Search

In this paper we continue our investigation of the topological filtration on the complex representation ring R(G) of a finite group, see [4] and [5]. To recall the basic definitions from (1): let map a k -dimensional representation ζ to the (flat) vector bundle over the classifying space B G associated to the universal G -bundle by the G-structure on C k . Then, if denotes the (2k − l)-skeleton of B G

The reactions of the olefins Ph2ArC·CHCH2(Ar = Ph and p-anisyl) with lead tetra-acetate and with iodine in the presence of silver acetate have been studied and conclusions have been reached about the mechanisms of oxidation (which, in all cases, is accompanied by rearrangement). In particular, evidence is adduced that a carbonium ion is formed at each of two phases of the reaction with each reagent. The olefins Ph2ArC·CMeCH2(Ar = Ph and p-anisyl) are not oxidised by lead tetra-acetate under the same conditions, although evidence was obtained that the latter olefin forms a complex with the oxidant.

The lacunae in our knowledge of the coefficients have made direct computations in the homology theory is?'(X, A) almost impossible. This note sidesteps the difficulty by exploiting the relationship between the theories KO* and Qsp, which corresponds to that between KU* and Qu, and which is fully discussed in Chapter II of [1]. In this way we are able to calculate the additive orders of some important elements in Qs*(Z,) (p prime), the module of principal Zp-manifolds with compatible weak symplectic structure. Perhaps the most interesting aspect of the computation is the difference between the cases p odd and p equals 2, reflecting the presence of 2-torsion in Qsp. I am grateful to Elmer Rees for discussing this problem with me and for showing me his version of the computations in [2] for real projective space.

The mass spectra of all three nitrophenyl(phenyl)methanes (nitrodiphenylmethanes) show an M–OH species produced directly from the molecular ion. In the case of the 2-isomer this arises almost entirely by the expected interaction between the ortho-substituents. Deuterium labelling shows that, for the 4-isomer, the hydrogen atom lost in the hydroxyl radical originates primarily in the aromatic ring bearing the nitro-substituent and a mechanism is suggested to account for this. The formation of the M–17 ion may be followed by loss of a second hydroxy-group. Discrepancies in the conclusions drawn from a study of the molecular ion region of two deuteriated analogues of 2-nitrodiphenylmethane highlight the danger of relying on evidence from the spectrum of a single labelled compound to confirm a suspected fragmentation mode. The mass spectra of some related compounds are also discussed.

Single crystals of Te-doped Bi95Sb5 have been grown by the zone- melting technique at a zone-pass rate of no more than 0.4 mm H-1 so as to avoid constitutional supercooling. The nominal tellurium concentration ranged from zero to 0.1 at.%. Measurements of the electrical resistivity, Hall coefficient and weak-field magneto-resistance, as well as the zero-field and high-field Seebeck coefficient, have been carried out at 80 degrees K. The results have been interpreted in terms of bismuth- like energy bands at the T points (holes) and L points (electrons) of the Brillouin zone. The observations are consistent with a ratio mBEg equal to 0.65 m0 eV-1, where mB is the density-of- states mass of the electron band at its edge, m0 is the free- electron mass and Eg is the direct energy gap.

The heat leaks through a themocouple mounted upon a multilayer stack are examined. With the thermoelectric materials at present available it is impossible to compensate completely for heat leaks through such mechanical supports across which large temperature differences exist. Nevertheless in these circumstances such an arrangement is often superior to the use of increased thicknesses of conventional insulants in applications where space and weight have to be limited.

Our investigation starts from the question: is the even dimensional cohomology of the non-abelian group of order p 3 and exponent p generated by Chern classes? From the computation of the complete cohomology ring in [8] one quickly sees that the essential problem is to express elements of the form cor ( γ k ), γ ∈ H 2 ( k , ℤ), K a subgroup of index p , in terms of Chern classes. For a more general pair of groups ( K ≤ G ) it is known, see [7] that the best for which one can hope is a description of some multiple of cor ( γ k ) in this way. Our first theorem shows that, under suitable hypotheses (satisfied in particular by the example of order p 3 ) the numerical factor may be removed. Thus

Like styrene, α-methylstyrene and cis- and trans-β-methylstyrene are oxidised by lead tetra-acetate by concurrent homolytic and heterolytic pathways. The relative significance of the two types of reaction is dependent on the conditions. For α-methylstyrene, the relative importance of the homolytic reaction is much smaller than for styrene, at least in part because the heterolytic reaction is so much faster (krel.= 19), whereas for the β-methylstyrenes both types of reaction are much slower than for styrene. The heterolytic reaction occurs by way of an adduct for which there are competitive reaction paths, namely, the migration of the phenyl group and the formation of an acetoxonium ion; for α-methylstyrene, the former dominates whereas, for the β-methylstyrenes, products to be expected from phenyl-migration could not be detected, and an explanation for this difference is suggested. The acetoxonium ion can be opened by reaction with water to give hydroxyacetates, and this has enabled the stereochemistry of the heterolytic reactions of the β-methylstyrenes with lead tetra-acetate to be studied; the results are compared with those for oxidation by the ‘wet’ Prevost procedure. Autoxidation is catalysed under the reaction conditions, and gives hydroxyacetates and the aromatic carbonyl compounds formed by cleavage of the olefinic bond.

Studies have been made of the temperature dependence of the switching characteristics of thin and thick chalcogenide switches. The onset of break down in both can be described quantitatively be thermal avalanching, although in the former switching disappears at the glass transition temperature. This observation, together with a large activation energy (1·6 ev) deduced from measurement of the recovery time after a single switching event, have been used to formulate a qualitative model of the switching action, after breakdown. It has been suggested that at the glass transition temperature a hightly-conducting phase is precipitated out of the glass matrix to stabilize the temperature, so preventing dielectric breakdown and enabling repeated switching from a resistive to a conducting state.

The mass spectrum of 1-chlorobenzotriazole contains ions derived from benzotriazole, a product of an exchange reaction with water in the source of the mass spectrometer. Relatively intense ions derived from iodine, iodine monobromide and other inter-halogen compounds are also observed. These species are produced by oxidation of involatile halide coatings in the source region by 1-chlorobenzotriazole. It is suggested that anomalous peaks produced by oxidation-reduction reactions in the source may be expected in the spectrum of any organic oxidant.

A model for the first fire process and subsequent threshold switching action suggested by Thomas, Fray and Bosnell (1972), in both monostable and bistable glassy semiconducting diodes is further experimentally investigated in this communication. We have carried out electron microscope and magneto-resistance studies of monostable switches. The microscopy studies have shown that in a formed monostable device, even when the device is still operating satisfactorily, a filament of substantially different composition is precipitated from the matrix. These observations were performed on thin film switches prepared by r.f. sputtering from a Si12Ge10Te48As30 target. This filament has been isolated and shown to contain large single crystals of tellurium embedded in a glassy matrix. The major axes of these tellurium crystals were aligned parallel to the applied electric field. Magnetoresistance studies, in fields up to 180 kG, in the on-state of a monostable switch showed that the resistivity is inversely p...

Switching behaviour, rather than dielectric breakdown, is believed to occur in the amorphous elements Si and Ge. We have found that the threshold voltage is dependent on the composition of the electrodes. We have suggested that this dependence is related to the appropriate crystallization temperatures of these amorphous semiconductors sandwiched between certain metals. Crystallization occurs during the switching process and probably stabilizes the temperature after thermal runaway initiates a switching event.

In this note we prove a gloss on the usuals-cobordism theorem, which may be of interest, since it holds one dimension lower than the theorem itself. Our result is that everys-cobordismis its own left and right inverse in the groupoid of allh-cobordisms, studied by Stallings in (3).

This survey article should be read in conjunction with that of Glen Bredon; the difference being that he discusses a large number of particular examples, while we wish to outline the progress which is being made towards classifying involutions in general. In particular the reader wishing for a summary of the important work of Montgomery and Yang on 7-spheres is referred to the article of Bredon. Our survey divides naturally into a discussion of free involutions and of involutions with a fixed point set. The subjects covered in this article reflect the author’s interests. They fully recognize their ignorance of the work of many other investigators, and that this is a reflection on them only.