Liouville numbers, Rajchman measures, and small Cantor sets

We show that the set of Liouville numbers carries a positive measure whose Fourier transform vanishes at infinity. The proof is based on a new construction of a Cantor set of Hausdorff dimension zero supporting such a measure.

     

Synthesis of dendritic macromolecules through divergent iterative thio‐bromo “Click” chemistry and SET‐LRP

The development of a novel nucleophilic thio‐bromo “Click” reaction, specifically base‐mediated thioetherification of thioglycerol with α‐bromoesters was reported in an earlier article. The combination of this thio‐bromo click reaction with subsequent acylation with 2‐bromopropionyl bromide provides an iterative two‐step divergent growth approach to the synthesis of a new class of poly(thioglycerol‐2‐ propionate) (PTP) dendrimers. In this article, the addition of a third step, the single‐electron transfer living radical polymerization (SET‐LRP) of methyl acrylate (MA), was shown to provides access to a three‐step “branch” and “grow” divergent approach to dendritic macromolecules wherein poly(methyl acrylate) (PMA) connects the branching subunits. This facile methodology can provide a diversity of dendritic macromolecular topologies and will ultimately provide the means to the development of self‐organizable dendritic macromolecules. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3940–3948, 2009     

Universal Extension and Excision for Topological Algebras

We construct a topology on the tensor algebra that makes the multiplication jointly continuous and is universal for algebras with jointly continuous multiplication. This result, together with the methods developed by Cuntz for m-algebras are used to prove the excision theorem of Cuntz and Quillen in the more general case of c-algebras.     

Simultaneous Quantification of Neomycin and Bacitracin by LC-ELSD

The first simultaneous quantification of neomycin and bacitracin using liquid chromatography evaporative light scattering detection as an alternative to MS detection and pre-/post-column derivatisation, respectively, was the aim of this study. The developed method was validated for two strength of neomycin and one strength of bacitracin in sterile pharmaceutical formulation and is a fast and efficient tool for content uniformity tests in quality control. With this method the separation of neomycin from sulfate and the base line separation of the four major components of bacitracin (bacitracin A, B1, B2 and B3) was achieved. These four components are responsible for 96% of the microbiological activity. A Phenomenex Synergi POLAR analytical column (250 mm × 4.6 mm, 4 μm I.D.) in combination with 0.5% perfluoropropionic acid and acetonitrile in gradient mode, the peaks of interest could be separated with high efficiency within 14 min. The calibration was performed using a second order regression with an R ² = 0.9999 for neomycin (B and C) sulfate and R ² = 0.9996 for bacitracin A, B1, B2 and B3. The results of the accuracy evaluation were 99.2 and 99.7%, respectively, for neomycin and 100.8% for bacitracin. Injection precision results are 0.4–1.5 RSD% recorded for six injections. The established method has a high potential for routine high-throughput analyses in the pharmaceutical industry.