Cyclic polyamines <Emphasis Type="BoldItalic">via</Emphasis> a molybdenum(0) templated Mannich-type reaction

Reaction of [Mo(CO)₃(3-azahexane-1,6-diamine)] with formaldehyde and the carbon acid nitroethane leads to cyclisation involving one terminal amine and either the internal secondary amine (minor product) or the other terminal primary amine (major product), with zinc/acid reduction yielding new cyclic tetraamines, also characterised as their cobalt(III) complexes. This is the first example of Mannich-style formation of a pendant-arm triazamacrocycle around a molybdenum(0) template. The unexpected N-(1′-aminopropyl)-6-methyl-1,4-diazacycloheptan-6-amine minor product has been characterised by an X-ray structure as its cis-dichlorocobalt(III) complex.     

Computational fluid dynamics modelling of gas jets impinging onto liquid pools

Gas jets impinging onto a gas–liquid interface of a liquid pool are studied using computational fluid dynamics modelling, which aims to obtain a better understanding of the behaviour of the gas jets used metallurgical engineering industry. The gas and liquid flows are modelled using the volume of fluid technique. The governing equations are formulated using the density and viscosity of the “gas–liquid mixture”, which are described in terms of the phase volume fraction. Reynolds averaging is applied to yield a set of Reynolds-averaged conservation equations for the mass and momentum, and the k–ε turbulence model. The deformation of the gas–liquid interface is modelled by the pressure jump across the interface via the Young–Laplace equation. The governing equations in the axisymmetric cylindrical coordinates are solved using the commercial CFD code, FLUENT. The computed results are compared with experimental and theoretical data reported in the literature. The CFD modelling allows the simultaneous evaluation of the gas flow field, the free liquid surface and the bulk liquid flow, and provides useful insight to the highly complex, and industrially significant flows in the jetting system.     

Simple currents and extensions of vertex operator algebras

We consider how a vertex operator algebra can be extended to an abelian interwining algebra by a family of weak twisted modules which aresimple currents associated with semisimple weight one primary vectors. In the case that the extension is again a vertex operator algebra, the rationality of the extended algebra is discussed. These results are applied to affine Kac-Moody algebras in order to construct all the simple currents explicitly (except forE ₈) and to get various extensions of the vertex operator algebras associated with integrable representations.Supported by NSF grant DMS-9303374 and a research grant from the Committee on Research, UC Santa Cruz.Supported by NSF grant DMS-9401272 and a research grant from the Committee on Research, UC Santa Cruz.     

A family of graphs and the degree/diameter problem

We investigate a family of graphs relevant to the problem of finding large regular graphs with specified degree and diameter. Our family contains the largest known graphs for degree/diameter pairs (3, 7), (3, 8), (4, 4), (5, 3), (5, 5), (6, 3), (6, 4), (7, 3), (14, 3), and (16, 2). We also find a new bound for (3, 6) by an unrelated method. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 118–124, 2001