Operations that preserve total dual integrality

There are many useful operations, such as adding slack variables, taking scalar multiples of inequalities, and applying Fourier-Motzkin elimination, that can be performed on a linear system such that if the system defines an integer polyhedron then so does the derived system. The topic dealt with here is whether or not these operations also preserve total dual integrality of linear systems.     

Rubber elasticity in relation to polyester networks

The equation of rubber elasticity has been applied to the dynamic shear modulus of styreneunsaturated polyester networks. Due to the non-ideal nature of the networks, the apparent front factor approached the theoretical value of 0.5 only when the crosslink density was low. At higher crosslink densities, it has been found that either the non-Gaussian theory of Smith or the steric interaction approach of Blanchard and Wooton satisfactorily describes the results.     

The synthesis of some pyrrolo[1,5-b:2,3-c′]dipyridazines

A facile method for the preparation of the aromatic pyrrolo[1,5-b:2,3-c']dipyridazine ring system is reported. A number of compounds have been prepared and the biological screening data reported.     

A note on the magnetic susceptibility of hydrogen and its isotopomers

A wavefunction used in an earlier calculation of the nuclear shielding of the hydrogen molecule has been tested by comparing the calculated magnetic susceptibility against that of Kolos and Wolniewicz. Good agreement is obtained. The procedure of Herman and Short for averaging over the nuclear motion has also been tested by comparing the predicted susceptibilities of H₂, Hd and D₂ with those obtained from averages of the Rydberg-Klein-Rees potential curves by Jain and Sahni. Again, good agreement is found.For the first time calculated values have been obtained for the susceptibilities of the isoropomers of hydrogen which contain tritium. It is predicted that accurate susceptibility measurements should not only be able to distinguish between all the various isotopomers but should also detect the temperature dependence of the susceptibility of any one isotopomer.     

Compounds of asymmetric convex bodies

Mahler obtained inequalities relating an0-symmetric convex body with its compounds. These results are extended to asymmetric convex bodies.     

1H NMR spectra and conformational analysis of some 1,4-dithiepan-6-ones

¹H NMR Parameters are reported for five 1,4-dithiepan-6-ones. 1,4-Dithiepan-6-one 1-oxide exists in solution as an equilibrium involving two different twist-chair conformations, which contrasts with its conformational behaviour in the solid state. Twist-chair conformers are also adopted by other members of the series, the favoured form varying with ring substitution. The S?O bond in 1,4-dithiepan-6-one 1-oxide and in its 5,5-dimethyl analogue exhibit a preference for the pseudoaxial site.     

Aromaticity and tautomerism—VII: Empirical resonance energy and conjugation energy of pyrazole and isoxazole from heats of dehydration data

The dehydration of various 4,5-dihydro-4- and -5-hydroxy derivatives of pyrazole and isoxazole has been investigated. Heats of dehydration of 4,5-duiydro-4-hydroxy-1,3,5-tripbenylpyrazole and 4,5-dihydro-5-hydroxy-isoxazole are evaluated and used to assess the empirical resonance energy and conjugation energy of pyrazole and isoxazole. The former possesses resonance stabilisation comparable to pyrrole but that of the latter is low.     

Characterization of microholograms recorded in a thermoplastic medium for three-dimensional optical data storage

A three-dimensional optical data storage system that combines a new recording material with a microholographic data format in which data are stored as single-bit microholograms is presented. This format offers less sensitivity to environmental conditions than the page-based holographic approach in addition to an increased compatibility with current storage technologies. The new recording material is based on a thermoplastic material. The results presented indicate that the dimensions of the microholograms are larger than those calculated by use of simple laser beam waist approximations and that multiple layers of microholograms would significantly affect signal levels. Data densities achievable with the microholographic format will likely be limited by those effects.