A proximal gradient method for control problems with non-smooth and non-convex control cost

Computational Optimization and Applications - We investigate the convergence of the proximal gradient method applied to control problems with non-smooth and non-convex control cost. Here, we focus...     

Réactions colorées de stéroĭdes

A number of colour reactions for the identification and determination of steroids are described.     

The Limiting Normal Cone to Pointwise Defined Sets in Lebesgue Spaces

We consider subsets of Lebesgue spaces which are defined by pointwise constraints. We provide formulas for corresponding variational objects (tangent and normal cones). Our main result shows that the limiting normal cone is always dense in the Clarke normal cone and contains the convex hull of the pointwise limiting normal cone. A crucial assumption for this result is that the underlying measure is non-atomic, and this is satisfied in many important applications (Lebesgue measure on subsets of \(\mathbb {R}^{d}\) or the surface measure on hypersurfaces in \(\mathbb {R}^{d}\)). Finally, we apply our findings to an optimization problem with complementarity constraints in Lebesgue spaces.     

Approximation of sparse controls in semilinear equations by piecewise linear functions

Semilinear elliptic optimal control problems involving the $L^1$ norm of the control in the objective are considered. A priori finite element error estimates for piecewise linear discretizations for the control and the state are proved. These are obtained by a new technique based on an appropriate discretization of the objective function. Numerical experiments confirm the convergence rates.     

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Coherent production ofρ − mesons in charged current antineutrino-neon interactions in BEBC

Coherent production ofρ ^? mesons in charged current antineutrino interactions on neon nuclei is studied in the BEBC bubble chamber exposed to the CERN SPS wide band beam. The cross section is measured to be (95±25)·10^?40 cm² per neon nucleus, averaged over the beam energy spectrum. The distributions of kinematical variables and the absolute value of the cross section are in agreement with theoretical predictions based on the CVC hypothesis and the vector meson dominance model.     

Evidence for higher twist effects in fast π− production by antineutrinos in neon

Evidence for a significant higher twist contribution to highz π^? production in antineutrino scattering is presented. In events withW>3 GeV andQ ²>1 GeV² in our data, it accounts for (51 ±8)% of all π^? withz above 0.5. It is consistent with thez?Q ² correlations of Berger's higher twist prediction. The data are inconclusive concerning the predictedy?z correlation andp _T dependence. Thez ?Q ² correlation is not adequately described by the Lund Monte-Carlo.