Inhibition of the reduction of Cr(VI) at the magnetite–water interface by calcium carbonate coatings

The effect of calcium carbonate coatings on the reduction of aqueous chromate on the magnetite(1 1 1) surface has been investigated using a combination of synchrotron based X-ray photoemission spectroscopy (PES) and X-ray absorption near edge structure (XANES) spectroscopy, along with laboratory-based powder X-ray diffraction (XRD) and scanning electron microscopy (SEM). CaCO₃ coatings (dominantly calcite with minor quantities of aragonite and vaterite) of thicknesses ranging from 10 Å to 20 m were grown on magnetite(1 1 1) surfaces by exposure to supersaturated aqueous solutions followed by evaporation of the solution—a process that mimics pore-water evaporation in vadose zones leading to the formation of caliche and calcium carbonate coatings on mineral grains. Coating thicknesses were determined from attenuation of the Fe 2p photoemission signal by the carbonate coating. For coatings less than 15 Å thick, Cr 2p photoemission and Cr L_II, L_III-edge XANES spectra show that chromate is reduced by the underlying magnetite surface; however, as the minimum coating thickness increases beyond 15 Å, the magnetite surface becomes passivated and further chromate reduction ceases. Our findings suggest that carbonate coatings on natural magnetite grains can significantly reduce or eliminate their ability to reduce Cr(VI), which is a toxic and highly mobile environmental contaminant.     

Fluorinations with complex metal fluorides. Part 6 [1] fluorination of yridine and related compounds with caesium tetrafluorocobaltate(III) [2]

Pyridine has been fluorinated over caesium tetrafluorocobaltate(III) (CsCo^IIIF₄) at 300–400°C to give a mixture of undecafluoro-N-methylpyrrolidine, bis(trifluoromethyl)amine, pentafluoropyridine and several polyfluoropyridines; the product composition depended to some extent on the geometry of the reactor. The fluorinations of pentafluoropyridine, piperidine and undecafluoropiperidine were also investigated.     

On the evolution of islands

Letn cells be arranged in a ring, or alternatively, in a row. Initially, all cells are unmarked. Sequentially, one of the unmarked cells is chosen at random and marked until, aftern steps, each cell is marked. After thekth cell has been marked the configuration of marked cells defines some number of islands: maximal sets of adjacent marked cells. Let ξ _k denote the random number of islands afterk cells have been marked. We give explicit expressions for moments of products of ξ _k ’s and for moments of products of 1/ξ _k ’s. These are used in a companion paper to prove that if a random graph on the natural number is made by drawing an edge betweeni≧1 andj>i with probabilityλ/j, then the graph is almost surely connected ifλ>1/4 and almost surely disconnected ifλ≦1/4.     

Estimating the largest singular values of large sparse matrices via modified moments

We describe a procedure for determining a few of the largest singular values of a large sparse matrix. The method by Golub and Kent which uses the method of modified moments for estimating the eigenvalues of operators used in iterative methods for the solution of linear systems of equations is appropriately modified in order to generate a sequence of bidiagonal matrices whose singular values approximate those of the original sparse matrix. A simple Lanczos recursion is proposed for determining the corresponding left and right singular vectors. The potential asynchronous computation of the bidiagonal matrices using modified moments with the iterations of an adapted Chebyshev semi-iterative (CSI) method is an attractive feature for parallel computers. Comparisons in efficiency and accuracy with an appropriate Lanczos algorithm (with selective re-orthogonalization) are presented on large sparse (rectangular) matrices arising from applications such as information retrieval and seismic reflection tomography. This procedure is essentially motivated by the theory of moments and Gauss quadrature.This author's work was supported by the National Science Foundation under grants NSF CCR-8717492 and CCR-910000N (NCSA), the U.S. Department of Energy under grant DOE DE-FG02-85ER25001, and the Air Force Office of Scientific Research under grant AFOSR-90-0044 while at the University of Illinois at Urbana-Champaign Center for Supercomputing Research and Development.This author's work was supported by the U.S. Army Research Office under grant DAAL03-90-G-0105, and the National Science Foundation under grant NSF DCR-8412314.     

Concentration for self‐bounding functions and an inequality of Talagrand

We see that the entropy method yields strong concentration results for general self‐bounding functions of independent random variables. These give an improvement of a concentration result of Talagrand much used in discrete mathematics. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006