Some extensions of Brioschi’s double alternant

We evaluate some determinants related to Brioschi’s extension of the classical double alternant of Cauchy, and Scott’s extension of Brioschi’s.     

The Möbius Category of Some Combinatorial Inverse Semigroups

\noindent The purpose of this paper is to point out some aspects of the relationship between combinatorial inverse semigroups and their Möbius categories, and to explore combinatorial results arising from combinatorial Brandt semigroups, fundamental simple inverse -semigroups and from the free monogenic inverse semigroup.     

Zero Duality Gap for Convex Programs: A Generalization of the Clark–Duffin Theorem

This article uses classical notions of convex analysis over Euclidean spaces, like Gale & Klee’s boundary rays and asymptotes of a convex set, or the inner aperture directions defined by Larman and Brøndsted for the same class of sets, to provide a generalization of the Clark–Duffin Theorem. On this ground, we are able to characterize objective functions and, respectively, feasible sets for which the duality gap is always zero, regardless of the value of the constraints and, respectively, of the objective function.     

Exact regularity of Bergman,Szegö and Sobolev space projections in non pseudoconvex domains

Mathematische Zeitschrift -     

The Bergman kernel function: Explicit formulas and zeroes

We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in defined by the inequality , have zeroes.

     

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.