A converse to the Eidelheit theorem in real Hilbert spaces

We establish the following converse to the Eidelheit theorem: an unbounded closed and convex set of a real Hilbert space may be separated by a closed hyperplane from every other disjoint closed and convex set, if and only if it has a finite codimension and a non-empty interior with respect to its affine hull.     

Integrated Planar Waveguide Demultiplexers for High-Density WDM Applications

A review is presented of state-of-the-art optical planar waveguide demultiplexers (DEMUXes), that is, phasars (arrayed waveguide) and etched grating devices designed for high-density (narrow channel spacing) wavelength division multiplexing (WDM) systems. Their advantages and disadvantages are discussed in comparison with other techniques for demultiplexing WDM signals. The advances made in their performance are reviewed, and ultimate limitations, set by technological constraints, are proposed. Finally, a comparison is made of the advantages and disadvantages of etched grating as opposed to phasar planar waveguide DEMUXes.     

Enantioselective epoxide polymerization using a bimetallic cobalt catalyst

A highly active enantiopure bimetallic cobalt complex was explored for the enantioselective polymerization of a variety of monosubstituted epoxides. The polymerizations were optimized for high rates and stereoselectivity, with s-factors (k(fast)/k(slow)) for most epoxides exceeding 50 and some exceeding 300, well above the threshold for preparative utility of enantiopure epoxides and isotactic polyethers. Values for mm triads of the resulting polymers are typically greater than 95%, with some even surpassing 98%. In addition, the use of a racemic catalyst allowed the preparation of isotactic polyethers in quantitative yields. The thermal properties of these isotactic polyethers are presented, with many polymers exhibiting high T(m) values. This is the first report of the rapid synthesis of a broad range of highly isotactic polyethers via the enantioselective polymerization of racemic epoxides.     

Traceless azido linker for the solid-phase synthesis of NH-1,2,3-triazoles via Cu-catalyzed azide-alkyne cycloaddition reactions

A broadly useful acid-labile traceless azido linker for the solid-phase synthesis of NH-1,2,3-triazoles is presented. A variety of alkynes were efficiently immobilized on a range of polymeric supports by Cu(I)-mediated azide-alkyne cycloadditions. Supported triazoles showed excellent compatibility with subsequent peptide chemistry. Release of pure material (typically >95%) from the solid support was readily achieved by treatment with aqueous TFA.     

Statistical quality control for ternary ordinal quality data

The paper considers various aspects of statistical quality control by means of sample data received on a ternary ordinal scale. A new method for evaluating quality level and dispersion, free of any latent numerical scale assumptions, is proposed. The emphasis is on working with large samples, which enable the statistical analysis, estimation and control by the use of approximate analytical expressions of these measures to be considerably simplified. Two complementary studies demonstrate the usage of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Interference law for coherent stochastic electromagnetic beams

Two-beam interference law for the superposition of stochastic, spatially coherent, electromagnetic beams is derived. Only a single phase is found to enter the interference law, in spite of the vector nature of the problem. The meaning of the phase is elucidated.     

Flow and heat transfer of non-Newtonian fluids in enameling dies

The present work analyses computationally the flow inside wire enameling dies within the framework of the lubrication theory approximation. Non-Newtonian flow behavior and heat transfer are accounted for as well. It is shown that the developed approach most accurately predicts the momentum and heat fluxes along the wire. As such it is proven as a reliable and computationally efficient tool for the design of flow optimized die shapes. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differences in porous characteristics of styrenic monoliths prepared by controlled thermal polymerization in molds of varying dimensions

Nitroxide‐mediated polymerization was used as a model system for preparing styrenic monolithic materials with significant mesopore contents in different mold formats, with the aim of assessing the validity of pore characterization of capillary monoliths by analysis of parallel bulk polymerized precursor solution. Capillary monoliths were prepared in 250 μm id fused silica tubes (quadruplicate samples, in total 17 m), and the batch polymerizations were carried out in parallel in 100 μL microvials and regular 2 mL glass vials, both in quintuplicate. The monoliths recovered from the molds were characterized for their meso‐ and macroporous properties by nitrogen sorptiometry (three repeated runs on each sample), followed by a single analysis by mercury intrusion porosimetry. A total of 14 monolith samples were thus analyzed. A Grubbs' test identified one regular vial sample as an outlier in the sorptiometric surface area measurements, and data from this sample were consequently excluded from the pore size calculations, which are based on the same nitrogen sorption data, and also from the mercury intrusion data set. The remaining data were subjected to single factor analyses of variance analyses to test if the porous properties of the capillary monoliths were different from those of the bulk monoliths prepared in parallel. Significant differences were found between all three formats both in their meso‐ and macroporous properties. When the dimension was shrunk from conventional vial to capillary size, the specific surface area decreased from 52.2±4.7 to 34.6±1.7 m²/g. This decrease in specific surface area was accompanied by a significant shift in median diameter of the through‐pores, from 310±3.9 to 544±13 nm. None of these differences were obvious from the scanning electron micrographs that were acquired for each sample type. The common practice of determining the mesopore characteristics from analysis of samples prepared by parallel bulk polymerization and looking for changes in the macropore structure by visual assessment of SEMs are therefore both rather questionable, at least for monoliths of the kind used in this study.