Gluing Eguchi‐Hanson Metrics and a Question of Page

In 1978, Gibbons‐Pope and Page proposed a physical picture for the Ricci flat Kähler metrics on the K3 surface based on a gluing construction. In this construction, one starts from a flat torus with 16 orbifold points and resolves the orbifold singularities by gluing in 16 small Eguchi‐Hanson manifolds that all have the same orientation. This construction was carried out rigorously by Topiwala, LeBrun‐Singer, and Donaldson. In 1981, Page asked whether the above construction can be modified by reversing the orientations of some of the Eguchi‐Hanson manifolds. This is a subtle question: if successful, this construction would produce Einstein metrics that are neither Kähler nor self‐dual. In this paper, we focus on a configuration of maximal symmetry involving eight small Eguchi‐Hanson manifolds of each orientation that are arranged according to a chessboard pattern. By analyzing the interactions between Eguchi‐Hanson manifolds with opposite orientation, we identify a nonvanishing obstruction to the gluing problem, thereby destroying any hope of producing a metric of zero Ricci curvature in this way. Using this obstruction, we are able to understand the dynamics of such metrics under Ricci flow as long as the Eguchi‐Hanson manifolds remain small. In particular, for the configuration described above, we obtain an ancient solution to the Ricci flow with the property that the maximum of the Riemann curvature tensor blows up at a rate of , while the maximum of the Ricci curvature converges to 0.© 2016 Wiley Periodicals, Inc.     

Special issue of FOA10 in honor of our colleagues in Japan and New Zealand

Tribute

Special issue of FOA10 in honor of our colleagues in Japan and New Zealand     

Determination of pesticide residues in honey by single-drop microextraction and gas chromatography

A novel, simple, and rapid single-drop microextraction (SDME) procedure combined with GC has been developed, validated, and applied for the determination of multiclass pesticide residues in honey samples. The SDME was optimized using a Plackett-Burman screening design considering all parameters that may influence an SDME procedure and a consequent central composite design to control the parameters that were found to significantly influence the pesticide determination. The developed analytical method required minimal volumes of organic solvents and exhibited good analytical characteristics with enrichment factors ranging from 3 for alpha-endosulfan to 10 for lindane, procymidone, and captan and method quantification limits ranging from 0.03 microg/kg for phosalone to 10.6 microg/kg for diazinon. The relative recoveries obtained ranged from 70.8% for captan to 120% for fenarimol, and the precision (RSD) ranged from 3 to 15%. The proposed SDME procedure followed by GC with an electron capture detector for quantification and GC/MS for identification was applied with success to the analysis of 17 honey samples. Monitoring results indicated a low level of honey contamination by diazinon, chlorpyrifos-ethyl, procymidone, bromopropylate, and endosulfan (alpha-, beta-, and endosulfan sulfate) residues that were far below the maximum residue limit values specified by the European Union for endosulfan (10 microg/kg) and bromopropylate (100 microg/kg) in honey samples.     

Synthesis of glycerol carbonate from glycerol and urea with gold-based catalysts

The reaction of glycerol with urea to form glycerol carbonate is mostly reported in the patent literature and to date there have been very few fundamental studies of the reaction mechanism. Furthermore, most previous studies have involved homogeneous catalysts whereas the identification of heterogeneous catalysts for this reaction would be highly beneficial. This is a very attractive reaction that utilises two inexpensive and readily available raw materials in a chemical cycle that overall, results in the chemical fixation of CO(2). This reaction also provides a route to up-grade waste glycerol produced in large quantities during the production of biodiesel. Previous reports are largely based on the utilisation of high concentrations of metal sulfates or oxides, which suffer from low intrinsic activity and selectivity. We have identified heterogeneous catalysts based on gallium, zinc, and gold supported on a range of oxides and the zeolite ZSM-5, which facilitate this reaction. The addition of each component to ZSM-5 leads to an increase in the reaction yield towards glycerol carbonate, but supported gold catalysts display the highest activity. For gold-based catalysts, MgO is the support of choice. Catalysts have been characterised by XRD, TEM, STEM and XPS, and the reaction has been studied with time-on-line analysis of products via a combination of FT-IR spectroscopy, HPLC, (13)C NMR and GC-MS analysis to evaluate the reaction pathway. Our proposed mechanism suggests that glycerol carbonate forms via the cyclization of a 2,3-dihydroxypropyl carbamate and that a subsequent reaction of glycerol carbonate with urea yields the carbamate of glycerol carbonate. Stability and reactivity studies indicate that consecutive reactions of glycerol carbonate can limit the selectivity achieved and reaction conditions can be selected to avoid this. The effect of the catalyst in the proposed mechanism is discussed.     

A Kirkwood-Buff Derived Force Field for Aqueous Alkali Halides

A classical nonpolarizable force field is presented for the simulation of aqueous alkali halide solutions (MX), where M = Li(+), Na(+), K(+), Rb(+), Cs(+) and X = F(-), Cl(-), Br(-), I(-), and their interactions with biomolecules. The models are specifically designed to reproduce the experimental Kirkwood-Buff integrals, and thereby the solution salt activities, as a function of salt concentration. Additionally, we demonstrate that these models reasonably reproduce other experimental properties including ion diffusion constants, dielectric decrements, and the excess heats of mixing. The parameters are developed by considering the properties of aqueous NaX and MCl solutions using a previously established model for NaCl. Transferability of the parameters to other salts is then established by the successful simulation of additional aqueous salt solutions, KI and CsBr, not originally included in the parameterization procedure.     

Semidefinite relaxations for quadratically constrained quadratic programming: A review and comparisons

At the intersection of nonlinear and combinatorial optimization, quadratic programming has attracted significant interest over the past several decades. A variety of relaxations for quadratically constrained quadratic programming (QCQP) can be formulated as semidefinite programs (SDPs). The primary purpose of this paper is to present a systematic comparison of SDP relaxations for QCQP. Using theoretical analysis, it is shown that the recently developed doubly nonnegative relaxation is equivalent to the Shor relaxation, when the latter is enhanced with a partial first-order relaxation-linearization technique. These two relaxations are shown to theoretically dominate six other SDP relaxations. A computational comparison reveals that the two dominant relaxations require three orders of magnitude more computational time than the weaker relaxations, while providing relaxation gaps averaging 3% as opposed to gaps of up to 19% for weaker relaxations, on 700 randomly generated problems with up to 60 variables. An SDP relaxation derived from Lagrangian relaxation, after the addition of redundant nonlinear constraints to the primal, achieves gaps averaging 13% in a few CPU seconds.     

Identifying preferred solutions to Multi-Objective Binary Optimisation problems,with an application to the Multi-Objective Knapsack Problem

In this paper we present a new framework for identifying preferred solutions to multi-objective binary optimisation problems. We develop the necessary theory which leads to new formulations that integrate the decision space with the space of criterion weights. The advantage of this is that it allows for incorporating preferences directly within a unique binary optimisation problem which identifies efficient solutions and associated weights simultaneously. We discuss how preferences can be incorporated within the formulations and also describe how to accommodate the selection of weights when the identification of a unique solution is required. Our results can be used for designing interactive procedures for the solution of multi-objective binary optimisation problems. We describe one such procedure for the multi-objective multi-dimensional binary knapsack formulation of the portfolio selection problem.     

Improper hydrogen bonded cyclohexane C-Hax···Yax contacts: theoretical predictions and experimental evidence from 1H NMR spectroscopy of suitable axial cyclohexane models

C-H(ax)···Y(ax) contacts are a textbook prototype of steric hindrance in organic chemistry. The nature of these contacts is investigated in this work. MP2/6-31+G(d,p) calculations predicted the presence of improper hydrogen bonded C-H(ax)···Y(ax) contacts of different strength in substituted cyclohexane rings. To support the theoretical predictions with experimental evidence, several synthetic 2-substituted adamantane analogues (1-24) with suitable improper H-bonded C-H(ax)···Y(ax) contacts of different strength were used as models of a substituted cyclohexane ring. The (1)H NMR signal separation, Δδ(γ-CH(2)), within the cyclohexane ring γ-CH(2)s is raised when the MP2/6-31+G(d,p) calculated parameters, reflecting the strength of the H-bonded C-H(ax)···Y(ax) contact, are increased. In molecules with enhanced improper H-bonded contacts C-H(ax)···Y(ax), like those having sterically crowded contacts (Y(ax) = t-Bu) or contacts including considerable electrostatic attractions (Y(ax) = O-C or O═C) the calculated DFT steric energies of the γ-axial hydrogens are considerably reduced reflecting their electron cloud compression. The results suggest that the proton H(ax) electron cloud compression, caused by the C-H(ax)···Y(ax) contacts, and the resulting increase in Δδ(γ-CH(2)) value can be effected not just from van der Waals spheres compression, but more generally from electrostatic attraction forces and van der Waals repulsion, both of which are improper H-bonding components.     

Double addition of H2 to transition metal-borane complexes: a 'hydride shuttle' process between boron and transition metal centres

The addition of H(2) across a transition metal-borane bond is reported for the first time providing a mechanism for recharging borane functional groups to borohydride.