Comparison of the extended kalman filter and marquardt algorithms for processing kinetic data

The extended Kalman filter and Marquardt's gradient expansion algorithm for nonlinear least squares are compared with respect to accuracy and precision of parameter extimates, computational burden, sensitivity to initial parameter estimates and ability to indicate model errors. Fits of synthetic first-order data and combined first- and zero-order data produce estimates of equivalent precision and accuracy in most cases. Similar results were obtained for both simulated and experimental data for combined zero-order/first-order processes. However, for the simulated zero-order/first-order data with small zero-order components processed over two half-lives of the first-order process, the Kalman filter overestimated the zero-order rate constant by a substantially larger amount than the Marquardt algorithm. Significant differences in computational burden and sensitivity to initial parameter estimates are demonstrated; however, neither algorithm has a significant advantage over the other for the detection of model error.     

High temperature and temperature programming in capillary electrochromatography

In electrochromatography, solvent electrophoretic mobility and solute partitioning are temperature dependent processes. If temperature variations are controlled, solute selectivity and analysis times can be tailored. In this study the feasibility of temperature programming in capillary electrochromatography (CEC) was demonstrated using a reversed-phase CEC mode. The outcome of programmed separations was compared with isothermal, isocratic and isorheic (constant flow) separations. The combined effects of column temperature and mobile phase flow-rate changes during the separation run, resulted in up to a 50% reduction in the separation run time, without adversely affecting the quality of separation. For capillary electrochromatography, temperature programming may be a valuable alternative to solvent programming modes because of the great technical difficulties associated with carrying out solvent gradient elution.     

Emprical distribution for linear system identification

Asymptotic properties of empirical distributions of approximate errors for least squares identification are developed in this work. As a preparation, it is first shown that a law of large numbers type of result holds for the empirical distribution. Then a scaled sequence is proved to converge to a Gaussian process with a Brownian bridge component. These results are useful for carrying out statistical inference tasks, goodness of fit tests, and related matters     

Establishing the kinetic competency of the cationic imine intermediate in nitroalkane oxidase

The flavoprotein nitroalkane oxidase catalyzes the oxidation of neutral nitroalkanes to the corresponding aldehydes and ketones. Cyanide inactivates the enzyme during turnover in a concentration-dependent fashion. Mass spectrometry of the flavin from enzyme inactivated by cyanide in the presence of nitroethane or nitrohexane shows that a flavin cyanoethyl or cyanohexyl intermediate has formed. At high concentrations of cyanide, inactivation does not consume oxygen. Rapid reaction studies show that formation of the adduct with 2-(2H2)-nitroethane shows a kinetic isotope effect of 7.9. These results are consistent with cyanide reacting with a species formed after proton abstraction but before flavin oxidation. The proposed mechanism for nitroalkane oxidase involves removal of a proton from the nitroalkane, forming a carbanion which adds to the flavin N(5). Elimination of nitrite from the resulting adduct would form an electrophilic imine which can be attacked by hydroxide. The present results are consistent with cyanide trapping this electrophilic intermediate.     

Synthesis and structural analysis of the anilides of glucuronic acid and orientation of the groups on the carbohydrate scaffolding

[structures: see text] The synthesis of anilides derived from glucuronic acid is described. Secondary anilides had a Z configuration in the solid state and showed intramolecular and intermolecular hydrogen bonding. However, on the basis of NMR and IR studies, there was generally no evidence for the same hydrogen bonding in solution. Tertiary anilides showed a strong preference for the E configuration on the basis of NOE studies and molecular mechanics calculations. The alkylation of the secondary anilides induces a configurational switch that alters the orientation of the aromatic group with respect to the pyranose, which has relevance for presentation or orientation of pharmacophoric groups on carbohydrate scaffolds.     

Covering hypercubes by isometric paths

An isometric path is merely any shortest path between two vertices. If the vertices of the hypercube Q_n are represented by the set of 0–1 vectors of length n, an isometric path is obtained by changing the coordinates of a vector one at a time, never changing the same coordinate more than once. The minimum number of isometric paths required to cover the vertices of Q_n is at least 2ⁿ/(n+1). We show that when n+1 is a power of 2, the lower bound is in fact the minimum. In doing so, we construct a family of disjoint isometric paths which can be used to find an upper bound for additional classes of hypercubes.     

Fluorescence Suppression of 7-Methoxycoumarin upon Inclusion into Cyclodextrins

The fluorescence intensity of 7-methoxycoumarin (7MC) in aqueoussolution is found to significantly decrease upon addition of variouscyclodextrins. This observed phenomenon is described asfluorescence suppression, to distinguish it from fluorescencereduction via bimolecular quenching. The decrease in fluorescenceof 7MC is proposed to be the result of the formation of ahost–guest inclusion complex with cyclodextrin. Since 7MC isa polarity-sensitive fluorophore, which is less fluorescent ina nonpolar environment, its fluorescence decreases uponinclusion into the relatively nonpolar internal cavity of thecyclodextrin. The same equation used for extracting the associationconstant in the case of 1 : 1 host–guest inclusion-induced fluorescenceenhancement is shown to be applicable to the case of fluorescencesuppression. In the case of β-cyclodextrin, the degree of fluorescencesuppression, as well as the value of the binding constant for formationof the inclusion complex, are found to be unaffected by modificationof the cyclodextrin rims, suggesting that the molecule iscompletely included within the β-cyclodextrin cavity. In the case ofγ-cyclodextrin, the degree of fluorescence suppression, butnot the value of the binding constant, is found to be significantlyaffected by modification of the cyclodextrin rims, suggesting thatthe molecule is experiencing a less polar environment in the modifiedγ-cyclodextrin cavity. The binding constant is three timeslarger in β- as compared to γ-cyclodextrin, indicatinga much better size match in the smaller β-cyclodextrin cavity.     

On the pointwise maximum of convex functions

We study the conjugate of the maximum, , of and when and are proper convex lower semicontinuous functions on a Banach space . We show that on the bidual, , of provided that and satisfy the Attouch-Brézis constraint qualification, and we also derive formulae for and for the ``preconjugate' of .