There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra where flatness- and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of plane curves. The three non-flat examples, the simple, double and variable length pendulums, are borrowed from non-linear physics. A high frequency control strategy is proposed such that the averaged systems become flat.

/pdf/flatness-and-defect-of-non-linear-systems-introductory-42ot9eoqmh.pdf

Flatness and defect of non-linear systems: introductory theory and examples

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

A simple adaptive control algorithm, for which theoretical stability and convergence properties had been previously demonstrated, has been successfully implemented on a biomethanation pilot reactor. The methane digester, operated in the CSTR mode was submitted to a shock load, and successfully computer controlled during the subsequent transitory state.

Adaptive control of anaerobic digestion processes-a pilot-scale application.

Adaptive control of bioreactors

https://perso.uclouvain.be/georges.bastin/paper31.pdf

A case study of adaptive nonlinear regulation of fed-batch biological reactors

http://perso.uclouvain.be/georges.bastin/paper58.pdf

Hybrid Modelling of Biotechnological Processes Using Neural Networks

We report the development of a new serum-free medium based on the use of factorial experiments. At first, a variety of hydrolysates were screened using a fractional factorial approach with High-Five cells. From this experiment yeastolate ultrafiltrate was found to have, by far, the most important effect on cell growth. Furthermore, Primatone RL was found to remarkably prolong the stationary phase of Sf-9 and High-Five cell cultures. The optimal concentrations for yeastolate and Primatone were determined to be 0.6 and 0.5%, respectively, on the basis of a complete factorial experiment. This new medium, called YPR, supported good growth of both Sf-9 and High-Five cells in batch cultures, with maximal densities of 5.4 and 6.1 x 10(6) cells/ml, respectively. In addition, both cell lines achieved good growth in bioreactor batch culture and had a prolonged stationary phase of 3-4 d in YPR medium compared to Insect-XPRESS medium. The ability of the new medium to support recombinant protein expression was also tested by infecting Sf-9 or High-Five cells at high density (2 x 10(6) cells/ml) with a baculovirus expressing secreted placental alkaline phosphatase (SEAP). The maximum total SEAP concentration after 7 d was about 43 lU/ml (58 mg/L) and 28 lU/ml (39 mg/L) for High-Five and Sf-9 cells, respectively.

/pdf/design-of-an-efficient-medium-for-insect-cell-growth-and-5d03ks7gkv.pdf

Georges Bastin

Papers

Adaptive control of anaerobic digestion processes-a pilot-scale application.

Adaptive control of bioreactors

A case study of adaptive nonlinear regulation of fed-batch biological reactors

Hybrid Modelling of Biotechnological Processes Using Neural Networks

Design of an efficient medium for insect cell growth and recombinant protein production