Continuous approximation of linear impulsive systems and a new form of robust stability

The time-scale tolerance for linear ordinary impulsive differential equations is introduced. How large the time-scale tolerance is directly reflects the degree to which the qualitative dynamics of the linear impulsive system can be affected by replacing the impulse effect with a continuous (as opposed to discontinuous, impulsive) perturbation, producing what is known as an impulse extension equation. Theoretical properties related to the existence of the time-scale tolerance are given for periodic systems, as are algorithms to compute them. Some methods are presented for general, aperiodic systems. Additionally, sufficient conditions for the convergence of solutions of impulse extension equations to the solutions of their associated impulsive differential equation are proven. Counterexamples are provided.     

Dotplot: A Program for Exploring Self-Similarity in Millions of Lines of Text and Code

Abstract

An interactive program, dotplot, has been developed for browsing millions of lines of text and source code, using an approach borrowed from biology for studying homology (self-similarity) in DNA sequences. With conventional browsing tools such as a screen editor, it is difficult to identify structures that are too big to fit on the screen. In contrast, with dotplots we find that many of these structures show up as diagonals, squares, textures, and other visually recognizable features, as will be illustrated in examples selected from biology and two new application domains, text (AP news, Canadian Hansards) and source code (5ESS®). In an attempt to isolate the mechanisms that produce these features, we have synthesized similar features in dotplots of artificial sequences. We also introduce an approximation that makes the calculation of dotplots practical for use in an interactive browser.     

Functional Nickel Oxide Nanostructures for Ethanol Oxidation in Alkaline Media

Nickel oxide (NiO) nanostructures are employed in the basic medium for the oxidation of ethanol. A variety of NiO nanostructures are synthesized by wet chemical growth method, using different hydroxide (OH^?) ion sources, particularly from ammonia, hexamethylenetetramine, urea and sodium hydroxide. The use of urea as (OH^?) ion source results in flower‐like NiO structures composed by extremely thin nanowalls (thickness lower than 10 nm,), which demonstrated to be the most active for ethanol oxidation. All the samples exhibit NiO cubic phase, and no other impurity was detected. The cyclic voltammetry (CV) curves of NiO nanostructures were found linear over the concentration range 0.1–3.5 mM (R²=0.99) of ethanol, with the limit of detection estimated to be 0.013 mM for ethanol. The NiO nanostructures exhibit a selective signal towards ethanol oxidation in the presence of different members of alcohol family. The proposed NiO nanostructures showed a significant practicality for the reproducible and sensitive determination of ethanol from brandy, whisky, mixture of brandy and rum, and vodka samples. The nanomaterial was used as a surface modifying agent for the glassy carbon electrode and it showed a stable electro‐oxidation activity for the ethanol for 16 days. These findings indicate that the presented NiO nanomaterial can be applied in place of noble metals for ethanol sensing and other environmental applications (like fuel cells).     

Radical Cyclisation of α‐Halo Aluminium Acetals: A Mechanistic Study

α‐Bromo aluminium acetals are suitable substrates for Ueno–Stork‐like radical cyclisations affording γ‐lactols and acid‐sensitive methylene‐γ‐lactols in high yields. The mechanistic study herein sets the scope and limitation of this reaction. The influence of the halide (or chalcogenide) atom X (X=Cl, Br, I, SPh, SePh) in the precursors α‐haloesters, as well as influence of the solvent and temperature was studied. The structure of the aluminium acetal intermediates resulting from the reduction of the corresponding α‐haloesters has been investigated by low‐temperature ¹³C‐INEPT diffusion‐ordered NMR spectroscopy (DOSY) experiments and quantum calculations, providing new insights into the structures of these thermally labile intermediates. Oxygen‐bridged dimeric structures with a planar Al₂O₂ ring are proposed for the least hindered aluminium acetals, while monomeric structures seem to prevail for the most hindered species. A comparison against the radical cyclisation of aluminium acetals derived from allyl and propargyl alcohols with the parent Ueno–Stork has been made at the BHandHLYP/6‐311++G(d,p) level of theory, highlighting mechanistic similarities and differences.     

Asymmetric synthesis of novel spirocycles via a chiral phosphoric acid catalyzed desymmetrization

A straightforward method for the asymmetric preparation of novel lactone and lactam spirocycles is described. An initial desymmetrization via a chiral Brønsted acid yields enantioenriched lactones which readily undergo a second cyclization to give the desired spirocycle.     

Automated on-line column-switching HPLC-MS/MS method with peak focusing for measuring parabens, triclosan, and other environmental phenols in human milk

Parabens (esters of p-hydroxybenzoic acid) and triclosan are widely used as preservatives and antimicrobial agents, respectively, in personal care products, pharmaceuticals, and food processing. Because of their widespread use and potential risk to human health, assessing human exposure to these compounds in breastfed infants is of interest. We developed a sensitive method, using a unique on-line solid-phase extraction-high performance liquid chromatography-tandem mass spectrometry system with peak focusing feature, to measure in human milk the concentrations of five parabens (methyl-, ethyl-, propyl-, butyl-, and benzyl parabens), triclosan, and six other environmental phenols: bisphenol A (BPA); ortho-phenylphenol (OPP); 2,4-dichlorophenol; 2,5-dichlorophenol; 2,4,5-trichlorophenol; and 2-hydroxy-4-methoxybenzophenone (BP-3). The method, validated by use of breast milk pooled samples, shows good reproducibility (inter-day coefficient of variations ranging from 3.5% to 16.3%) and accuracy (spiked recoveries ranging from 84% to 119% at four spiking levels). The detection limits for most of the analytes are below 1 ng mL(-1) in 100 microL of milk. We tested the usefulness of the method by measuring the concentrations of these twelve compounds in four human milk samples. We detected methyl paraben, propyl paraben, triclosan, BPA, OPP, and BP-3 in some of the samples tested. The free species of these compounds appear to be the most prevalent in milk. Nevertheless, to demonstrate the utility of these measures for exposure and risk assessment purposes, additional data about sampling and storage of the milk, and on the stability of the analytes in milk, are needed.