In this paper, we investigate the following quasilinear and singular problem : { −∆pu = λ uδ + u q in Ω u|∂Ω = 0 , u > 0 in Ω (1) where Ω is an open bounded domain with smooth boundary, 1 < p, p− 1 < q and λ, δ > 0. We first prove that there exist weak solutions for λ > 0 small in W 1,p 0 (Ω)∩C(Ω̄) if and only if δ < 2+ 1 p−1 . Investigating the radial symmetric case (Ω = BR(0)), we prove by a s...

The present study examined the organization of complex familiar activities, known as "scripts" (e.g., "going fishing"). We assessed whether events in a script are processed in a linear-sequential manner or clustered-hierarchical manner, and we evaluated the neural basis for this processing capacity. Converging evidence was obtained from functional neuroimaging in healthy young adults and from b...

For the real-time computation of closed-loop controls, guidance methods have been recently developed by the authors which are based on the theory of neighboring extremals and/or the multiple shooting algorithm. Because of their close relationship, these methods have a comparable domain of controllability, i.e., the set of all deviations from the nominal optimal trajectory which can be compensat...

This article deals with the problem of computing energy-minimal trajectories between the invariant manifolds in the neighborhood of the equilibrium point L1 of the restricted 3-body problem. Initializing a simple shooting method with solutions of the corresponding linear optimal control problem, we numerically compute energy-minimal extremals from the Pontryagin’s Maximum principle, whose optim...

Uniqueness of and numerical techniques for the inverse Sturm-Liouville problem with eigenparameter dependent boundary conditions will be discussed. We will use a Gel’fand-Levitan technique to show that the potential q in u00 þ qu 1⁄4 u, 0 < x < 1 uð0Þ 1⁄4 0, ða þ bÞuð1Þ 1⁄4 ðc þ d Þu0ð1Þ can be uniquely determined using spectral data. In the presence of finite spectral data, q can be reconstruc...

We discuss the indirect multiple shooting approach for the solution of PDE-based parabolic optimal control problems with control constraints. The method is formulated within an abstract function space setting and uses a space-time Galerkin finite element discretization. The emphasis is on the embedding of indirect multiple shooting into the optimal control framework as well as the detailed desc...

Traditional shooting range simulators involve large investment in real estate, and other infrastructural resources. This paper describes a novel application of projector-camera systems to create a virtual shooting range. Projector-based display systems offer an attractive combination of dense pixels over large regions. When coupled with a camera, the feedback system enables the display to be ad...