On the top coefficients of Kazhdan-Lusztig polynomials

Kazhdan and Lusztig in 1979 defined, for any Coxeter group W, a family of polynomial that is know as Kazhdan-Lusztig polynomials. These polynomials are indexed by pairs of elements of W and they have fundamental importance in several areas of mathematics as representation theory, geometry, combinatorics and topology of Schubert varieties. In this paper we want to show the combinatorial connection between special matchings and the top coefficient of Kazhdan-Lusztig polynomial. In particular we study a Conjecture, due to Brenti, in different Coxeter groups and pair of elements

Effet des variations d'énergie lumineuse associées à l'agitation verticale sur le bilan photosynthétique de cultures intensives d'algues en bassin

Une série d'expériences a été réalisée pour évaluer les effets de l'agitation sur le bilan photosynthétique de cultures d'algues en masse en bassins extérieurs. La méthode utilisée compare la production d'échantillons marqués au C14 disposés (1) selon un profil vertical classique, (2) sur un système rotatif faisant transiter un flacon entre la surface et le tond du bassin. Des mesures ont été effectuées périodiquement en milieu de journée sur un cycle annuel, et ont été complétées par 8 incubations réalisées entre le lever et le coucher du soleil pour un jour donné. Dans toutes les expériences réalisées durant la période estivale, la photosynthèse est supérieure dans le flacon mobile. Les effets des variations lumineuses (par le biais des mouvements de l'eau) sur te bilan photosynthétique de la colonne d'eau sont particulièrement notables au lever et au coucher du soleil; ce bilan peut être jusqu'à 2.5 fois plus important pour une colonne d'eau en mouvement. Le calcul d'un bilan journalier par extrapolation des profils de photosynthèse instantanés permet d'estimer le gain de production obtenu par agitation du milieu. Par contre pendant la période hivernale, la photosynthèse est supérieure dans le flacon immobile. Ces résultats ont des implications évidentes sur le monitoring de cultures d'algues en masse en bassins extérieurs.Experiments were carried out to define the effect of a particular mixing system (circular round a horizontal axis) upon the primary productivity of high-rate alga cultures. We know that mixing prevent algal cell sedimentation, gaseous and nutritional gradients, and variations in algae light reception. So, we wanted to quantity the effect of mixing on algal productivity with regard to flashing light (positive effect in comparison with continuous light).We used water from waste stabilization ponds (secondary pond output), with the native algae population dominated by Euglena and Chlorella (in Aveyron, South of France). The method used compares algal production of a water column with 14C-labelled samples i) in ten flasks placed along a classical vertical profile, ii) in a rotating system with a flask moving between the top and the bottom of the pond (0.5 m). The production is here considered as the mean of a mixed vertical profile. At the same time, physico-chemical and biological parameters were recorded (high load for N and P).Experiments were made periodically in the mid-afternoon over one year, and were completed by 8 incubations made between sunrise and sunset for on day (in August 1989). The aim was to evaluate the mixing affect with various environmental conditions. Physico-chemical parameters vary greatly over a day, and higher production values are measured in the mid-afternoon. Production observed for the stationary profile fitted the Steele model, and showed active photosynthetic from sunrise until sunset, with inhibition at high light intensities; maximal photosynthesis rates were measured between 4.00 and 5.00 PM.Results are compared to moving flask values : in all the summer experiments photosynthesis was higher in the moving flask. Light variation effects (through water movements) on the water column photosynthetic budget are particularly notable at sunrise and sunset bouts : this budget may be over 2,5 times that of homogeneous nonturbulent water. During winter however, photosynthesis is higher for the stationary profile. We compared production recorded with the two systems, and calculated the mathematical relationship between the two systems over one day (exponential) and over the year (linear relationship).By extrapolation of the instant photosynthesis profile to a 24-hour period, we can evaluate the production gain with culture mixing. We calculated the net production for various days over the year; around the end of April, the mixed system became more productive than the stationary one.Considering our results in environmental conditions, it is obvious that they are not representative of all mixing systems, particularly the techniques in which algae cell position shift continually with respect to the photic zone : the positive effect of mixing in our ponds may be linked to the flashing light effect. In the literature, we can see that photosynthetic activity increases with flash time duration. Our production figures for various hours along the day (or various flash durations) are in agreement with these results.During low photosynthetic activity periods, the flashing light effect can not act since light is available at all depths of pond. The most important factor acting, in our experiments, seems to be light, since the two systems are in similar conditions.These results have clear implications for monitoring intensive outdoor algal cultures

Design and validation of an innovative soft-sensor for pharmaceuticals freeze-drying monitoring

The paper is focused on the development of a Kalman filter type observer for the monitoring of the primary drying phase of the freeze-drying of pharmaceutical products in vials. The proposed soft-sensor is able to estimate the evolution of temperature of the product, the duration of the primary drying phase, the value of the overall heat transfer coefficient between the heating shelf and the product, as well as the mass transfer resistance of the dried cake to vapor flow. Accurate results are obtained for various types of products, characterized by a different dependence of the mass transfer resistance on the dried cake thickness. Theoretical results are confirmed by experimental tests carried out in a pilot-scale freeze-dryer. Finally, the strength and the weakness of the proposed observer are pointed out

CONSIDERATIONS ON THE DEVELOPMENT OF MEDIATION IN ROMANIA

Taking into consideration that our society faces a continuous development, it would be good that the principles and the methodes of managing the society would develope, because these seems to be overwhelmed.Also, regarding the mediation, it takes time to implement it into the society’s structure, in the social, economical and political sistem