Silchester Roman Town Insula IX: the development of an urban property c. AD 40-50 - c. AD 250

The development of an urban property in the Roman town of Calleva Atrebatum (Silchester, Hampshire, England) is traced from the late 1st to the mid-3rd century AD. Three successive periods of building with their associated finds of artefacts and biological remains are described and interpreted with provisional reconstructions of the buildings. Links are provided to a copy of the Integrated Archaeological Database (IADB), archived by the Archaeology Data Service, which holds the primary excavation and finds records.

Analytical potentials for triatomic molecules IX. The prediction of anharmonic force constants from potential energy surfaces based on harmonic force fields and dissociation energies for SO2 and O3

Analytical potential energy functions which are valid at all dissociation limits have been derived for the ground states of SO2 and O3. The procedure involves minimizing the errors between the observed vibrational spectra and spectra calculated by a variational procedure. Good agreement is obtained between the observed and calculated spectra for both molecules. Comparisons are made between anharmonic force fields, previously determined from the spectral data, and the force fields obtained by differentiating the derived analytical functions at the equilibrium configurations.

Vibrational intensities IX: C2F6, extension and revision

The intensity of the low fundamental of C2F6 at 219 cm—1 was measured using a CsI prism. This completed earlier studies on the other fundamentals, and permits extension and revision of the interpretation. Effective bond moments are compared with those of other fluorocarbons.

Megnin re-analysed: the case of the newborn baby girl, Paris, 1878

This paper analyses acarological evidence from a 130-year-old forensic investigation. It was the first case in forensic acarology, i.e., the first case where mites provided substantial information to estimate the post-mortem interval (PMI). In 1878, the mites found in the mummified body of a newborn baby girl in Paris, France, were studied by acarologist and forensic entomologist Jean Pierre M,gnin. M,gnin estimated around 2.4 million mites in the skull and identified them as Tyroglyphus longior (Gervais), a junior synonym of Tyrophagus longior. He suggested that the arrival of these mites at the corpse would have occurred by phoresy on carrier insects, roughly 5 months before the autopsy. There is no doubt about the identification of the mites, M,gnin was a highly respected acarologist. However, two main factors affecting the biology of Tyrophagus mites were not included in the original analysis. First, M,gnin stated that the mites were phoretic. However, he probably did not have access to information about the natural history of the species, because as a rule Tyrophagus mites are non-phoretic. Considering the omnipresence of Tyrophagus mites in soil, most likely the mites will have arrived almost immediately after death. Second, temperature was not taken into account during the estimations of the mite population growth rate. The new analysis is based on current knowledge of Tyrophagus biology and includes temperature, estimated following a handful of weather reports of the years 1877 and 1878. The new projections indicate that non-phoretic mites may have colonised the body just after death and the colony would have built up over 8 months, contrary to the 5 months proposed by M,gnin. This new lapse of time agrees with the PMI proposed by Brouardel: on 15 January 1878 he postulated the death of the newborn to have occurred some 8 months before the autopsy.

Perspex machine IX: transreal analysis

We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In particular, we find a well defined value for zero to the power of zero. We also note that the computation of products via the transreal logarithm is identical to the transreal product, as expected. We then generalise all of the common, real, trigonometric functions to transreal functions and show that transreal (sin x)/x is well defined everywhere. This raises the possibility that transreal analysis is total, in other words, that every function and every limit is everywhere well defined. If so, transreal analysis should be an adequate mathematical basis for analysing the perspex machine - a theoretical, super-Turing machine that operates on a total geometry. We go on to dispel all of the standard counter "proofs" that purport to show that division by zero is impossible. This is done simply by carrying the proof through in transreal arithmetic or transreal analysis. We find that either the supposed counter proof has no content or else that it supports the contention that division by zero is possible. The supposed counter proofs rely on extending the standard systems in arbitrary and inconsistent ways and then showing, tautologously, that the chosen extensions are not consistent. This shows only that the chosen extensions are inconsistent and does not bear on the question of whether division by zero is logically possible. By contrast, transreal arithmetic is total and consistent so it defeats any possible "straw man" argument. Finally, we show how to arrange that a function has finite or else unmeasurable (nullity) values, but no infinite values. This arithmetical arrangement might prove useful in mathematical physics because it outlaws naked singularities in all equations.