Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures

We consider the question of which of the major classes defined by topological diagonalizations of open or Borel covers is hereditary. Many of the classes in the open case are not hereditary already in ZFC, and none of them are provably hereditary. This is in contrast with the Borel case, where some of the classes are provably hereditary. Two of the examples are counter-examples of sizes and , respectively, to the Menger and Hurewicz Conjectures, and one of them answers a question of Steprans on perfectly meager sets.

     

Selective CH Functionalization of Methane,Ethane, and Propane by a Perfluoroarene Iodine(III) Complex

Direct partial oxidation of methane, ethane, and propane to their respective trifluoroacetate esters is achieved by a homogeneous hypervalent iodine(III) complex in non‐superacidic (trifluoroacetic acid) solvent. The reaction is highly selective for ester formation (>99 %). In the case of ethane, greater than 0.5 M EtTFA can be achieved. Preliminary kinetic analysis and density functional calculations support a nonradical electrophilic CH activation and iodine alkyl functionalization mechanism.     

A theoretical analysis of topography and molecular parameters of the CFCl3···O3 complex: Linear and bifurcate halogen‐oxygen bonding interactions

A theoretical analysis of linear and bifurcate halogen‐oxygen bonds is presented in this work. B3LYP/6‐311++G(d,p) and MP2/6‐311++G(d,p) calculations were used to determine the optimized geometries of intermolecular systems formed by CFCl₃ and O₃. Molecular properties often analyzed in hydrogen‐bonded complexes were used here to describe the interaction between chlorine (CFCl₃) and oxygen (O₃). The halogen‐oxygen bond in the CFCl₃···O₃ complex was characterized using the topological parameters derived from the quantum theory of atoms in molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Formation and elimination of surface nanodefects on ultraflat metal surfaces produced by template stripping

Ultraflat metal surfaces are used in template stripping (TS), which is a method for obtaining a metal with an average surface roughness on the order of <1 nm. This is important for plasmonics, for the production of high-quality SAM surfaces, and for many other applications. Herein we show for the first time that TS indeed introduces a very high density of surface nanodefects (twinning and stacking faults), which can strongly hinder surface-induced properties such as SAM ordering and plasmonic phenomena, despite the seemingly overall ultrahigh flatness. We have used state of the art characterization techniques such as HRXRD, spherical-aberration-corrected HRTEM, and STM. We also demonstrate how these nanodefects can be completely eliminated.     

Sphere-separable partitions of multi-parameter elements

We show the optimality of sphere-separable partitions for problems where n vectors in d-dimensional space are to be partitioned into p categories to minimize a cost function which is dependent in the sum of the vectors in each category; the sum of the squares of their Euclidean norms; and the number of elements in each category. We further show that the number of these partitions is polynomial in n. These results broaden the class of partition problems for which an optimal solution is guaranteed within a prescribed set whose size is polynomially bounded in n. Applications of the results are demonstrated through examples.     

Voronoi Diagrams of Lines in 3-Space Under Polyhedral Convex Distance Functions

The combinatorial complexity of the Voronoi diagram ofnlines in three dimensions under a convex distance function induced by a polytope with a constant number of edges is shown to beO(n²α(n)log n), where α(n) is a slowly growing inverse of the Ackermann function. There are arrangements ofnlines where this complexity can be as large as Ω(n²α(n)).     

-bounded groups and other topological groups with strong combinatorial properties

We construct several topological groups with very strong combinatorial properties. In particular, we give simple examples of subgroups of (thus strictly -bounded) which have the Menger and Hurewicz properties but are not -compact, and show that the product of two -bounded subgroups of may fail to be -bounded, even when they satisfy the stronger property . This solves a problem of Tkacenko and Hernandez, and extends independent solutions of Krawczyk and Michalewski and of Banakh, Nickolas, and Sanchis. We also construct separable metrizable groups of size continuum such that every countable Borel -cover of contains a -cover of .

     

A modified lead–matrix separation procedure shown for lead isotope analysis in Trojan silver artefacts as an example

A modified Pb–matrix separation procedure using NH₄HCO₃ solution as eluent has been developed and validated for determination of Pb isotope amount ratios by thermal ionization mass spectrometry. The procedure is based on chromatographic separation using the Pb·Spec resin and an in-house-prepared NH₄HCO₃ solution serving as eluent. The advantages of this eluent are low Pb blanks (<40 pg?mL^?1) and the property that NH₄HCO₃ can be easily removed by use of a heating step (>60 °C). Pb recovery is >95 % for water samples. For archaeological silver samples, however, the Pb recovery is reduced to approximately 50 %, but causes no bias in the determination of Pb isotope amount ratios. The validated procedure was used to determine lead isotope amount ratios in Trojan silver artefacts with expanded uncertainties (k?=?2) <0.09 %.