A homologous series of regioselectively tetradeprotonated group 8 metallocenes: new inverse crown ring compounds synthesized via a mixed sodium-magnesium tris(diisopropylamide) synergic base

Subjecting ferrocene, ruthenocene, or osmocene to the synergic amide base sodium-magnesium tris(diisopropylamido) affords a unique homologous series of metallocene derivatives of general formula [(M(C(5)H(3))(2))Na(4)Mg(4)(i-Pr(2)N)(8)] (where M = Fe (1), Ru (2), or Os (3)). X-ray crystallographic studies of 1-3 reveal a common molecular "inverse crown" structure comprising a 16-membered [(NaNMgN)(4)](4+) "host" ring and a metallocenetetraide [M(C(5)H(3))(2)](4-) "guest" core, the cleaved protons of which are lost selectively from the 1, 1', 3, and 3'-positions. Variable-temperature NMR spectroscopic studies indicate that 1, 2, and 3 each exist as two distinct interconverting conformers in arene solution, the rates of exchange of which have been calculated using coalescence and EXSY NMR measurements.     

Towards the biaxial nematic phase through molecular design

In this article, the search for the elusive biaxial nematic phase (NB) in liquid crystals is considered. The structure of the phase is described along with theoretical and computational work which suggests how it might be realised. An overview of the work of the Exeter group in this area is then given showing the different approaches adopted and illustrating how one of these has led to a new type of amphiphilicity based on shape.     

Exact solution of Maxwell's equations for optical interactions with a macroscopic random medium

We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial modes sampled at the Nyquist rate or better. The results point toward the emerging feasibility of direct, exact Maxwell equations modeling of light propagation through many millimeters of biological tissues. More generally, our results have a wider implication: Namely, the study of electromagnetic wave propagation within random media is moving toward exact rather than approximate solutions of Maxwell's equations.     

Shape amphiphiles: mixing rods and disks in liquid crystals

Mixtures of rodlike and disklike liquid crystals suffer from phase separation. However, such mixtures can be homogenized if a molecule is added which comprises a rod- and a disklike fragment linked together covalently. We have termed such a molecule a shape amphiphile and believe that this represents a new class of amphiphilicity.     

Bis(carbene)pyridine complexes of Cr(III): exceptionally active catalysts for the oligomerization of ethylene

Pincer-heterocyclic carbene complexes of Cr(III), of the form [2,6-(1-alkylimidazol-2-ylidene)pyridine]CrCl3, have been prepared and evaluated as catalysts for the oligomerization of ethylene to alpha-olefins. In combination with methylaluminoxane cocatalyst, exceptionally high activities are obtained, ranging up to ca. 40 000 g mmol-1 bar-1 h-1.     

A Functional Equation Arising from Simultaneous Utility Representations

Suppose that two classes of utility representations of preferences, one additive and one increasing increments, hold simultaneously over uncertain binary alternatives (gambles). This assumption leads to the functional equation $$ f[h(x-y)+y]=f[h(x)]-f[h(y)]+f(y)\qquad (\kappa >x\geq y\geq 0), $$ and to the inequality h(z) ≤ z (z ∈ [0, κ[), where the functions ? and h are strictly increasing maps of the real interval [0, κ[ onto the real intervals [0, λ[ and [0, μ[, respectively, κ, λ, μ ∈]0, ∞]. We present all solutions under the additional assumption of (first-order) differentiability.     

Promoting student engagement with mathematics support

This article reports the findings of qualitative research undertakento seek to identify the key reasons why some students are notengaging with mathematics support provided by Loughborough University.The research involved a number of focus groups and ‘onthe spot’ interviews with ‘non-users’ fromacross the campus. Barriers identified include a lack of awarenessof the location of support and a fear of embarrassment. Furtherinterviews were conducted with regular users of the supportin an attempt to understand how some of these barriers to usagemight be overcome. The article will discuss actions that maybe taken to improve student engagement with mathematics supportand the issue of how student motivation may affect such action.