Presence or absence of analytic structure in maximal ideal spaces

We study extensions of Wermer’s maximality theorem to several complex variables. We exhibit various smoothly embedded manifolds in complex Euclidean space whose hulls are non-trivial but contain no analytic disks. We answer a question posed by Lee Stout concerning the existence of analytic structure for a uniform algebra whose maximal ideal space is a manifold.     

Sample conditions to avoid pH distortion in RP‐LC

Band deformations might take place for acids and bases in preparative applications and adsorption studies where it is necessary to use overloaded injections. In this study, we focus on how deformations can be prevented without using highly concentrated buffers that may precipitate in the eluent. We have systematically investigated how the elution zones depend on which protolytic form the analyte has when it is dissolved. Basic and acidic model compounds are investigated using eluents with different pH values and the resulting elution profiles are compared when the analytes are dissolved in their protonated and deprotonated form, i.e., in uncharged form or as different kinds of salts. Depending on the analyte's protolytic form, a sample zone is created at the column inlet whose pH deviates, more or less, from the bulk eluent's. If the local adsorption strength in this sample zone is greater than the bulk eluent's, the elution profiles are compressed. Under opposite conditions, the eluted bands are more or less deformed and may even be split; completely different deformations can even take place for different kinds of salt combinations. Explanations of these, and other, effects, together with detailed guidelines for proper sample preparation to avoid peak deformations, are given.     

A systematic investigation of algorithm impact in preparative chromatography with experimental verifications

Computer-assisted optimization of chromatographic separations requires finding the numerical solution of the Equilibrium-Dispersive (ED) mass balance equation. Furthermore, the competitive adsorption isotherms needed for optimization are often estimated numerically using the inverse method that also solves the ED equations. This means that the accuracy of the estimated adsorption isotherm parameters explicitly depends on the numerical accuracy of the algorithm that is used to solve the ED equations. The fast and commonly used algorithm for this purpose, the Rouchon Finite Difference (RFD) algorithm, has often been reported not to be able to accurately solve the ED equations for all practical preparative experimental conditions, but its limitations has never been completely and systematically investigated. In this study, we thoroughly investigate three different algorithms used to solve the ED equations: the RFD algorithm, the Orthogonal Collocation on Finite Elements (OCFE) method and a Central Difference Method (CDM) algorithm, both for increased theoretical understanding and for real cases of industrial interest. We identified discrepancies between the conventional RFD algorithm and the more accurate OCFE and CDM algorithms for several conditions, such as low efficiency, increasing number of simulated components and components present at different concentrations. Given high enough efficiency, we experimentally demonstrate good prediction of experimental data of a quaternary separation problem using either algorithm, but better prediction using OCFE/CDM for a binary low efficiency separation problem or separations when the compounds have different efficiency. Our conclusion is to use the RFD algorithm with caution when such conditions are present and that the rule of thumb that the number of theoretical plates should be greater than 1000 for application of the RFD algorithm is underestimated in many cases.