A generalization of a theorem on biseparating maps

In J. Math. Anal. Appl. 12 (1995) 258–265, Araujo et al. proved that for any linear biseparating map  from C(X) onto C(Y), where X and Y are completely regular, there exist ω in C(Y) and an homeomorphism h from the realcompactification vX of X onto vY, such that

The compact version of this result was proved before by Jarosz in Bull. Canad. Math. Soc. 33 (1990) 139–144. In Contemp. Math., Vol. 253, 2000, pp. 125–144, Henriksen and Smith asked to what extent the result above can be generalized to a larger class of algebras. In the present paper, we give an answer to that question as follows. Let A and B be uniformly closed Φ-algebras. We first prove that every order bounded linear biseparating map from A onto B is automatically a weighted isomorphism, that is, there exist ω in B and a lattice and algebra isomorphism ψ between A and B such that

(a)=ωψ(a) for all aA.

We then assume that every universally σ-complete projection band in A is essentially one-dimensional. Under this extra condition and according to a result from Mem. Amer. Math. Soc. 143 (2000) 679 by Abramovich and Kitover, any linear biseparating map from A onto B is automatically order bounded and, by the above, a weighted isomorphism. It turns out that, indeed, the latter result is a generalization of the aforementioned theorem by Araujo et al. since we also prove that every universally σ-complete projection band in the uniformly closed Φ-algebra C(X) is essentially one-dimensional.     

Role of interfacial chemistry on the rheology and thermo-mechanical properties of clay-polymer nanocomposites for building applications

This study is directed towards investigating the role of the surface treatment of clay particles on the rheological and thermomechanical behaviour of clay-epoxy blends. Nanocomposites were prepared by mixing small amounts (5–10 mass %) of commercial organoclays or raw clays with an epoxy system commonly used in civil engineering. Rheological characterisations in the liquid state revealed a pronounced thixotropic character of the organoclay-based systems, which all exhibited a shear-thinning behaviour above a critical stress threshold (yield stress), depending on both the intensity of interfacial interactions and the degree of filler dispersion. On the other hand, systems based on raw clay particles behaved like Newtonian fluids, in the same way as the unreinforced polymer matrix. Complementary dynamic mechanical analyses (DMA) performed on the cured cross-linked nanocomposites also showed significant changes in the viscoelastic behaviour of the epoxy matrix due to the introduction of organoclays, whereas only minor variations were observed following the introduction of raw fillers. These results were consistent with nanoscale morphological characterisations performed by conventional X-ray diffraction (XRD) on the various hybrid systems. In this context, rheology and DMA appear as attractive alternative methods for assessing the filler dispersion at a macroscopic (and possibly more relevant) scale. This research is of practical interest for civil engineers, since clay reinforced-epoxies could in the future be used as coating materials with enhanced barrier performances, in order to protect infrastructures against environmental ageing or corrosion.     

Varying Track Etch Rates along the Fission Fragments＇ Trajectories in CR-39 Detectors

We determine the behavior of track etch rate VT along the tracks in CR-39 detectors exposed to fission fragments from ^252Cf source. CR-39 detectors are etched at 70℃ in different concentrations of Na2COa-mixed 6M NaOH solutions for different etching time intervals of 5-10min starting from 15 min up to 210min. Two values of track etch rate are determined along the fission fragment trajectories. The variation in VT is correlated with the energy loss rate of the fission fragment in the detector material.     

Blends of carbon blacks and multiwall carbon nanotubes as reinforcing fillers for hydrocarbon rubbers

The reinforcement of a styrene‐butadiene rubber (SBR) by single fillers—carbon black (CB) or multiwall carbon nanotubes (MWNTs)—or by mixtures of CB and MWNTs, is investigated. The morphologies, mechanical and electrical properties of the composites, are analyzed. A significant improvement in the tensile properties is observed for samples containing a dual phase. Using atomic force (AFM) and transmission electron (TEM) microscopies, we demonstrate that the double loading improves the dispersion of the nanotubes in SBR. Electrical measurements show lower resistivity and a lower percolation threshhold for composites containing blends of fillers, which provides further evidence of better dispersion. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 46: 1939–1951, 2008     

Two local search approaches for solving real-life car sequencing problems

The NP-hard problem of car sequencing appears as the heart of the logistic process of many car manufacturers. The subject of the ROADEF’2005 challenge addressed a car sequencing problem proposed by the car manufacturer RENAULT, more complex than the academic problem generally addressed in the literature. This paper describes two local search approaches for this problem. In the first part, a new approach by very large-scale neighborhood search is presented. This approach, designed during the qualification stage preceding the final, is based on an original integer linear programming formulation. The second part is dedicated to the approach which enabled us to win the ROADEF’2005 challenge. Inspired by the latest works on the subject, this one is based on very fast explorations of small neighborhoods. Our contribution here is mainly algorithmic, in particular by showing how much exploiting invariants speeds up the neighborhood evaluation and contributes to the diversification of the search. Finally, the two approaches are compared and discussed through an extensive computational study on RENAULT’s benchmarks. The main conclusion drawn at this point is that sophisticated metaheuristics are useless to solve car sequencing problems. More generally, our victory on ROADEF’2005 challenge demonstrates that algorithmic aspects, sometimes neglected, remain the key ingredients for designing and engineering high-performance local search heuristics.     

Guanidinium Alkynesulfonates with Single‐Layer Stacking Motif: Interlayer Hydrogen Bonding Between Sulfonate Anions Changes the Orientation of the Organosulfonate R Group from “Alternate Side” to “Same Side”

Hydrolyses of HC?CSO₃SiMe₃ ( 1 ) and CH₃C?CSO₃SiMe₃ ( 2 ) lead to the formation of acetylenic sulfonic acids HC?CSO₃H?2.33 H₂O ( 3 ) and CH₃C?CSO₃H?1.88 H₂O ( 4 ). These acids were reacted with guanidinium carbonate to yield [⁺C(NH₂)₃][HC?CSO₃^?] ( 5 ) and [⁺C(NH₂)₃][CH₃C?CSO₃^?] ( 6 ). Compounds 1 – 6 were characterized by spectroscopic methods, and the X‐ray crystal structures of the guanidinium salts were determined. The X‐ray results of 5 show that the guanidinium cations and organosulfonate anions associate into 1D ribbons through ${{\rm R}{{2\hfill \atop 2\hfill}}}$ (8) dimer interactions, whereas association of these ions in 6 is achieved through ${{\rm R}{{2\hfill \atop 2\hfill}}}$ (8) and ${{\rm R}{{1\hfill \atop 2\hfill}}}$ (6) interactions. The ribbons in 5 associate into 2D sheets through ${{\rm R}{{2\hfill \atop 2\hfill}}}$ (8) dimer interactions and ${{\rm R}{{3\hfill \atop 6\hfill}}}$ (12) rings, whereas those in 6 are connected through ${{\rm R}{{1\hfill \atop 2\hfill}}}$ (6) and ${{\rm R}{{2\hfill \atop 2\hfill}}}$ (8) dimer interactions and ${{\rm R}{{4\hfill \atop 6\hfill}}}$ (14) rings. Compound 6 exhibits a single‐layer stacking motif similar to that found in guanidinium alkane‐ and arenesulfonates, that is, the alkynyl groups alternate orientation from one ribbon to the next. The stacking motif in 5 is also single‐layer, but due to interlayer hydrogen bonding between sulfonate anions, the alkynyl groups of each sheet all point to the same side of the sheet.     

Molecular hydrogen "pairing" interaction in a metal organic framework system with unsaturated metal centers (MOF-74)

Infrared (IR) absorption spectroscopy measurements of molecular hydrogen in MOF-74-M (M = metal center) are performed as a function of temperature and pressure [to 45 kTorr (60 bar) at 300 K, and at lower pressures in the 20-200 K range] to investigate the nature of H(2) interactions with the unsaturated metal centers. A small shift (～?-30 cm(-1) with respect to the unperturbed H(2) molecule) is observed for the internal stretch frequency of H(2) molecules adsorbed on the metal site at low loading. This finding is in contrast to much larger shifts (～?-70 cm(-1)) observed in previous studies of MOFs with unsaturated metal centers (including MOF-74) and the general assumption that H(2) stretch shifts depend on adsorption energies (FitzGerald et al., Phys. Rev. B 2010, 81, 104305). We show that larger shifts (～?-70 cm(-1)) do occur, but only when the next available site ("oxygen" site) is occupied. This larger shift originates from H(2)-H(2) interactions on neighboring sites of the same pore, consistent with the short distance between H(2) in these two sites ～2.6 ? derived from an analysis of neutron diffraction experiments of D(2)-D(2) at 4 K (Liu et al., Langmuir 2008, 24, 4772-4777). Our results at 77 K and low loading can be explained by a diffusion barrier against pair disruption, which should be enhanced by this interaction. Calculations indicate that the vibrational shifts do not correlate with binding energies and are instead very sensitive to the environment (interaction potential and H(2)-H(2) interactions), which complicates the use of variable temperature IR methods to calculate adsorption energies of specific adsorption sites.