An image system and surface singularity solutions for potential flow past an elliptical cylinder

The Milne-Thomson circle theorem is extended to give a simplegeneral expression for the image system in an elliptical cylinderintroduced into an otherwise specified unbounded potential flowwhich contains no singularities in the region to be occupiedby the ellipse. This image system is used to obtain an expressionfor the corresponding source-sink surface singularity distributionon the ellipse, thus providing new benchmark test cases forsource-sink solutions as obtained numerically by a panel method.Several typical examples are given to illustrate the generaltheoretical approach.     

Post-column labeling techniques in amino acid analysis by liquid chromatography

Amino acid analysis (AAA) has always presented an analytical challenge in terms of sample preparation, separation, and detection. Because of the vast number of amino acids, various separation methods have been applied taking into consideration the large differences in their chemical structures, which span from nonpolar to highly polar side chains. Numerous separation methods have been developed in the past 60 years, and impressive achievements have been made in the fields of separation, derivatization, and detection of amino acids (AAs). Among the separation methods, liquid chromatography (LC) prevailed in the AAA field using either pre-column or post-column labeling techniques in order to improve either separation of AAs or selectivity and sensitivity of AAA. Of the two approaches, the post-column technique is a more rugged and reproducible method and provides excellent AAs separation relatively free from interferences. This review considers current separations combined with post-column labeling techniques for AAA, comparison with the pre-column methods, and the strategies used to develop effective post-column methodology. The focus of the article is on LC methods coupled with post-column labeling techniques and studying the reactions to achieve optimum post-column derivatization (PCD) conditions in order to increase sensitivity and selectivity using various types of detectors (UV–Vis, fluorescence, electrochemical etc.) and illustrating the versatility of the PCD methods for practical analysis.

Presentations of the first homotopy groups of the unitary groups

We describe explicit presentations of all stable and the first nonstable homotopy groups of the unitary groups. In particular, for each n 2 we supply n homotopic maps that each represent the (n - 1)!-th power of a suitable generator of _2n SU(n) _n!. The product of these n commuting maps is the constant map to the identity matrix.