Understanding Electrophoretic Stacking Of In-Capillary Generated Reaction Products

The separation of small molecules by capillary electrophoresis is governed by a complex interplay among several physical effects. Until recently, a systematic understanding of how the influence of all of these effects is observed experimentally has remained unclear. The work presented in this thesis involves the use of transient isotachophoretic stacking (tITP) and computer simulation to improve and better understand an in-capillary chemical assay for creatinine. This assay involves the use of electrophoretically mediated micro-analysis (EMMA) to carry out the Jaffé reaction inside a capillary tube. The primary contribution of this work is the elucidation of the role of the length and concentration of the hydroxide plug used to achieve tITP stacking of the product formed by the in-capillary EMMA/Jaffé method. Computer simulation using SIMUL 5.0 predicts that a 3-4 fold gain in sensitivity can be recognized by timing the tITP stacking event such that the Jaffé product peak is at its maximum height as that peak is electrophoresing past the detection window. Overall, the length of the hydroxide plug alters the timing of the stacking event and lower concentration plugs of hydroxide lead to more rapidly occurring tITP stacking events. Also, the inclusion of intentional tITP stacking in the EMMA/Jaffé method improves the sensitivity of the assay, including creatinine concentrations within the normal biological range. Ultimately, improvement in assay sensitivity can be rationally designed by using the length and concentration of the hydroxide plug to engineer the timing of the tITP stacking event such that stacking occurs as the Jaffé product is passing the detection window.

Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality

Given the weight sequence for a subnormal recursively generated weighted shift on Hilbert space, one approach to the study of classes of operators weaker than subnormal has been to form a backward extension of the shift by prefixing weights to the sequence. We characterize positive quadratic hyponormality and revisit quadratic hyponormality of certain such backward extensions of arbitrary length, generalizing earlier results, and also show that a function apparently introduced as a matter of convenience for quadratic hyponormality actually captures considerable information about positive quadratic hyponormality.