Congruences on generalized inverse semigroups

A generalized inverse semigroup is a regular semigroup whose idempotents satisfy a permutation identity X₁ X₂...X_n=X_p1 X_p2...X_pn, where (P₁, P₂..., P_n) is a nontrivial permutation of (1, 2,..., n). Yamada [4] has given a complete classification of generalized inverse semigroups in terms of inverse semigroups, left normal bands, and right normal bands. In this paper we show that every congruence on a generalized inverse semigroup is uniquely determined by a congruence on its associated inverse semigroup, left normal band, and right normal band. A converse is also provided. This paper is extracted from the doctoral thesis of the author written at Monash University under the direction of Professor G. B. Preston. The research was carried out while the author held a Commonwealth Postgraduate Award.     

The stabilizing effect of d orbitals on the central nitrogen atom in nitrogen-oxygen molecules and ions

The role of d orbitals in nitrogen-oxygen systems is studied by 4-31G calculations performed with and without inclusion of five gaussian d orbitals on each central nitrogen atom. The optimum NO distance generally contracts when polarization functions are included. Their stabilizing effect increases with oxidation state.     

Rheological study of an aromatic polyamide-hydrazide

Rheological and rheo-optical data are reported for the poly(terephthalamide of p-aminobenzhydrazide), X-500, in dimethyl sulfoxide solutions in the concentration range 0.2 to 6.0 g/100 ml. The objective of these measurements is to seek evidence of shear-induced isotropic → nematic phase transition. Three types of measurement, Couette, cone and plate, and capillary rheometer, all indicate that this system exhibits flow instabilities at high shear rates and concentrations. In this region both the viscosity and the primary normal stress difference decrease with time under shear. In the capillary rheometer the apparent viscosity is smaller for shorter capillaries and, for short capillaries, there is a range of shear rates in which plug flow and a coiled extrudate are observed. These instabilities may arise from the existence of a mixture of isotropic and nematic phases. At lower shear rates, where the flow behavior appears normal, the concentration dependence of the flow birefringence increases at a critical polymer concentration C This value is in reasonable accord with the concentration corresponding to the change of slope of logη (measured at low shear rate) vs. logC_p. Both the latter measurements appear to be sensitive to the onset of the phenomenon, which may be due to a shear-induced transition or the rheological effect of chain entanglements.     

Preparation of cyclonona-1,2,5-triene,cyclonona-1,2,5,7-tetraene and cyclodeca-1,2,5,6-tetraene

Cyclonona-1,2,5-triene (13a) and 7-methoxycyclonona-1,2,5-triene (13b) have been prepared in satisfactory yields by the action of MeLi on (12a) and (12b), respectively; cyclodeca-1,2,5,6-tetraene (29) has similar been prepared from 16. Cyclonona-1,2,5-7-tetraene (22), which was prepared from 20 at below ?40°, readily dimerizes to give 21; the half-time of the reaction is 10–20 min in CDCl₃ solution at 0°.     

Fmoc solid phase synthesis of polyamides containing pyrrole and imidazole amino acids

[structure: see text]. Polyamides containing N-methylimidazole (Im) and N-methylpyrrole (Py) amino acids are synthetic ligands that have an affinity and specificity for DNA comparable to those of many naturally occurring DNA binding proteins. A machine-assisted Fmoc solid phase synthesis of polyamides has been optimized to afford high stepwise coupling yields (>99%). Two monomer building blocks, Fmoc-Py acid and Fmoc-Im acid, were prepared in multigram scale. Cleavage by aminolysis followed by HPLC purification affords up to 200 mg quantities of polyamide with purities and yields greater than or equal to those reported using Boc chemistry. A broader set of reaction conditions will increase the number and complexity of minor groove binding polyamides which may be prepared and help ensure compatibility with many commercially available peptide synthesizers.     

Prenatal screening and the reduction of birth defects in populations

OBJECTIVES: Birth defects occur in populations in 3-5% of births. This paper assesses whether population-wide screening programmes for pregnant women would be likely to result in major decreases in the prevalence of birth defects. METHOD: Relevant literature on this question is reviewed and synthesized. RESULTS: Given certain assumptions, a decrease from 3-5 to 2-4% in the prevalence of defects at birth may be possible. The resources required to put in place an appropriately delivered programme to achieve this are substantial. CONCLUSIONS: As well as the potential benefit of a decrease, there are opportunity costs, and potential serious harms. Unless undertaken in a carefully planned and monitored way, a population-based birth defects reduction programme is likely to bring harm and anxiety rather than benefit.     

Stress-energy tensors and the Lichnerowicz Laplacian

To a critical point of a variational problem, we associate a divergence-free symmetric 2-tensor, called the stress-energy tensor. We calculate the Laplacian of this object as defined by Lichnerowicz. This has the property that it commutes with the divergence provided the Ricci curvature is covariantly constant. We deduce relations between different stress-energy tensors, discuss growth formulae and harmonic maps between spheres.