Electron-rich heteroaroylphosphonates and their reaction with trimethyl phosphite

Dialkyl heteroaroylphosphonates based on thiophene, pyrrole or furan have been prepared and their reactions with trimethyl phosphite investigated. Deoxygenation of the carbonyl groups in these heteroaroylphosphonates occurs to give carbene intermediates, which then undergo further reaction. In the case of the furan-3-oylphosphonates and those systems containing a thiophene or pyrrole ring, the major reaction pathway involves intermolecular trapping of the carbene intermediates by the trimethyl phosphite, leading to the formation of ylidic phosphonates that can be readily converted into the corresponding 1,1-bisphosphonates. However, in some furan-2-oylphosphonates the carbenes generated undergo ring-opening to initially give acyclic alkynylphosphonates which may react further to give other novel phosphorus compounds. The effects of substituents on the extent to which intermolecular trapping of the initially formed carbene competes with intramolecular rearrangement has been investigated. The latter process appears to be suppressed by a substituent at the 5-position of the furan ring, the resulting ylidic phosphonates being a rare example of an efficient intermolecular trapping of a furan-2-yl carbene.     

Topological insights in polynuclear Ni/Na coordination clusters derived from a schiff base ligand

This article presents the syntheses, crystal structures, topological features and magnetic properties of two Ni^II/Na^I coordination clusters formulated [Ni ₃ ^II Na(L1)₃(HL1)(MeOH)₂] (1) and [Ni ₆ ^II Na(L1)₅(CO₃)(MeO)(MeOH)₃(H₂O)₃]·4(MeOH) 2(H₂O) [2 4(MeOH) 2(H₂O)] where H₂L1 is the semi-rigid Schiff base ligand (E)-2-(2-hydroxy-3-methoxybenzylideneamino)-phenol). Compound 1 possesses a rare Ni ₃ ^II Na^I cubane (3M4-1) topology, and compound 2 is the first example in polynuclear Ni/Na chemistry that exhibits a 2,3,4M7-1 topology.     

A Fibonacci quotient

In this article, we describe the outcome of a mathematical collaboration between a university lecturer and an undergraduate student. The resulting investigation concerned a particular divisibility property of the Fibonacci numbers, and indeed it seems that a new result was found in this regard. An interesting point to be made here is that, although the mathematical content was relatively straightforward, this joint exploration did, in a very modest sense, mirror certain key aspects of the research process.     

A pair of Fibonacci-like polynomials arising from a special mapping

We study here a pair of sequences of polynomials that arise from a particular iterated mapping on the plane. We show how these sequences come about, and give some of their interesting mathematical properties.     

On the Ramsey number of the triangle and the cube

The Ramsey number r(K ₃,Q _n ) is the smallest integer N such that every red-blue colouring of the edges of the complete graph K _N contains either a red n-dimensional hypercube, or a blue triangle. Almost thirty years ago, Burr and Erd?s conjectured that r(K ₃,Q _n )=2 ⁿ⁺¹?1 for every n∈?, but the first non-trivial upper bound was obtained only recently, by Conlon, Fox, Lee and Sudakov, who proved that r(K ₃,Q _n )?7000·2 ⁿ . Here we show that r(K ₃,Q _n )=(1+o(1))2 ⁿ⁺¹ as n→∞.     

Studying the perturbative Reggeon

We consider the flavour non-singlet Reggeon within the context of perturbative QCD. This consists of ladders built out of “reggeized” quarks. We propose a method for the numerical solution of the integro-differential equation for the amplitude describing the exchange of such a Reggeon. The solution is known to have a sharp rise at low values of Bjorken-x when applied to non-singlet quantities in deep-inelastic scattering. We show that when the running of the coupling is taken into account this sharp rise is further enhanced, although the dependence is suppressed by the introduction of the running coupling. We also investigate the effects of simulating non-perturbative physics by introducing a constituent mass for the soft quarks and an effective mass for the soft gluons exchanged in the t-channel. Received: 30 June 1999 / Published online: 16 November 1999     

THE ‘NO BOUNDARY CONDITION’ OUTFLOW BOUNDARY CONDITION

We use a one-dimensional model problem of advection– diffusion to investigate the treatment recently advocated by Papanastasiou and colleagues to deal with boundary conditions at artificial outflow boundaries. Using finite elements of degree p, we show that their treatment is equivalent to imposing the condition that the (p+1 )st derivative of the dependent variable should vanish at a point close to the outflow. This is then shown to lead to errors of order 𝒪((h+1/Pe)1.6^p+1) in the numerical solutions (where h is the maximum element size and Pe is the global Peclet number), which is superior to the errors of order 𝒪(h^p+1+1/Pe) obtained using a standard no-flux outflow condition. These findings are verified by numerical experiments. © 1997 by John Wiley and Sons, Ltd.     

NO dissociation and N2 production in the presence of co-adsorbed SO2 and D2 on Pt(3 3 2)

NO dissociation and subsequent N₂ production in the presence of co-adsorbed S¹⁸O₂ and D₂ on the surface of stepped Pt(3 3 2) were studied using Fourier transform infra red reflection–absorption spectroscopy (FTIR-RAS) combined with thermal desorption spectroscopy (TDS). Reduction of NO by D (D₂ is adsorbed dissociatively on Pt surfaces) proceeds to a limited extent, because this reaction is rate-controlled by NO dissociation and the supply of D atoms at the higher surface temperatures at which NO dissociation becomes significant (350 K and higher). NO–D reaction is suppressed in the presence of S¹⁸O₂, depending significantly on the S¹⁸O₂ coverage and the competition between the reactions NO–D and S¹⁸O₂–D. When the supply of D₂ is limited, e.g., 0.1 L in this study, the presence of S¹⁸O₂ suppresses the NO–D reaction. With a sufficient supply of D₂, e.g., 0.4 L and higher, D-atom competing reactions do not play a role any more because the reactions of both NO and S¹⁸O₂ with D proceed only to a very limited extent. As such, generation of O atoms from S¹⁸O₂ dissociation is the main reaction that leads to the suppression in NO dissociation and consequently, N₂ production.It is also concluded that the presence of S¹⁸O₂ does not seriously poison the active sites on the Pt surface, providing that there is a sufficient D supply to remove O atoms from both NO dissociation and S¹⁸O₂ dissociation.     

Synthesis and characterization of a new fluorogenic substrate for alpha-galactosidase

Alpha-galactosidase A hydrolyzes the terminal alpha-galactosyl moieties from glycolipids and glycoproteins in lysosomes. Mutations in α-galactosidase cause lysosomal accumulation of the glycosphingolipid, globotriaosylceramide, which leads to Fabry disease. Small-molecule chaperones that bind to mutant enzyme proteins and correct their misfolding and mistrafficking have emerged as a potential therapy for Fabry disease. We have synthesized a red fluorogenic substrate, resorufinyl α-d-galactopyranoside, for a new α-galactosidase enzyme assay. This assay can be measured continuously at lower pH values, without the addition of a stop solution, due to the relatively low pK _a of resorufin (~6). In addition, the assay emits red fluorescence, which can significantly reduce interferences due to compound fluorescence and dust/lint as compared to blue fluorescence. Therefore, this new red fluorogenic substrate and the resulting enzyme assay can be used in high-throughput screening to identify small-molecule chaperones for Fabry disease. Zhen-Dan Shi and Omid Motabar contributed equally to this work     

Towards the automatic analysis of NMR spectra: part 6. Confirmation of chemical structure employing both 1H and 13C NMR spectra

A method of comparing predicted and experimental chemical shifts was used to confirm or refute postulated structures. 1H NMR spectra returned all true positives with a false positive rate of 4%. When an analogous procedure was adopted for 13C NMR spectra, the false positive rate dropped to 1%, whereas the more practical HSQC data yielded a false positive rate of 2%. If the HSQC results were combined with 1H results, a false positive rate of 1% resulted, 4 times more accurate than 1H alone.