Correction to: Complete enumeration of pure‐level and mixed‐level orthogonal arrays

We correct an error found in Schoen, Endebak, Nguyen, J Combin Designs 18 (2010), 123–140. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 488, 2010     

Toposes for semigroups: an invitation

This is an expository paper in which we explain the basic ideas of topos theory in connection with semigroup theory. We focus mainly on the classifying topos of an inverse semigroup or pseudogroup, and to some extent on creating a dictionary between the language of semigroups and topos theory. We begin with the algebraic theory having to do with inverse semigroups, and then turn to an analysis of pseudogroups using sheaf theory. Our work includes some new material on wide semigroup homomorphisms and their geometric morphisms.

     

Cycloaddition-elimination reactions of 4-methyl-5-(substituted)-imino-Δ2-1,2,3,4-thiatriazolines with isocyanates

4-Methyl-5-(substituted)imino-1,2,3,4-thiatriazolines 1 (R² ≠ Me) undergo cycloaddition-elimination reactions with isocyanates to yield 4-methyl-5-(substituted)imino-1,2,4-thiadiazolidine-3-ones 5 via the thermodynamically less stable isomers 4 . The latter have not been isolated, except for 4q which was shown to iso-merize rapidly into 5q with phenylsulfonyl isocyanate. The reactions of 1 are accelerated by using less bulky R² substituents and more electrophilic isocyanates, in accordance with the viewpoint that 1 reacts as a masked 1,3-dipole. The products 4i-n (= 5i-n ), derived from 1b , add isocyanates reversibly to give 2,3,4,5-tetrahydro-6aλ⁴-thia-1,3,4,6-tetraazapentalene-2,5-diones 9i-n , which have been isolated and characterized spectroscopically. Such compounds with a hypervalent sulfur atom thus occur as intermediates during the isomerization of 4 to 5 under the influence of isocyanates.     

(35/37)Cl and (16/18)O isotope resolved (195)Pt NMR: unique spectroscopic 'fingerprints' for unambiguous speciation of [PtCl(n)(H(2)O)(6-n)](4-n) (n = 2-5) complexes in an acidic aqueous solution

At high magnetic fields the 128.8 MHz (195)Pt NMR of all the species in the series [PtCl(n)(H(2)O)(6-n)](4-n) (n = 2-6) display unique (35/37)Cl isotope effects resulting in a unique 'fine-structure' of each individual resonance, which constitutes an unambiguous spectroscopic 'fingerprint' characteristic of the structure of the octahedral platinum(iv) complex, provided (195)Pt NMR are recorded at optimum magnetic field homogeneity and carefully controlled temperature (293 ± 0.1 K). The detailed (195)Pt resonance fine-structure observed experimentally can readily be accounted for by an isotopologue and isotopomer model for each complex, showing particularly noticeable differences between stereoisomer pairs such as the cis/trans- and fac/mer-complexes. Moreover partial isotopic (18)O enrichment of the coordinated water molecules in the series [Pt(35/37)Cl(n)(H(2)(16/18)O)(6-n)](n-2) (n = 2-6) confirms this model. This technique can thus be considered a novel, direct spectroscopic method of chemical speciation of appropriate platinum(iv) complexes in solution without reference to accurate chemical shifts of authentic members of such a series. These effects are interpreted qualitatively in terms of the high sensitivity of (195)Pt NMR shielding to very small and subtle Pt-(35/37)Cl and Pt-(16/18)OH(2) bond displacements. Preliminary work shows this also applied to the corresponding bromido-complexes.     

Effect of surface roughness and softness on water capillary adhesion in apolar media

The roughness and softness of interacting surfaces are both important parameters affecting the capillary condensation of water in apolar media, yet are poorly understood at present. We studied the water capillary adhesion between a cellulose surface and a silica colloidal probe in hexane by AFM force measurements. Nanomechanical measurements show that the Young's modulus of the cellulose layer in water is significantly less (~7 MPa) than in hexane (~7 GPa). In addition, the cellulose surface in both water and hexane is rather rough (6-10 nm) and the silica probe has a comparable roughness. The adhesion force between cellulose and silica in water-saturated hexane shows a time-dependent increase up to a waiting time of 200 s and is much (2 orders of magnitude) lower than that expected for a capillary bridge spanning the whole silica probe surface. This suggests the formation of one or more smaller bridges between asperities on both surfaces, which is confirmed by a theoretical analysis. The overall growth rate of the condensate cannot be explained from diffusion mediated capillary condensation alone; thin film flow due to the presence of a wetting layer of water at both the surfaces seems to be the dominant contribution. The logarithmic time dependence of the force can also be explained from the model of the formation of multiple capillary bridges with a distribution of activation times. Finally, the force-distance curves upon retraction show oscillations. Capillary condensation between an atomically smooth mica surface and the silica particle show less significant oscillations and the adhesion force is independent of waiting time. The oscillations in the force-distance curves between cellulose and silica may stem from multiple bridge formation between the asperities present on both surfaces. The softness of the cellulose surface can bring in additional complexities during retraction of the silica particle, also resulting in oscillations in the force-distance curves.     

Non-stationary forward flux sampling

We present a method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform sampling of trajectories in phase space and time, leading to accurate estimates for time-dependent switching propensities and time-dependent phase space probability densities. It is suitable for equilibrium or non-equilibrium systems, in or out of stationary state, including non-Markovian or externally driven systems. We demonstrate the validity of the technique by applying it to a one-dimensional barrier crossing problem that can be solved exactly, and show its usefulness by applying it to the time-dependent switching of a genetic toggle switch.     

Electrical double layer and adsorption of iodide ions at the Bi|ethylene carbonate interface

The adsorption of I^? anions on the Bi(111) single-crystal plane from solutions in ethylene carbonate has been investigated by impedance measurement method. The ionic charge due to the specific adsorption has been obtained by integration of differential capacitance curves, and the Gibbs excess has been calculated using the mixed-electrolyte method applied for both electrode charge and electrode potential as the independent electrical variables. The Gibbs energy of I^? anion adsorption has been calculated using the virial adsorption isotherm. It was found that under comparable conditions, the results obtained at constant electrode potential and at constant electrode charge were coincident. The Gibbs energy of I^? anion adsorption and the calculated electrosorption valency value were found to be very close to these values obtained in propylene carbonate.     

Multipolymers with Fischer-Tropsch olefins

Multipolymers consisting of ethylene, 1-heptene, 3-methylpentene and 4-methylpentene were prepared with a heterogeneous Ziegler-Natta catalyst. The polymers were prepared in such a way that the molar fraction of the comonomers remained the same. Copolymers of ethylene/1-heptene and ethylene/4-methylpentene were prepared in order to study the changes in polymer characteristics as one moves from an ethylene/linear alpha olefin copolymer through ethylene multipolymers to an ethylene/4-methylpentene copolymer. The mechanical, rheological and application properties showed expected trends.     

Crosslinking of porcine aortic leaflets with butane‐1,4‐diol diglycidyl ether

Currently, efforts are being made to reduce xenograft calcification and to optimize biomechanical properties by applying different crosslinking methods and techniques. Porcine aortic leaflets could be stabilized with a bisepoxy compound, butane‐1,4‐diol diglycidyl ether (BDDGE), under acidic (pH 4.5) or alkaline conditions (pH > 8.5). Maximum values of the shrinkage temperature (83°C), which are comparable to glutaraldehyde‐crosslinked materials, are achieved at pH 9.0 and 10.0 within 48 h with a BDDGE concentration of 4 wt6percnt;. The crosslinking efficacy decreased at higher pH values or at prolonged reaction times due to a higher proportion of one‐side or masking reactions. Crosslinking of aortic leaflets at pH 4.5, which consisted in a reaction between the epoxide groups of BDDGE and the carboxylic acid groups of the tissue, afforded crosslinked material with a shrinkage temperature of 76°C after 7 days of reaction.