Necessary optimality conditions and regularity results for state and adjoint state of nonlinear control problems

For optimal control problems of nonlinear evolution equations of first order we derive regularity properties for the corresponding adjoint states where the proof is based on the necessary optimal conditions and smoothness properites of the optimal states. These results are used for the characterization of the optimal solution and the corresponding adjoint state of the periodic three-dimensionel NAVIER-STOKES system.     

Flow over rectangular porous block in a fixed width channel: influence of porosity and aspect ratio

Flow over a rectangular porous block placed in a fixed width channel is considered and the influence of block aspect ratio on the heat transfer rate from the block is examined. A non-porous solid block is also accommodated to compare the effect of porosity on the flow field and heat transfer characteristics. Aspect ratio and the porosity of the block are varied in the simulations. A numerical scheme employing a control volume approach is considered when predicting the flow and temperature fields. The Reynolds number is selected to yield the mix convection situation in the flow field. It is found that the aspect ratio significantly influences Nu and Gr numbers, in which case increasing the aspect ratio enhances Nu while lowering Gr. Increasing porosity improves the heat transfer rates from the porous block, provided that at high aspect ratios, this situation ceases due to blockage effect of the body in the channel.     

Time optimality and the maximum principle in infinite dimension

We present three counterexamples related to the maximum principle for the time optimal problem. The system is linear, infinite dimensional, with point target and “full” control     

What can statistical process control show us about ionization chamber stability?

PurposeStatistical process control (SPC) has been shown to be a suitable tool for medical physicists to monitor quality and keep variability low and within specifications. We report our findings regarding ionisation chamber stability in our department when using a radioactive stability check device (RSCD) and we compare them with similar previously published records, including calibration results.MethodsWe retrospectively studied the stability of a PPC 40 parallel-plate chamber, and two Farmer chambers (FC65-G and FC65-P) by checking them with dedicated RSCDs. We analysed the data following SPC methodology which includes plotting I-MR control charts, monitoring out-of-control observations, calculating process capability ratios (C_p), and estimating conformance to specifications. We also estimated the C_p and adherence to specifications of previously published data.ResultsThe PPC40 chamber hardly went out of the control limits over the whole six-year period assessed. However, Farmer chamber verifications drifted in opposite directions in phase II, and the deviations observed did not agree with their calibration records, which only increased by a maximum of 0.5%. In phase I the most unstable chamber was the FC65-P with a C_p equal to 0.9 at a specification level of ±1%. The PPC40 chamber was stable to within a maximum C_p of 1.3. Several sets of analysed data, including ours and those from other authors, fitted well within these limits: within ±1.9% and ±1.5% for a C_p of 1.5 and 1.33 respectively.ConclusionsSPC with constant long-term RSCD checking gave us a meaningful plot of the instability of our ionisation chambers. Although a period of two years between calibrations should not be surpassed, in the interim this check can conform to specifications of ±1.5%.     

Resonant control of solitons

It is shown that the effect of “scattering on resonance” can be used to control envelope solitons in the driven nonlinear Schrödinger equation. The control occurs by the frequency modulated driving with multiple crossing of the resonant frequency of the soliton.     

Operations research in the space industry

Operations research techniques have been used in the space industry since its infancy, and various competing methods and codes, with widely varying characteristics, have been used over time. This survey is intended to give an overview of current application cases of different operations research techniques and methodologies in the domain of space engineering and space science.     

On the Relative Gain Array (RGA) with singular and rectangular matrices

This paper identifies a significant deficiency in the literature on the application of the Relative Gain Array (RGA) formalism in the case of singular matrices. Specifically, it is shown that the conventional use of the Moore–Penrose pseudoinverse is inappropriate because it fails to preserve critical properties that can be assumed in the nonsingular case. It is then shown that such properties can be rigorously preserved using an alternative generalized matrix inverse.     

高校“双困”毕业生就业状况调研及对策建议--以福建省厦门市高校毕业生为例

对福建省厦门市5所高校的223名家庭经济困难且就业存在困难的毕业生进行了问卷调查，系统调研了“双困生”的就业意向、就业信心、求职渠道、职业认知、职业规划等，为社会、政府、企业、高校等机构科学、高效地开展“双困生”就业援助工作提供合理建议。