Density functional study on the structure and stability of positive iron rare-gas complexes, FeXn (X=Ar, Xe; n=1–6)

The structures and atomization energies of positively charged complexes of iron with argon and xenon, Fe⁺X_n (X=Ar, Xe; n=1–6) are investigated by density functional theory calculations. We explain the special stability of some of these complexes (“magic numbers”) – that has been observed in previous laser ablation and multi-photon ionization experiments – and predict their geometries.     

The first example of a recursive function which is not primitive recursive

The first example of a recursive function which is not primitive recursive is usually attributed to W. Ackermann. The authors of the present paper show that such an example can also be found in a paper by G. Sudan, published concomitantly with Ackermann's paper.     

Experiencing the space we share: rethinking subjectivity and objectivity

Mathematics in schools exists substantially as pedagogical material crafted for supposed modes of apprehension. But of course such apprehension depends on how we understand mathematical objects and how we understand human subjects. The apprehension of mathematical objects is examined through sessions with student teachers researching their own spatial awareness from a pedagogical point of view. The paper is guided by the recent work of Alain Badiou whose philosophical model develops a Lacanian conception of human subjectivity and defines a new conception of objectivity. In this model the conception of subjectivity comprises a refusal to allow humans to settle on certain self-images that have fuelled psychology and set the ways in which humans are seen as apprehending the mathematically defined world. The assertion of an object, meanwhile, is associated with finding a place for it in a given supposed world, and it may reconfigure that world. The composite model understands learning as shared participation in renewal where there is a mutual dependency between the growth of human subjects and of mathematical objects. Renewal is referenced to a diversity of ever shifting discursive parameters that enable learning through negotiating the spaces within which we operate and the objects those spaces allow. Learning to teach then comprises developing sensitivity towards the discursive spaces that allow others to build objects. The paper provides examples from teacher education activities centred in addressing these concerns.     

Monomer Sequencing in Living Anionic Polymerization Using Kinetic Control

Alternating copolymers containing diphenylethylene (DPE) or diphenylethylene derivatives were prepared by living anionic polymerization using kinetic control. Due to steric hindrance DPE cannot homopolymerize. Therefore alternating copolymers can be prepared by ensuring the rate of cross-propagation (k₁₂) of the co-monomer is favoured over the rate of self-propagation (k₁₁). This reactivity ratio (r₁ = k₁₁/k₁₂) can be controlled by many different factors, such as choice of monomer, electron-donating or withdrawing substituents on DPE, choice of solvent, etc. We report our progress on preparing alternating copolymers by varying these factors.     

On the computability-theoretic complexity of trivial, strongly minimal models

We show the existence of a trivial, strongly minimal (and thus uncountably categorical) theory for which the prime model is computable and each of the other countable models computes . This result shows that the result of Goncharov/Harizanov/Laskowski/Lempp/McCoy (2003) is best possible for trivial strongly minimal theories in terms of computable model theory. We conclude with some remarks about axiomatizability.

     

Remote optical control of an optical flip-flop

We experimentally demonstrate control of a holding-beam-enabled optical flip-flop by means of optical signals that act in a remote fashion. These optical-control signals vary the holding-beam power by means of cross-gain modulation within a remotely located semiconductor optical amplifier (SOA). The power-modulated holding beam then travels through a resonant-type SOA, where flip-flop action occurs as the holding-beam power falls above and below the switching thresholds of the bistable hysteresis. Control is demonstrated using submilliwatt pulses whose wavelengths are not restricted to the vicinity of the holding beam. Benefits of remote control include the potential for controlling multiple flip-flops with a single pair of optical signals and for realizing all-optical control of any holding-beam-enabled flip-flop.     

Sulfur K-edge X-ray absorption spectroscopy as a probe of ligand-metal bond covalency: metal vs ligand oxidation in copper and nickel dithiolene complexes

A combination of Cu L-edge and S K-edge X-ray absorption data and density functional theory (DFT) calculations has been correlated with 33S electron paramagnetic resonance superhyperfine results to obtain the dipole integral (Is) for the S 1s-->3p transition for the dithiolene ligand maleonitriledithiolate (MNT) in (TBA)2[Cu(MNT)2] (TBA= tetra-n-butylammonium). The results have been combined with the Is of sulfide derived from XPS studies to experimentally obtain a relation between the S 1s-->4p transition energy (which reflects the charge on the S atom, QSmol) and the dipole integral over a large range of QSmol. The results show that, for high charges on S, Is can vary from the previously reported Is values, calculated using data over a limited range of QSmol. A combination of S K-edge and Cu K- and L-edge X-ray absorption data and DFT calculations has been used to investigate the one-electron oxidation of [Cu(MNT)2]2- and [Ni(MNT)2]2-. The conversion of [Cu(MNT)2]2- to [Cu(MNT)2]- results in a large change in the charge on the Cu atom in the molecule (QCumol) and is consistent with a metal-based oxidation. This is accompanied by extensive charge donation from the ligands to compensate the high charge on the Cu in [Cu(MNT)2]- based on the increased S K-edge and decreased Cu L-edge intensity, respectively. In contrast, the oxidation of [Ni(MNT)2]2- to [Ni(MNT)2]- results in a small change in QNimol, indicating a ligand-based oxidation consistent with oxidation of a molecular orbital, psiSOMO (singly occupied molecular orbital), with predominant ligand character.     

Quantum control of two-qubit entanglement dissipation

We investigate quantum control of the dissipation of entanglement under environmental decoherence. We show by means of a simple two-qubit model that standard control methods – coherent or openloop control – will not in general prevent entanglement loss induced by a Markovian environment. However, we propose a control method utilizing a Wiseman–Milburn feedback/measurement control scheme which will effectively negate environmental entanglement dissipation.     

The Euler Class in homological algebra

Let G_τ be the topological group of orientation preserving homeomorphisms of the circle, and G_δ the same group with the discrete topology. Motivated by the classical problem of reducing a circle bundle with structure group G_τ to a totally disconnected subgroup K⊂G_δ, and more currently, applications to mapping class groups, we analyze, in a homological algebra setting, the role played by the Topological and Discrete Euler Classes. In particular we describe the Discrete Euler Class of G, and any of its subgroups K, explicitly as a group extension. We apply our constructions to show that the values of the Discrete Euler Class are bounded on any space, and we state triviality and non-triviality conditions for its powers in the based mapping class groups.