Cutting-plane proofs in polynomial space

Following Chvátal, cutting planes may be viewed as a proof system for establishing that a given system of linear inequalities has no integral solution. We show that such proofs may be carried out in polynomial workspace.Research supported by Sonderforschungsbereich 303 (DFG), Institut für Operations Research, Universität Bonn, FR Germany and by NSF grant ECS-8611841.     

A facile approach toward multicomponent supramolecular structures: selective self-assembly via charge separation

A novel approach toward the construction of multicomponent two-dimensional (2-D) and three-dimensional (3-D) metallosupramolecules is reported. Simply by mixing carboxylate and pyridyl ligands with cis-Pt(PEt(3))(2)(OTf)(2) in a proper ratio, coordination-driven self-assembly occurs, allowing for the selective generation of discrete multicomponent structures via charge separation on the metal centers. Using this method, a variety of 2-D rectangles and 3-D prisms were prepared under mild conditions. Moreover, multicomponent self-assembly can also be achieved by supramolecule-to-supramolecule transformations. The products were characterized by (31)P and (1)H multinuclear NMR spectroscopy, electrospray ionization mass spectrometry, and pulsed-field-gradient spin echo NMR techniques together with computational simulations.     

Polymerization kinetics of phosphonic acids and esters using an iodonium initiator

Phosphonic acids are known to be useful monomers in dental restorative materials because of their good potential to provide enhanced adhesion to hydroxyapatite and their high hydrolytic stability. In this study, the photopolymerization of phosphonic acid‐based monomer via the camphorquinone (CQ)/ethyl‐4‐(dimethylaminobenzoate) (EDAB) photoredox system is compared with a ternary system composed of iodonium hexafluorophosphate and CQ/EDAB. Photocalorimetry shows that the ternary system does not provide a significant acceleration of the polymerization with either acrylamide or methacrylate phosphonic acids. The complexation of the iodonium by the phosphonic moiety of the acidic monomers leads to a lowered iodonium reactivity and reduced polarizability of the medium and as a consequence limits the rate enhancement effect normally observed by phosphonic acids on the polymerization rate. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 5046–5055     

In-situ identification of iron--zinc intermetallics in galvannealed steel coatings and iron oxides on exposed steel

Identification of all the compounds present in various coatings on steels is particularly difficult. Non-destructive, in-situ analysis is necessary if the fraction of each compound as well as its probable layering within the coating, is to be determined. Mössbauer spectroscopy is one valuable probe capable of uniquely identifying all iron compounds which form as coatings on steel and other iron alloy surfaces. To investigate a complete coating several criteria need to be considered. Removing the coating inevitably leaves a small and perhaps important component intact on the substrate. Therefore investigating the coating as it remains intact on the steel is important if complete identification of the iron compounds is to be made. This also preserves crystalline texture or preferred growth orientation within the coating to which the Mössbauer effect is sensitive. Mössbauer spectroscopy is a non-destructive technique which allows the integrity of the coating to be maintained during analysis. The combined transmission and scattering Mössbauer geometries generally result in accurate analysis of the coating composition. For the scattering geometry added information on compound layering is obtained if separate Mössbauer spectra are recorded using the re-emitted gamma rays as well as the conversion electrons and subsequently emitted X-rays. In-situ scattering Mössbauer spectroscopy has been used to characterize the iron--zinc alloys which form in the coatings of commercially produced corrosion resistant galvannealed sheet steel, a product of great interest to automotive producers. The results show that different amounts of four iron--zinc phases are present depending on the production conditions of the coating. The different phases are also distinctly layered. Mössbauer analyses of corrosion coatings formed on the surface of steels which have been exposed to different environments has also been undertaken. Materials include structural steels exposed for up to 25 years in marine, rural and industrial environments, and the interior surfaces of boiler pipes subjected to adverse chemical and temperature environments.     

Distributions in fuzzy logic

Probability distributions associated with several ‘ply’-operators are discussed. These exact distributions are compared with relevant Gaussian approximations.     

Long-lived charge carrier generation in ordered films of a covalent perylenediimide–diketopyrrolopyrrole–perylenediimide molecule

The photophysics of a covalently linked perylenediimide–diketopyrrolopyrrole–perylenediimide acceptor–donor–acceptor molecule (PDI–DPP–PDI, 1) were investigated and found to be markedly different in solution versus in unannealed and solvent annealed films. Photoexcitation of 1 in toluene results in quantitative charge separation in τ = 3.1 ± 0.2 ps, with charge recombination in τ = 340 ± 10 ps, while in unannealed/disordered films of 1, charge separation occurs in τ < 250 fs, while charge recombination displays a multiexponential decay in ∼6 ns. The absence of long-lived, charge separation in the disordered film suggests that few free charge carriers are generated. In contrast, upon CH₂Cl₂ vapor annealing films of 1, grazing-incidence X-ray scattering shows that the molecules form a more ordered structure. Photoexcitation of the ordered films results in initial formation of a spin-correlated radical ion pair (electron–hole pair) as indicated by magnetic field effects on the formation of free charge carriers which live for ∼4 μs. This result has significant implications for the design of organic solar cells based on covalent donor–acceptor systems and shows that long-lived, charge-separated states can be achieved by controlling intramolecular charge separation dynamics in well-ordered systems.