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.     

Auditory backward recognition masking in children with a specific language impairment and children with a specific reading disability

The auditory backward recognition masking (ABRM) and intensity discrimination (ID) thresholds of children with a specific language impairment and poor reading (SLI-poor readers), children with an SLI and average reading (SLI-average readers), children with a specific reading disability and average spoken language skills (SRD-average language), and children with normal spoken and written language (controls) were estimated with "child-friendly" psychophysical tasks. The pattern of ABRM and ID scores suggests that a subset of children with concomitant oral language and reading impairments has poor ABRM thresholds, and that a subgroup of children with an SLI or SRD has poorer ID thresholds than controls. The latter result warns against using rapid auditory processing tasks that do not actively control for auditory discrimination ability. Further, some unusually poor ABRM scores and ID scores question the validity of extreme scores produced by children on psychophysical tasks. Finally, the poor oral language scores of many of the children who had impaired reading highlight the need to test the oral language skills of SRD samples to ascertain how homogeneous and specifically disabled they really are.     

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.     

Applying Unconventional Spectroscopies to the Single-Molecule Magnets,Co(PPh3)2X2 (X=Cl,Br, I): Unveiling Magnetic Transitions and Spin-Phonon Coupling

Large separation of magnetic levels and slow relaxation in metal complexes are desirable properties of single-molecule magnets (SMMs). Spin-phonon coupling (interactions of magnetic levels with phonons) is ubiquitous, leading to magnetic relaxation and loss of memory in SMMs and quantum coherence in qubits. Direct observation of magnetic transitions and spin-phonon coupling in molecules is challenging. We have found that far-IR magnetic spectra (FIRMS) of Co(PPh₃)₂X₂ ( Co-X ; X=Cl, Br, I) reveal rarely observed spin-phonon coupling as avoided crossings between magnetic and u-symmetry phonon transitions. Inelastic neutron scattering (INS) gives phonon spectra. Calculations using VASP and phonopy programs gave phonon symmetries and movies. Magnetic transitions among zero-field split (ZFS) levels of the S=3/2 electronic ground state were probed by INS, high-frequency and -field EPR (HFEPR), FIRMS, and frequency-domain FT terahertz EPR (FD-FT THz-EPR), giving magnetic excitation spectra and determining ZFS parameters (D, E) and g values. Ligand-field theory (LFT) was used to analyze earlier electronic absorption spectra and give calculated ZFS parameters matching those from the experiments. DFT calculations also gave spin densities in Co-X , showing that the larger Co(II) spin density in a molecule, the larger its ZFS magnitude. The current work reveals dynamics of magnetic and phonon excitations in SMMs. Studies of such couplings in the future would help to understand how spin-phonon coupling may lead to magnetic relaxation and develop guidance to control such coupling.     

Short wavelength light reflecting films from side‐chain liquid crystal homopolymers with chiral spacers

A series of acrylate monomers with alkoxy tails of varying lengths are synthesised and polymerised. The butoxy analogue had a stable enantiotropic cholesteric liquid crystalline phase which formed a grandjean texture when prepared as a thin film between glass slides. The polymer was mixed with a low molar mass nematic liquid crystal in various proportions and the pitch of the chiral nematic phases were determined using a cano‐wedge cell technique. The polymer prepared from (S)‐2‐(4‐butoxyphenyl‐4′‐benzoyloxy)‐1‐methyl ethyl acrylate had a pitch length of 113 nm which indicates that the polymer film could be employed in optical devices requiring selective reflection of light with short wavelengths in the region of 170 nm. Copyright © 2001 John Wiley & Sons, Ltd.