Gold(III) template synthesis of a pendant-arm macrocycle

Gold(III)-directed condensation of ethane-1,2-diamine with nitroethane and formaldehyde yielded the gold-coloured macrocyclic complex (cis-6,13-dimethyl-6,13-dinitro-1,4,8,11-tetraazacyclotetradecan-1-ido)gold(III) and the orange acyclic complex (1,9-diamino-5-methyl-5-nitro-3,7-diazanoran-3-ido)gold(III) in good yields. Dissolution in strongly acidic solution gave the colourless fully protonated complexes. The pendant nitro groups are disposed on the same side of the macrocycle in a cis geometry, as confirmed by crystal structure analysis. In both complexes the gold ion lies in a square-planar environment of four nitrogen donors, and the co-ordinate bond to the deprotonated amine is shorter than the remaining Au-N distances.

Simulation of mixing in unsteady flow through a periodically obstructed channel

Fluid mixing in steady and unsteady Bow through a channel containing periodic square obstructions has been studied using a finite-difference simulation to determine fluid velocities, followed by the use of passive marker particle advection to look at fluid transport out of the cavities formed between each of the obstructions. The geometry and Bow conditions were chosen from the work by Perkins (1989, M.S. Thesis, Lehigh University; 1992, Ph.D. Thesis, Lehigh University); who investigated heat transfer enhancement due to unsteady flow through such an obstructed channel. Particle advection shows that Bow regimes which are predicted to give good mixing based on snapshots of instantaneous streamline contour plots were not necessarily able to efficiently mix fluid which started in the cavity regions throughout the channel. The use of Poincare sections shows regular regions existing under these conditions which inhibit efficient fluid transport. These regular regions are found to disappear when the unsteady Bow velocity is increased. (C) 1997 Elsevier Science Ltd.

Macrocycle formation through carbon acid-formaldehyde condensation reactions of bis(propane-1,2-diamine)- and bis (2-methylpropane-1,2-diamine)-copper(II) ions

The reaction of the bis(1,2-diamine) copper(II) complexes of racemic propane-1,2-diamine (pn) and 2-methylpropane-1,2-diamine (dmen) with formaldehyde and nitroethane in methanol under basic conditions yields minor macrocyclic condensation products in addition to the major acyclic products. Where C-pendant methyl groups on the pair of coordinated diamines are in cis dispositions, the first -NH-CH2-C(CH3)(NO2)-CH2-NH- ring formation occurs at amine pairs distant from these C-methyl substituents, and further reaction to yield a macrocycle is not observed. However, where the C-methyl substituents are in trans dispositions, the chemistry proceeds to yield the macrocycle. Commencing with pn, trans-(6,13-diammonio-2,6,9,13-tetramethyl-1,4,7,10-tetraazacyclotetradecane)copper(II) perchlorate formed and crystallized in the space group P2(1)/n, with a 9.782(2), b 9.2794(6), c 17.017(4) Angstrom, beta 103.24(1)degrees. The copper ion is found in a square-planar environment, with the two methyl groups of the pn residues and the pairs of introduced pendant groups all in trans arrangements.

Geometric and electronic information from the spectroscopy of six-coordinate copper(II) compounds

The ground and excited state geometry of the six-coordinate copper(II) ion is examined in detail using the CuF64- and Cu(H2O)(6)(2+) complexes as examples. A variety of spectroscopic techniques are used to illustrate the relations between the geometric and electronic properties of these complexes through the characterization of their potential energy surfaces.

Constructing a class of designs with proportional balance

Text serves as a sequel to 'Computational and Constructive Design Theory,' c1996; containing research papers and surveys of recent research work on design construction and computer-aided study of designs. For researchers in theory of computational designs.

The mu-way intersection problem for m-cycle systems

An m-cycle system of order upsilon is a partition of the edge-set of a complete graph of order upsilon into m-cycles. The mu -way intersection problem for m-cycle systems involves taking mu systems, based on the same vertex set, and determining the possible number of cycles which can be common to all mu systems. General results for arbitrary m are obtained, and detailed intersection values for (mu, m) = (3, 4), (4, 5),(4, 6), (4, 7), (8, 8), (8, 9). (For the case (mu, m)= (2, m), see Billington (J. Combin. Des. 1 (1993) 435); for the case (Cc,m)=(3,3), see Milici and Quattrochi (Ars Combin. A 24 (1987) 175. (C) 2001 Elsevier Science B.V. All rights reserved.

The metamorphosis of lambda-fold 4-wheel systems into lambda-fold 4-cycle systems

A 4-wheel is a simple graph on 5 vertices with 8 edges, formed by taking a 4-cycle and joining a fifth vertex (the centre of the 4-wheel) to each of the other four vertices. A lambda -fold 4-wheel system of order n is an edge-disjoint decomposition of the complete multigraph lambdaK(n) into 4-wheels. Here, with five isolated possible exceptions when lambda = 2, we give necessary and sufficient conditions for a lambda -fold 4-wheel system of order n to be transformed into a lambda -fold Ccyde system of order n by removing the centre vertex from each 4-wheel, and its four adjacent edges (retaining the 4-cycle wheel rim), and reassembling these edges adjacent to wheel centres into 4-cycles.

Star decompositions of cubes

Let Sk denote the complete bipartite graph K-1k and let e,, denote the ii-cube. We prove that the obvious necessary conditions for the existence of an S-k-decomposition of Q(n) are sufficient.

A new integrable model of strongly correlated electrons with Hubbard-like interaction

A new completely integrable model of strongly correlated electrons is proposed which describes two competitive interactions: one is the correlated one-particle hopping, the other is the Hubbard-like interaction. The integrability follows from the fact that the Hamiltonian is derivable from a one-parameter family of commuting transfer matrices. The Bethe ansatz equations are derived by algebraic Bethe ansatz method.