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.     

Synthesis of 5-alkylidene-2,5-dihydropyrrol-2-ones based on cyclizations of 1,3-bis(trimethylsilyloxy)-1,3-butadienes with oxalyl chloride

The acid-mediated reaction of amines with γ-alkylidenebutenolides, readily available by cyclization of 1,3-bis(silyloxy)-1,3-butadienes with oxalyl chloride, allows a convenient synthesis of a variety of 5-alkylidene-2,5-dihydropyrrol-2-ones. The configuration of the exocyclic double bond of the products depends on the substitution pattern of the products.     

Global Convergence of a Nonlinear Programming Method Using Convex Approximations

The method of moving asymptotes (MMA) and its globally convergent extension SCP (sequential convex programming) are known to work well for certain problems arising in structural optimization. In this paper, the methods are extended for a general mathematical programming framework and a new scheme to update certain penalty parameters is defined, which leads to a considerable improvement in the performance. Properties of the approximation functions are outlined in detail. All convergence results of the traditional methods are preserved.