Diruthenium(II,III) tetramidates as a new class of oxygenation catalysts

Two new diruthenium(II,III) tetramidate compounds, Ru(2)(NHOCC(CH(3))(2))(4)Cl (1) and Ru(2)(NHOCCH(2)CH(3))(4)Cl (2) have been prepared and structurally characterized by X-ray crystallography. The activity of promoting sulfide oxygenation using simple oxidants such as hydrogen peroxide (H(2)O(2)) and tert-butyl hydroperoxide (TBHP) was studied. A UV-kinetics study indicated that the initial rates of 1 and 2 are comparable to the previously studied diruthenium tetracarboxylates in promoting TBHP oxygenation of methyl phenyl sulfide (MPS). Using excess oxidant and CH(3)CN as the solvent, organic sulfides MPS and diphenyl sulfide (PPS) were oxidized using 1 mol% of the catalytic species. Compound 1 is more effective than 2 in converting sulfides to sulfoxide under the same conditions. Fast conversion was achieved when the reactions were carried out in the solvent-free conditions, and the major oxidation product was the sulfoxide. The electronic structure of the title compounds was studied with DFT calculations to gain an understanding of the activation of peroxy reagents.     

Layered inorganic-organic frameworks based on the 2,2-dimethylsuccinate ligand: structural diversity and its effect on nanosheet exfoliation and magnetic properties

The structures of four new 2,2-dimethylsuccinate frameworks suitable for exfoliation into nanosheets using ultrasonication are reported. These hybrid compounds contain either monovalent (Li(+)) or divalent (Co(2+) and Zn(2+)) cations, and they all feature hydrophobically capped covalently bonded layers that only interact with each other via weak van der Waals forces. Critically this shows that the use of this dicarboxylate ligand generally yields two dimensional compounds suitable for simple and affordable nanosheet exfoliation. This extends the range of frameworks that can be exfoliated and highlights the 2,2-dimethylsuccinate ligand as an excellent versatile platform for the production of nanosheets. The topologies of the layers in each framework were found to vary significantly and this appears to have a significant effect on the relative size of the nanosheets produced; increased space between methyl groups and more extensive inorganic connectivity appears to favour the formation of thin nanosheets with larger lateral dimensions. Additionally the magnetic properties of two of these frameworks were examined, and it was found that both exhibit strong low dimensional antiferromagnetic coupling despite their well-separated layers preventing three dimensional magnetic order.     

Synthesis of U(IV) imidos from Tp*2U(CH2Ph) (Tp* = hydrotris(3,5-dimethylpyrazolyl)borate) by extrusion of bibenzyl

Addition of organic azides, N(3)R (R = 2,4,6-trimethylphenyl (Mes), phenyl (Ph), 1-adamantyl (Ad)), to a solution of the uranium(III) alkyl complex, Tp*(2)U(CH(2)Ph) (Tp* = hydrotris(3,5-dimethylpyrazolyl)borate) (1), results in the formation of a family of uranium(iv) imido derivatives, Tp*(2)U(NR) (2-R). Notably, these complexes were synthesized in high yields by coupling of the benzyl groups to form bibenzyl. The uranium(IV) imido derivatives, 2-Mes, 2-Ph, and 2-Ad, were all characterized by both (1)H NMR and IR spectroscopy, and 2-Mes and 2-Ad were also characterized by X-ray crystallography. In the molecular structure of 2-Mes, typical κ(3)-coordination of the Tp* ligands was observed; however in the case of 2-Ad, one pyrazole ring of a Tp* ligand has rotated away from the metal centre, forcing a κ(2)-coordination of the pyrazoles. This results in a uranium-hydrogen interaction with the Tp* B-H. Treating these imido complexes with para-tolualdehyde results in multiple bond metathesis, forming the terminal uranium(IV) oxo complex, Tp*(2)U(O), and the corresponding imine.     

Chermak–Delgado Lattice Extension Theorems

If G is a finite group with subgroup H, then the Chermak–Delgado measure of H (in G) is defined as |H||C _G (H)|. The Chermak–Delgado lattice of G, denoted 𝒞𝒟(G), is the set of all subgroups with maximal Chermak–Delgado measure; this set is a moduar sublattice within the subgroup lattice of G. In this paper we provide an example of a p-group P, for any prime p, where 𝒞𝒟(P) is lattice isomorphic to 2 copies of ?₂ (a quasiantichain of width 2) that are adjoined maximum-to-minimum. We introduce terminology to describe this structure, called a 2-string of 2-diamonds, and we also give two constructions for generalizing the example. The first generalization results in a p-group with Chermak–Delgado lattice that, for any positive integers n and l, is a 2l-string of n-dimensional cubes adjoined maximum-to-minimum and the second generalization gives a construction for a p-group with Chermak–Delgado lattice that is a 2l-string of ? _p+1 (quasiantichains, each of width p + 1) adjoined maximum-to-minimum.     

The visibility of models: using technology as a bridge between mathematics and engineering

Engineering mathematics is traditionally conceived as a set of unambiguous mathematical tools applied to solving engineering problems, and it would seem that modern mathematical software is making the toolbox metaphor ever more appropriate. The validity of this metaphor is questioned and the case is made that engineers do in fact use mathematics as more than a set of passive tools— that mathematical models for phenomena depend critically on the settings in which they are used and the tools with which they are expressed. The perennial debate over whether mathematics should be taught by mathematicians or by engineers looks increasingly anachronistic in the light of technological change, and the authors suggest that it is more instructive to examine the potential of technology for changing the relationships between mathematicians and engineers, and for connecting their respective knowledge domains in new ways.     

Flame chemistry of tetrahydropyran as a model heteroatomic biofuel

The flame chemistry of tetrahydropyran (THP), a cyclic ether, has been examined using vacuum-ultraviolet (VUV)-photoionization molecular-beam mass spectrometry (PI-MBMS) and flame modeling, motivated by the need to understand and predict the combustion of oxygen-containing, biomass-derived fuels. Species identifications and mole-fraction profiles are presented for a fuel-rich (Φ = 1.75), laminar premixed THP–oxygen–argon flame at 2.66 kPa (20.0 Torr). Flame species with up to six heavy atoms have been detected. A detailed reaction set was developed for THP combustion that captures relevant features of the THP flame quite well, allowing analysis of the dominant kinetic pathways for THP combustion. Necessary rate coefficients and transport parameters were calculated or were estimated by analogies with a recent reaction set [Li et al., Combust. Flame 158 (2011) 2077–2089], and necessary thermochemical properties were computed using the CBS-QB3 method. Our results show that under the low-pressure conditions, THP destruction is dominated by H-abstraction, and the three resulting THP-yl radicals decompose primarily by β-scissions to two- and four-heavy-atom species that are generally destroyed by β-scission, abstraction, or oxidation.     

Properties of an h-Bernstein-like basis and curves

Blossoming is a useful technique to study bases and curve representations in computer-aided geometric design. Recently Simeonov et al. (Comput Aided Geom Des 28:549–565, 2011) have used a blossom generalization, namely the h-blossom, to derive new results about the h-Bernstein basis and h-Bézier curves that have previously been studied in approximation theory and computer-aided geometric design. This paper introduces a basis related to the h-Bernstein basis. There is a close relationship between this new basis and the h-Bernstein basis, between the new basis and the h-blossom, and between the new basis and “progressive” curves. This paper explores these relationships and uses them to derive properties both of the new basis itself, and of curves represented in terms of the new basis.     

Role of Context in Risk-Based Reasoning

In this article we report the influence of contextual factors on mathematics and science teachers' reasoning in risk-based decision-making. We examine previous research that presents judgments of risk as being subjectively influenced by contextual factors and other research that explores the role of context in mathematical problem-solving. Our own approach has been to develop carefully designed software tools that support the user to empathize with a hypothetical person, Deborah, who suffers from a medical condition. The tools were used by a group of teachers who were asked to help Deborah decide whether to have an operation that could cure the condition but which carries particular risks. In order to make this decision, the teachers were required to model the risks of the operation and also the lifestyle decisions that Deborah might make. We trace the teachers' efforts to coordinate judgments of likelihood and impact. The data emphasize the sensitivity of reasoning to matters of context; we set out in detail the various ways in which the process was affected by context.     

Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice

We show that the spin-liquid phase of the half-filled Hubbard model on the triangular lattice can be described by a pure spin model. This is based on a high-order strong coupling expansion (up to order 12) using perturbative continuous unitary transformations. The resulting spin model is consistent with a transition from three-sublattice long-range magnetic order to an insulating spin-liquid phase, and with a jump of the double occupancy at the transition. Exact diagonalizations of both models show that the effective spin model is quantitatively accurate well into the spin-liquid phase, and a comparison with the Gutzwiller projected Fermi sea suggests a gapless spectrum and a spinon Fermi surface.