Convergence of the control parameterization Ritz method for nonlinear optimal control problems

This paper studies the local convergence properties of the control parameterization Ritz method in which the control variable is approximated over a finite-dimensional subspace. The nonlinear free-endpoint optimal control problem is considered, and error bounds are derived for both the cost functional and state-control convergence. Explicit error bounds are obtained for the particular case of approximations over spline spaces. On specializing the general results to the linear-quadratic regulator problem, global convergence results are obtained. Computational results supporting the theoretically derived error bounds are presented.This research was supported by the University Grants Committee of New Zealand.     

Solution of nonlinear two-point boundary-value problems using spline functions

Journal of Optimization Theory and Applications - This paper describes a technique for computing spline function approximations to the solution of two-point boundary-value problems. A performance...     

Development of automated amperometric detection of antibodies against <Emphasis Type="Italic">Bacillus anthracis</Emphasis> protective antigen

Picogram levels of antibodies against the protective antigen (PA) of Bacillus anthracis were detected in an automated electrochemical sandwich-type enzyme-linked immunosorbant assay. The antibodies were captured and detected using an 8 × 3 array of 50-μm-diameter cavities. The reagent and sample volumes were as low as 200 nL in a less than 25-min assay from capture to signal generation. The electrochemical detection of the antibodies was demonstrated at 0.05–10 μg/mL containing only 10–5,000 pg antibodies. The limit of detection is 10 fg for a 200-nL sample. Detection of anti-PA immunoglobulin G performed in spiked normal human serum and fresh whole human blood did not show a significant difference from detection in a buffer. The initial automation of the assay involved the use of a digital syringe pump for the delivery of reagents to the capture surface.     

Application of radiochemical neutron activation and flame atomic absorption spectrometry for the determination of manganese in blood

The triplet-triplet absorption spectra of various aromatic compounds in benzene solution were studied by pulse radiolysis. It has been found that methylation of naphthalene characteristic absorption band in this group of compounds at 430±10 nm (naphthalene, 2-methylnaphthalene, 2,6-dimethylaphthalene, anthracene, phenanthrene, pyrene and fluorene); new bands appeared with phenanthrene and pyrene at 495 and 525 nm respectively. The decay remains of the first order in the whole group with similar rate constant values. Diphenyl and 1,1-dinaphthyl show significant changes in their T-T spectra in comparison with the preceding group of compounds. T-T spectrum of o-terphenyl differs significanly from those of p-and m-isomers, which can be caused by greater overlapping of electron orbitals in o-isomer molecule. Aromatic ketones show a complex picture both in spectra and decay kinetics.