Finding best approximation pairs relative to two closed convex sets in Hilbert spaces

We consider the problem of finding a best approximation pair, i.e., two points which achieve the minimum distance between two closed convex sets in a Hilbert space. When the sets intersect, the method under consideration, termed AAR for averaged alternating reflections, is a special instance of an algorithm due to Lions and Mercier for finding a zero of the sum of two maximal monotone operators. We investigate systematically the asymptotic behavior of AAR in the general case when the sets do not necessarily intersect and show that the method produces best approximation pairs provided they exist. Finitely many sets are handled in a product space, in which case the AAR method is shown to coincide with a special case of Spingarn's method of partial inverses.     

Anthracene‐thieno[3,4‐c]pyrrole‐4,6‐dione based donor–acceptor conjugated copolymers for applications in optoelectronic devices

Three novel alternating copolymers of thieno[3,4‐c]pyrrole‐4,6‐dione (TPD) and triisopropylsilylacetylene‐functionalized anthracene were prepared via Suzuki polymerization. Various solubilizing substituents were attached to the TPD moiety in order to ascertain the impact they have upon the optical, electrochemical, and thermal properties of the resulting polymers. All copolymers showed good solubility and thermal stability with decomposition temperatures in excess of 300°C. Optical properties revealed that PTATPD(O), PTATPD(DMO), and PTATPD(BP) displayed optical energy gaps in excess of 2.0 eV. It is speculated that steric repulsion between solubilizing groups on repeat units along polymer chains reduces their planarity and decreases their electronic conjugation. The amorphous nature of the polymers was confirmed with differential scanning calorimetry and powder X‐ray diffraction. The highest occupied molecular orbital levels of the three polymers are unaffected by the different solubilizing chains. However, they exert some influence over the lowest unoccupied molecular orbital (LUMO) levels with PTATPD(BP) and PTATPD(O) displaying the lowest LUMO levels (?3.4 eV). In contrast, PTATPD(DMO) displayed the highest LUMO level (?3.3 eV). © 2015 The Authors. Polymers for Advanced Technologies Published by John Wiley & Sons Ltd.     

Local A‐Site Layering in Rare‐Earth Orthochromite Perovskites by Solution Synthesis

Cation size effects were examined in the mixed A‐site perovskites La_0.5Sm_0.5CrO₃ and La_0.5Tb_0.5CrO₃ prepared through both hydrothermal and solid‐state methods. Atomically resolved electron energy loss spectroscopy (EELS) in the transmission electron microscope shows that while the La and Sm cations are randomly distributed, increased cation‐radius variance in La_0.5Tb_0.5CrO₃ results in regions of localised La and Tb layers, an atomic arrangement exclusive to the hydrothermally prepared material. Solid‐state preparation gives lower homogeneity resulting in separate nanoscale regions rich in La³⁺ and Tb³⁺. The A‐site layering in hydrothermal La_0.5Tb_0.5CrO₃ is randomised upon annealing at high temperature, resulting in magnetic behaviour that is dependent on synthesis route.     

Miniaturized pipette‐tip‐based electrospun polyacrylonitrile nanofibers for the micro‐solid‐phase extraction of nitro‐based explosive compounds

In this study, a self‐assembly of miniaturized pipette‐tip‐based solid‐phase extraction for the simultaneous extraction of nitroaromatic compounds was developed, with electrospun polyacrylonitrile nanofibers used as sorbents. The electrospun polyacrylonitrile nanofibers were characterized by scanning electron microscopy, FTIR analysis and surface area analysis. Good linearities for the four nitroaromatic compounds (2,6‐dinitrotoluene, 2‐nitrotoluene, 3‐nitrotoluene, and 4‐nitrotoluene) were obtained in a range of 250–1000 μg/L with coefficients of determination > 0.99. The limits of detection of these analytes were between 21 and 38 μg/L. The results showed that the pipette‐tip‐based solid‐phase extraction was effective in extracting nitrotoluenes in the pH regime of environmental interest (≈ 6). The investigation also revealed that the optimum mass of electrospun polyacrylonitrile nanofibers sorbent was 15 mg and 20 aspirating/dispensing cycles gave the maximum recovery of nitrotoluenes with 200 μL acetonitrile as the best eluting solvent. Moreover, the performance of the present method was studied for the extraction and determination of nitroaromatic compounds in real environmental water samples and good recoveries ranging from 70 to 115% were found, and respective relative standard deviations of <12% were obtained.     

Molecular Weight Development of Surface and Solution Polymers in Surface‐Initiated Atom Transfer Radical Polymerization and Their Dependence on Radical Termination Modes

In the surface‐initiated atom transfer radical polymerization, the polymerization proceeds both in solution and on surface. This work reports a modeling study, describing the growth of the molecular weight and polydispersity of polymer both on surface and in solution. It is found that both surface radical termination and solution monomer consumption significantly suppress the growth rate of polymer layer. Besides, the former affects the molecular weights of polymer both on surface and in solution. If the termination rate constant in solution (k_t,sol–sol) is the same as that of surface and solution interfaces (k_t,sol–surf), and the surface termination (k_{t,surf–surf}) is negligible, then the polymers both on surface and in solution have the same molecular weight. However, if surface radicals terminate among themselves, the molecular weight of polymer on surface will lower than that in solution. Such termination is promoted by surface radical migration through activation/deactivation reactions in solution. When k_t,sol–surf <k_t,sol–sol, the molecular weight of surface polymer becomes higher than that in solution. This situation is resulted from surface radical trap due to a high grafting density.

     

Excited States of Xanthene Analogues: Photofragmentation and Calculations by CC2 and Time‐Dependent Density Functional Theory

Action spectroscopy has emerged as an analytical tool to probe excited states in the gas phase. Although comparison of gas‐phase absorption properties with quantum‐chemical calculations is, in principle, straightforward, popular methods often fail to describe many molecules of interest—such as xanthene analogues. We, therefore, face their nano‐ and picosecond laser‐induced photofragmentation with excited‐state computations by using the CC2 method and time‐dependent density functional theory (TDDFT). Whereas the extracted absorption maxima agree with CC2 predictions, the TDDFT excitation energies are blueshifted. Lowering the amount of Hartree–Fock exchange in the DFT functional can reduce this shift but at the cost of changing the nature of the excited state. Additional bandwidth observed in the photofragmentation spectra is rationalized in terms of multiphoton processes. Observed fragmentation from higher‐lying excited states conforms to intense excited‐to‐excited state transitions calculated with CC2. The CC2 method is thus suitable for the comparison with photofragmentation in xanthene analogues.     

Intra‐ and Intermolecular Nickel‐Catalyzed Reductive Cross‐Electrophile Coupling Reactions of Benzylic Esters with Aryl Halides

Nickel‐catalyzed cross‐electrophile coupling reactions of benzylic esters and aryl halides have been developed. Both inter‐ and intramolecular variants proceed under mild reaction conditions. A range of heterocycles and functional groups are tolerated under the reaction conditions. Additionally, the first example of a stereospecific cross‐electrophile coupling of a secondary benzylic ester is described.