The degree of shape preserving weighted polynomial approximation

We analyze the degree of shape preserving weighted polynomial approximation for exponential weights on the whole real line. In particular, we establish a Jackson type estimate.     

Résolution du problème de Dirichlet pour lʼéquation du Jacobien prescrit via lʼéquation de Monge–Ampère

We give an alternative proof, based on the Monge–Ampère equation, of Dacorogna and Moser?s result (Dacorogna and Moser, 1990) [4] on the solvability with optimal regularity of the Dirichlet problem for the prescribed Jacobian equation.     

Structural properties of optimal schedules with preemption

Scheduling problems with preemption are considered, where each operation can be interrupted and resumed later without any penalty. We investigate some basic properties of their optimal solutions. When does an optimal schedule exist (provided that there are feasible schedules)? When does it have a finite/polynomial number of interruptions? Do they occur at integral/rational points only? These theoretical questions are also of practical interest, since structural properties can be used to reduce the search space in a practical scheduling application. In this paper we answer some of these basic questions for a rather general scheduling model (including, as the special cases, the classicalmodels such as parallelmachine scheduling, shop scheduling, and resource constrained project scheduling) and for a large variety of the objective functions including nearly all known. For some two special cases of objective functions (including, however, all classical ones), we prove the existence of an optimal solution with a special “rational structure.” An important consequence of this property is that the decision versions of these optimization scheduling problems belong to class NP.     

Congested traffic dynamics, weak flows and very degenerate elliptic equations

Starting from a model of traffic congestion, we introduce a minimal-flow-like variational problem whose solution is characterized by a very degenerate elliptic PDE. We precisely investigate the relations between these two problems, which can be done by considering some weak notion of flow for a related ODE. We also prove regularity results for the degenerate elliptic PDE, which enables us in some cases to apply the DiPerna–Lions theory.     

Quantitative, dynamic and noninvasive determination of skeletal muscle perfusion in mouse leg by NMR arterial spin-labeled imaging

Because mouse may relatively easily be genetically tailored to develop equivalent of human muscular diseases or to present controlled alterations of mechanisms involved in vasoregulation, it has become the prevalent species to explore such questions. However, the very small size of the animals represents a serious limitation when evaluating the functional consequences of these genetic manipulations. In this context, the recourse to arterial spin labeling (ASL) nuclear magnetic resonance (NMR) methods in which arterial water spins act as an endogenous and freely diffusible tracer of perfusion is tempting but challenging. This article shows that despite the small size of the animal, mouse muscle perfusion may be measured, at rest and in conditions of reactive hyperemia, using saturation inversion recovery sequence, a pulsed ASL variant, combined with NMR imaging. Baseline perfusion values in the mouse leg were 17+/-11 ml.min(-1).100 g(-1) (n=11) and were comparable to microsphere data from the literature. Under ischemia, leg perfusion was 1.2+/-9.3 ml.min(-1).100 g(-1) (n=11). The difference observed between basal and ischemic measurements was statistically different (P=.0001). The temporal pattern of hyperemia in mouse muscle was coherent with previously published measurements in humans and in rats. The mean peak perfusion was 62+/-24 ml.min(-1).100 g(-1) (n=6) occurring 48+/-27 s after the end of occlusion. In conclusion, this study demonstrated the ability of ASL combined to NMR imaging to quantify skeletal muscle perfusion in mice legs, both at rest and dynamically.     

Time reversal of flexural waves in a beam at audible frequency

There has been very limited work on the application of time reversal to the propagation of audible frequency waves in mechanical structures. The present work concentrates on the application of time reversal to the focusing of audible range, flexural waves in an infinite beam, and to the detection of local heterogeneity in such a beam. Practical applications of time reversal of flexural waves in structures include vibration energy focusing, detection of vibratory or acoustic sources, and detection of defects in mechanical structures. An analytical model of flexural wave propagation in the beam as well as sensing and emission using piezoelectric transducers is presented. Time reversal experiments are conducted and compared to the model results in either a homogeneous beam or a beam with point mass heterogeneities. In the various situations tested, it is shown that time reversal effectively compensates the spreading in time of the impulse due to the dispersive propagation of flexural waves. One interesting aspect of this property is the generation of large amplitude impulsive responses in the beam using remote actuators. Finally, the "Decomposition de l'Operateur de Retournement Temporel" approach is examined to detect and localize point mass scatterers in the beam.     

Etude par spectrometrie de photoelectrons de la structure electronique des ynals et des ynones conjugues

This study proposes an interpretation of the UV photoelectron spectrum of propynal mainly with semi-empirical calculations. The electronic structure of 16 other conjugated ynals and ynones has been studied by the same techniques, and the variations of the first ionization potential, associated with the exceptionally deep oxygen lone pair, may be interpreted in terms of polar effect and intramolecular interactions. The discussion about the set π_-, π_≡ that cannot be separated yields only some qualitative results.     

Unprecedented metal template effect on the coupling of dithiafulvene moieties

Coordination of two dithiafulvenyldiphenylphosphines on a Mo(CO)(4) fragment allows a carbon-carbon bond formation upon oxidation, leading to a novel type of metallacycle substituted by a redox active vinylogous tetrathiafulvalene.