Linear dependence, computational, control

Some care was required in the control of computational linear dependence, which was achieved by deleted diffuse, bond centre functions. It is suggested that a total Hartree-Fock energy of an accuracy comparable with that obtained for the CO molecule was thereby achieved. 

For a one-centre basis set, in contrast to multi-centre basis sets, problems arising from overcompleteness can usually be controlled if not avoided. The one-centre approach provides control over the convergence of a calculation with respect to the size of the basis set and control over computational linear dependence. Furthermore, because of the ea% with which integrals involving one-centre functions can be handled, the method can be used to explore the use of alternative types of basis function. The one-centre method is ideally suited to the calculation of energy derivatives with respect to the nuclear coordinates. 

The program can solve both steady-state problems as well as time-dependent problems, and has provisions for both linear and nonlinear problems. The boundary conditions and material properties can vary with time, temperature, and position. The property variation with position can be a straight line function or or a series of connected straight line functions. User-written Fortran subroutines can be used to implement more exotic changes of boundary conditions, material properties, or to model control systems. The program has been implemented on MS DOS microcomputers, VAX computers, and CRAY supercomputers. The present work used the MS DOS microcomputer implementation. 

Experimental (simplex and window diagram). The chromatographic system consisted of a Model 501 supercritical fluid chromatograph (Lee Scientific, Salt Lake City, Utah) with the flame ionization detector (FID) set at 375°C. The instrument was controlled with a Zenith AT computer. A pneumatically driven injector with a 200 nL or a 500 nL loop was used in conjunction with a splitter. Split ratios used were between 5 1 and 50 1, depending on sample concentration and the chosen linear velocity, while the timed injection duration ranged from 50 ms to 1 s. We found that the variation of both the split ratio and injection time allowed greater control over the... 

Model-based approaches allow fast derivative computation by relying on a process model, yet only approximate derivatives are obtained. In self-optimizing control [12,21], the idea is to use a plant model to select linear combinations of outputs, the tracking of which results in optimal performance, also in the presence of uncertainty in other words, these linear combinations of outputs approximate the process derivatives. Also, a way of calculating the gradient based on the theory of neighbouring extremals has been presented in [13] however, an important limitation of this approach is that it provides only a first-order approximation and that the accuracy of the derivatives depends strongly on the reliability of the plant model. 

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