Optimality Conditions for Semivectorial Bilevel Convex Optimal Control Problems

We present optimality conditions for bilevel optimal control problems where the upper level, to be solved by a leader, is a scalar optimal control problem and the lower level, to be solved by several followers, is a multiobjective convex optimal control problem. Multiobjective optimal control problems arise in many application areas where several conflicting objectives need to be considered. Minimize several objective functionals leads to solutions such that none of the objective functional values can be improved further without deteriorating another. The set of all such solutions is referred to as efficient (also called Pareto optimal, noninferior, or nondominated) set of solutions. The lower level of the semivectorial bilevel optimal control problems can be considered to be associated to a ”grande coalition” of a p-player cooperative differential game, every player having its own objective and control function. We consider situations in which these p-?players react as ”followers” to every decision imposed by a ”leader” (who acts at the so-called upper level). The best reply correspondence of the followers being in general non uniquely determined, the leader cannot predict the followers choice simply on the basis of his rational behavior. So, the choice of the best strategy from the leader point of view depends of how the followers choose a strategy among his best responses. In this paper, we will consider two (extreme) possibilities: (i) the optimistic situation, when for every decison of the leader, the followers will choose a strategy amongst the efficient controls which minimizes the (scalar) objective of the leader; in this case the leader will choose a strategy which minimizes the best he can obtain amongst all the best responses of the followers: (ii) the pessimistic situation, when the followers can choose amongst the efficient controls one which maximizes the (scalar) objective of the leader; in this case the leader will choose a strategy which minimizes the worst he could obtain amongst all the best responses of the followers. This paper continues the research initiated in [17] where existence results for these problems have been obtained.

Resonant tunneling via stress-induced valence-band mixings in GaAs-(Ga,Al)As asymmetrical double quantum wells

International audienceOptical band-to-band transition energies and oscillator strengths are calculated in the envelope-function approximation, for GaAs-(Ga,Al)As asymmetrically coupled double quantum wells, subjected to externally applied in-plane uniaxial stress. It is shown that the spatial probability distribution of holes should be strongly affected by this perturbation, due to the superimposition of stress-induced mixings of valence states, together with tunneling effects across the thin intermediate barrier. As a consequence, the electron and hole envelope functions overlap, and thus the probability of a given subband-to-subband transition is expected to be modified. Since simple, parity-related selection rules are no longer in effect in such structures, due to the lack of symmetry, the optical transitions are expected to shift, appear, or disappear, depending on the initial degree of coupling between the quantum wells, and on the magnitude of the stress

Uniaxial-stress investigation of asymmetrical GaAs-(Ga,Al)As double quantum wells.

International audienceWe present low-temperature-reflectance experiments, performed on GaAs-Ga1−xAlxAs asymmetrical double quantum wells, under in-plane uniaxial stress. The results, when compared to what is obtained from single quantum wells, exhibit some peculiar behaviors, which are typical effects of the asymmetry of the structures. A careful examination of these results is proposed in light of theoretical predictions about subband-to-subband transition energies and oscillator strengths. Our conclusion is that asymmetry makes it possible to obtain novel couplings between excitonic states, which cannot be accounted for without an accurate theoretical treatment of the Coulombic interaction, including intersubband mixings of valence wave functions

Reflectance study of inter-well couplings in GaAs-(Ga,Al)As double quantum wells.

International audienceReflectance spectra are studied for both symmetric and asymmetric double-quantum-well structures separated by intermediate barriers with various thicknesses. It is shown that the interwell couplings versus the tunneling of the carriers across the barrier has a significant influence on the optical transition properties. Quantitative analyses are presented, which help to identify a number of transitions involving excited states, in asymmetric double wells. A theoretical model agrees with experimental results in several aspects: the interband transition energies, the transition probabilities, and the broadening of the reflectance structures. The effects of interfacial roughness and alloy disorder, in both symmetric and asymmetric systems, are carefully analyzed, which provides a new insight into the broadening of the optical transitions, due to interfacial morphology

Effects of Music Therapy on Labour Pain and Anxiety in Taiwanese First-time Mothers

AIMS: The purpose of the study was to investigate the effects of music on pain reaction and anxiety during labour. BACKGROUND: Music therapy has been used on clinical medicine. Only few scientific studies validate the value on labour women. DESIGN: Randomised controlled trial. METHODS: Sixty primiparas expected to have a normal spontaneous delivery were randomly assigned to either the experimental group (n = 30) or the control group (n = 30). The experimental group received routine care and music therapy, whereas the control group received routine care only. A self-report visual analogue scale for pain and a nurse-rated present behavioural intensity were used to measure labour pain. Anxiety was measured with a visual analogue scale for anxiety and finger temperature. Pain and anxiety between groups were compared during the latent phase (2-4 cm cervical dilation) and active phase (5-7 cm) separately. RESULTS: Our results revealed that compared with the control group, the experimental group had significantly lower pain, anxiety and a higher finger temperature during the latent phase of labour. However, no significant differences were found between the two groups on all outcome measures during the active phase. CONCLUSIONS: This study provides evidence for the use of music as an empirically based intervention of women for labour pain and anxiety during the latent phase of labour. RELEVANCE TO CLINICAL PRACTICE: The findings support that music listening is an acceptable and non-medical coping strategy for labouring women. Especially, apply in reducing the pain and anxiety for women who are at the early phase of labour