The finite element approximation of a coupled reaction-diffusion problem with non-Lipschitz nonlinearities

Summary. A coupled semilinear elliptic problem modelling an irreversible, isothermal chemical reaction is introduced, and discretised using the usual piecewise linear Galerkin finite element approximation. An interesting feature of the problem is that a reaction order of less than one gives rise to a "dead core" region. Initially, one reactant is assumed to be acting as a catalyst and is kept constant. It is shown that error bounds previously obtained for a scheme involving numerical integration can be improved upon by considering a quadratic regularisation of the nonlinear term. This technique is then applied to the full coupled problem, and optimal and error bounds are proved in the absence of quadrature. For a scheme involving numerical integration, bounds similar to those obtained for the catalyst problem are shown to hold. Received May 25, 1993 / Revised version received July 5, 1994     

A Popov-theory-based approach to digital H{infty} control with measurement feedback for Pritchard-Salamon systems

In this paper, we deal with the digital output-measurement-feedbackH control problem for Pritchard-Salamon infinite-dimensionalsystems with unbounded input and output operators. A discretePopov-theory-based solution is given in terms of the solvabilityof Kalman-Szegö-Popov-Yakubovitch systems associated withthe equivalent discrete-time time-invariant system obtainedby lifting the T-periodic continuous-time system.     

Pulsed photothermal laser deflection for low-level smoke and NO2 measurements in engine exhausts

Pulsed Photothermal Laser Deflection (PLD) is developed to make temporally and spatially resolved measurements of NO₂ and smoke. The rapid response PLD signal is produced when a HeNe probe beam is deflected by a thermal lens produced by a pulsed XeCl-excimer laser pumped dye laser. The fast time response (30 ns) and good spatial resolution make the PLD method a candidate for future in situ measurements in turbulent engine exhausts. The PLD signals, measured in a sample cell, exhibit a linear response for NO₂ concentrations from 3 ppm to 208 ppm and for smoke concentrations from 0.3 mg/m³ to 10 mg/m³. With a low pulse energy of 4 mJ, single-shot PLD measurements in a sample cell have accuracies of ± 14 ppm for NO₂ indicating accuracies of ±0.7 mg/m³ for smoke. With increased pulse energy and multi-shot averaging, sensitivities of ± 0.4 ppm of NO₂ or ± 20 µg/m³ of smoke are expected.     

The nilpotence height of

A 20-year-old conjecture about the mod 2 Steenrod algebra The method of Walker and Wood is used to completely determine the nilpotence height of the elements in the Steenrod algebra at the prime 2. In particular, it is shown that for all , . In addition, several interesting relations in are developed in order to carry out the proof.