Matrix decomposition algorithms for the finite element Galerkin method with piecewise Hermite cubics

Matrix decomposition algorithms (MDAs) employing fast Fourier transforms are developed for the solution of the systems of linear algebraic equations arising when the finite element Galerkin method with piecewise Hermite bicubics is used to solve Poisson’s equation on the unit square. Like their orthogonal spline collocation counterparts, these MDAs, which require O(N ²logN) operations on an N×N uniform partition, are based on knowledge of the solution of a generalized eigenvalue problem associated with the corresponding discretization of a two-point boundary value problem. The eigenvalues and eigenfunctions are determined for various choices of boundary conditions, and numerical results are presented to demonstrate the efficacy of the MDAs. Weiwei Sun was supported in part by a grant from City University of Hong Kong (Project No. CityU 7002110).     

Metal–π Interactions Dominate in the Solid‐State Structures of Molecular Heterobimetallic Alkali‐Metal–Europium(II) Aryloxo Complexes

Treatment of Eu metal, 2,6‐diphenylphenol (HOdpp), and MOdpp (M=Na, K) at elevated temperature in the presence of mercury afforded heterobimetallic complexes which were structurally characterized after crystallization from toluene. The structures of [MEu(Odpp)₃]?nPhMe (M=Na, n=1, 1 ; K, n=2.5, 2 ) consist solely of bridging aryloxide ligands and feature extensive π‐Ph–metal interactions. Rather than a heterobimetallic species, treatment of Eu metal and HOdpp with LiOdpp under similar conditions afforded a number of products, including a mixed‐valent europium complex, [Eu₂(Odpp)₃][Eu(Odpp)₄]?4 PhMe ( 3 ). The structural framework of the [Eu₂(Odpp)₃]⁺ cation of 3 is similar to that of the molecular heterobimetallics 1 and 2 , including the presence of π‐Ph–Eu interactions. The reluctance of the reaction to provide a Eu/Li heterobimetallic complex was exemplified by the simultaneous crystallization of [Eu₂(Odpp)₄]?PhMe ( 6 ) and the homoleptic cubane [Li₄(Odpp)₄]?2 C₆H₁₄ ( 5 ) from toluene/hexane.     

Imaging with complex ray-optical refractive-index interfaces between complex object and image distances

Building on recent work on windows that can be modeled as interfaces between materials with a complex ray-optical refractive-index ratio, we define here objects and images at complex positions. We give an example of an optical component that performs imaging between real and complex object and image positions.     

Synthesis,Characterization, Photo-physical Evaluation and Crystal Structure of 2-Methoxy-1-Methylquinolinium Tetrafluoroborate,a Potentially Selective Agent for the Quantitative Measurement of Biologically Relevant Thiols

Abstract  

We report the quantitative and facile conversion of 2-chloro-1-methylquinolinium tetrafluoroborate to 2-methoxy-1-methylquinolinium tetrafluoroborate via stirring in methanol at room temperature. The resulting compound was evaluated for use as a selective tag for biologically relevant thiols. The results displayed a fivefold increase in fluorescent quantum yield (Ф_FLUOR = 0.20) and an increased stability in pH when compared to 2-chloro-1-methylquinolinium tetrafluoroborate (Ф_FLUOR = 0.04), however, results demonstrated that it did not offer an improvement to 2-chloro-1-methylquinolinium tetrafluoroborate as a thiol specific tag. The compound was fully characterised by ¹HNMR, ESI mass spectroscopy and by single-crystal X-ray diffraction. The title compound crystallizes in the monoclinic space group P2₁/m with a = 8.2420(3) ?, b = 6.6751(2) ?, c = 10.8415 ? and β = 105.164(2)°, Z = 2, V = 575.69(3) ?³. Work is on-going to synthesise and evaluate other such analogues for their potential use as thiol tags.     

A hybrid genetic algorithm for estimating the equilibrium potential of an ion-selective electrode

Non-linear equations can be used to model the measured potential of ion-selective electrodes (ISEs) as a function of time. This can be done by using non-linear least squares regression to fit parameters of non-linear equations to an ISE response curve. In iterative non-linear least squares regression (which can be considered as local optimisers), the determination of starting parameter estimates that yield convergence to the global optimum can be difficult. Starting values away from the global optimum can lead to either abortive divergence or convergence to a local optimum. To address this issue, a global optimisation technique was used to find initial parameter estimates near the global optimum for subsequent further refinement to the absolute optimum. A genetic algorithm has been applied to two non-linear equations relating the measured potential from selected ISEs to time. The parameter estimates found from the genetic algorithm were used as starting values for non-linear least squares regression, and subsequent refinement to the absolute optimum. This approach was successfully used for both expressions with measured data from three different ISEs; namely, calcium, chloride and lead ISEs.     

CO oxidation mechanism on CeO(2)-supported Au nanoparticles

Density functional theory was used to study the CO oxidation catalytic activity of CeO(2)-supported Au nanoparticles (NPs). Experimental observations on CeO(2) show that the surface of CeO(2) is enriched with oxygen vacancies. We compare CO oxidation by a Au(13) NP supported on stoichiometric CeO(2) (Au(13)@CeO(2)-STO) and partially reduced CeO(2) with three vacancies (Au(13)@CeO(2)-3VAC). The structure of the Au(13) NP was chosen to minimize structural rearrangement during CO oxidation. We suggest three CO oxidation mechanisms by Au(13)@CeO(2): CO oxidation by coadsorbed O(2), CO oxidation by a lattice oxygen in CeO(2), and CO oxidation by O(2) bound to a Au-Ce(3+) anchoring site. Oxygen vacancies are shown to open a new CO oxidation pathway by O(2) bound to a Au-Ce(3+) anchoring site. Our results provide a design strategy for CO oxidation on supported Au catalysts. We suggest lowering the vacancy formation energy of the supporting oxide, and using an easily reducible oxide to increase the concentration of reduced metal ions, which act as anchoring sites for O(2) molecules.     

Developments in the synthesis of maleated polyolefins by reactive extrusion

The maleation of conventional and metallocene linear low density polyethylenes by reactive extrusion has been explored with a view to defining the conditions necessary for a robust process that provides both high grafting efficiencies (>80%) and minimal degradation or cross-linking. The dependence of grafting efficiency on various operating parameters (maleic anhydride level, maleic anhydride:initiator ratio, throughput rate, direction of screw rotation, temperature) has been established. Literature methods for characterization of the grafted product based on FTIR or ¹H NMR analysis have been critically examined with respect to their ability to distinguish between single unit and oligomeric maleic anhydride grafts and found to yield ambiguous results.     

Evaluation of propagation rate constants for the free radical polymerization of methacrylonitrile by pulsed laser photolysis

Propagation rate constants for the free radical polymerization of methacrylonitrile (MAN) have been obtained by pulsed laser photolysis (PLP). The temperature dependence of the propagation rate constants indicates a frequency factor of 10^{(6,43 ± 0,26)} L · mol⁻¹ · s⁻¹ and an activation energy of 29,7 ± 1,5 kJ · mol⁻¹. These parameters suggest that the relatively slow rate of propagation in MAN polymerization in relation to other common monomers (methyl methacrylate, styrene) can be attributed to the relative steric bulk and stability of the propagation species.     

1,7,8‐Tri‐O‐acetyl‐6‐O‐benzoyl­castanospermine

The title compound (alternatively 1,7,8‐tri­acetoxy­per­hydro­indolizin‐6‐yl benzoate), C₂₁H₂₅NO₈, was obtained during studies of castanospermine derivatives. The crystal structure consists of independent mol­ecules with only van der Waals contacts. The fused six‐ and five‐membered rings adopt chair and twist conformations, respectively.