Extremum principles for optimal control in normed linear spaces

Extremum principles intended for use in optimal control are derived in the form of necessary conditions and sufficient conditions, formulated in general normed linear spaces. The method of application is illustrated by several examples involving optimal control problems, mathematical programming problems, lumped-parameter systems, and distributed-parameter systems. The basic theorems provide a unified approach which is applicable to a wide variety of problems in open-loop optimal control.     

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.

     

Dynamic behavior of photoablation products of corneal tissue in the mid-IR: a study with FELIX

2 . Dynamic parameters such as the extension of the ablation cloud, the initial velocity and momentum of the ablated particles as well as the ablation threshold, the ablated mass, and the particle size were investigated. The ablation plume was made visible with a stroboscopic technique. For a fluence of 3.1 J/cm² the average initial velocity of the ejected particles was deduced from the extension of the plume to range from 120–400 m/s. Measurements of the recoil momentum using a sensitive pendulum led to values between 0.5 and 2.0 mm g/s. All measured properties were related to the spectroscopically determined absorption coefficient of cornea α_cornea. Where absorption due to proteins is high (at λ=6.2 and 6.5 μm), ablated mass, velocity and recoil momentum behave according to α_cornea. For the first time, variations of the ablation plume from pulse to pulse were observed. Those, as well as the particle size, not only depend on the absorption coefficient, but also on the predominant absorber. Received: 4 November 1997/Revised version: 7 September 1998     

Laser fluorescence on radio-active isotopes produced in very low yield

East particle-photon coincidence techniques, developed at Daresbury with strontium isotopes, allow ultrasensitive laser fluorescence spectroscopy of beams of radio-active isotopes which can only be produced in very low yields. The technique has now been applied to neutron-deficient barium isotopes down to¹²⁰Ba. From measured hyperfine splittings and isotope shifts, nuclear moments and changes in mean square radii have been determined. The work has revealed an abrupt increase in the mean square radius for¹²¹Ba large enough to disrupt the systematic staggering of nuclear size seen for the series. In a recent experiment an isomeric state of¹²⁷Ba with a half-life of about 2 seconds has been produced in a very low yield; nevertheless we have succeeded in obtaining a fluorescence spectrum.     

Aeroacoustic sources of motorcycle helmet noise

The prevalence of noise in the riding of motorcycles has been a source of concern to both riders and researchers in recent times. Detailed flow field information will allow insight into the flow mechanisms responsible for the production of sound within motorcycle helmets. Flow field surveys of this nature are not found in the available literature which has tended to focus on sound pressure levels at ear as these are of interest for noise exposure legislation. A detailed flow survey of a commercial motorcycle helmet has been carried out in combination with surface pressure measurements and at ear acoustics. Three potential noise source regions are investigated, namely, the helmet wake, the surface boundary layer and the cavity under the helmet at the chin bar. Extensive information is provided on the structure of the helmet wake including its frequency content. While the wake and boundary layer flows showed negligible contributions to at-ear sound the cavity region around the chin bar was identified as a key noise source. The contribution of the cavity region was investigated as a function of flow speed and helmet angle both of which are shown to be key factors governing the sound produced by this region.