a steep X-ray spectrum is a better indicator of an ``extreme'' set of physical properties in Seyfert galaxies than is the narrowness of the optical H-beta line. (Abridged)Comment: 17 pages, 4 figures, accepted for publication in MNRA

Thermally stable laminating resins Final report

Polyimide resin and resin reinforced composite

Development of autoclave moldable addition-type polyimides

Chemistry and processing modifications of the poly(Diels Alder) polyimide (PDA) resin were performed to obtain structural composites suitable for 589 K (600 F) service. This work demonstrated that the PDA resin formulation is suitable for service at 589 K (600 F) for up to 125 hours when used in combination with Hercules HTS graphite fiber. Sandwich panels were autoclave molded using PDA/HTS skins and polyimide/glass honeycomb core. Excellent adhesion between honeycomb core and the facing skins was demonstrated. Fabrication ease was demonstrated by autoclave molding three-quarter scale YF-12 wing panels

Smart Materials as Intelligent Insulation

In order to provide a robust infrastructure for the transmission and distribution of electrical power, understanding and monitoring equipment ageing and failure is of paramount importance. Commonly, failure is associated with degradation of the dielectric material; therefore the introduction of a smart moiety into the material is a potentially attractive means of continual condition monitoring. It is important that any introduction of smart groups into the dielectric does not have any detrimental effect on the desirable electrical and mechanical properties of the bulk material. Initial work focussed on the introduction of fluorophores into a model dielectric system. Fluorescence is known to be a visible effect even at very low concentrations of active fluorophores and therefore was thought well suited to such an application. It was necessary both to optimise the active fluorophore itself and to determine the most appropriate manner in which to introduce the fluorophores into the insulating system. This presentation will describe the effect of introducing fluorophores into polymeric systems on the dielectric properties of the material and the findings thus far [1]. Alternative smart material systems will also be discussed along with the benefits and limitations of smart materials as electric field sensors