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.     

Copper-mediated N- and O-arylations with arylboronic acids in a continuous flow microreactor: a new avenue for efficient scalability

A continuous flow procedure has been elaborated for the copper(II)-mediated N- and O-arylation of a range of compounds with arylboronic acids using a commercial microreactor setup. The compounds could be continuously generated in good yields paving the way for efficient scalability.     

Implicit QR algorithms for palindromic and even eigenvalue problems

In the spirit of the Hamiltonian QR algorithm and other bidirectional chasing algorithms, a structure-preserving variant of the implicit QR algorithm for palindromic eigenvalue problems is proposed. This new palindromic QR algorithm is strongly backward stable and requires less operations than the standard QZ algorithm, but is restricted to matrix classes where a preliminary reduction to structured Hessenberg form can be performed. By an extension of the implicit Q theorem, the palindromic QR algorithm is shown to be equivalent to a previously developed explicit version. Also, the classical convergence theory for the QR algorithm can be extended to prove local quadratic convergence. We briefly demonstrate how even eigenvalue problems can be addressed by similar techniques. D. S. Watkins partly supported by Deutsche Forschungsgemeinschaft through Matheon, the DFG Research Center Mathematics for key technologies in Berlin.     

Equality of multiplicity free skew characters

In this paper we show that two skew diagrams λ/μ and α/β can represent the same multiplicity free skew character [λ/μ]=[α/β] only in the the trivial cases when λ/μ and α/β are the same up to translation or rotation or if λ=α is a staircase partition λ=(l,l−1,…,2,1) and λ/μ and α/β are conjugate of each other.     

Grid Graphs,Gorenstein Polytopes,and Domino Stackings

We examine domino tilings of rectangular boards, which are in natural bijection with perfect matchings of grid graphs. This leads to the study of their associated perfect matching polytopes, and we present some of their properties, in particular, when these polytopes are Gorenstein. We also introduce the notion of domino stackings and present some results and several open questions. Our techniques use results from graph theory, polyhedral geometry, and enumerative combinatorics.