Characterization Theorems for Differential Operators on White Noise Spaces

We characterize through their action on stochastic exponentials the class of white noise operators which are derivations with respect to both the point-wise and Wick products. We define the class of second order differential operators and second order Wick differential operators and we characterize the white noise operators belonging to both classes. We find that the intersection of these two classes, in the first and second order cases, is identified by a skewness condition on the coefficients of the differential operator. Our technique relies on simple algebraic properties of commutators and on the Gaussian structure of our white noise space. Our approach is suitable to study differential operators of any orde

A quantum approach to Laplace operators

In this paper, a theory of stochastic processes generated by quantum extensions of Laplacians is developed. Representations of the associated heat semigroups are discussed by means of suitable time shifts. In particular the quantum Brownian motion associated to the Levy-Laplacian is obtained as the usual Volterra-Gross Laplacian using the Cesaro Hilbert space as initial space of our process as well as multiplicity space of the associated white noise

Quantum Laplacians on generalized operators on Boson Fock Space

By adapting the white noise theory, the quantum analogues of the (classical) Gross Laplacian and L´evy Laplacian, so called the quantum Gross Laplacian and quantum L´evy Laplacian, respectively, are introduced as the Laplacians acting on the spaces of generalized operators. Then the integral representations of the quantum Laplacians in terms of quantum white noise derivatives are studied. Correspondences of the classical Laplacians and quantum Laplacians are studied. The solutions of heat equations associated with the quantum Laplacians are obtained from a normal-ordered white noise differential equation

Localization and composition of seed oils of Crithmum maritimum L. (Apiaceae)

The use of some halophytes for rehabilitation of salt affected area has been reported. Crithmum maritimum L. halophyte and apiaceae can tolerate high levels of salt. Their seed was endospermic and had a suitable size for oil extraction. The aim of this report is to localize the lipids in the seed and determine their oils composition. The results showed that the lipids were accumulated in endosperm tissue as oil globoids. The percentage of oils was 44.4% dry weight basis. The C. maritimum L. seed oil was rich with oleic acid (78.6%), low level of palmitic acid (4.8%) and non negligible amount of linoleic acid (15.4%). This composition is similar to olive oil and canola oil. These results confirmed the good quality of C. maritimum L. seed oils.Keys word: Halophytes; Crithmum maritimum L.; seed oils

Polyamide from lactams by reactive rotational molding via anionic ring-opening polymerization: Optimization of processing parameters

A reactive rotational molding (RRM) process was developed to obtain a PA6 by activated anionic ring-opening polymerization of epsilon-caprolactam (APA6). Sodium caprolactamate (C10) and caprolactam magnesium bromide (C1) were employed as catalysts, and difunctional hexamethylene-1,6-dicarbamoylcaprolactam (C20) was used as an activator. The kinetics of the anionic polymerization of !-caprolactam into polyamide 6 was monitored through dynamic rheology and differential scanning calorimetry measurements. The effect of the processing parameters, such as the polymerization temperature, different catalyst/activator combinations and concentrations, on the kinetics of polymerization is discussed. A temperature of 150°C was demonstrated to be the most appropriate. It was also found that crystallization may occur during PA6 polymerization and that the combination C1/C20 was well suited as it permitted a suitable induction time. Isoviscosity curves were drawn in order to determine the available processing window for RRM. The properties of the obtained APA6 were compared with those of a conventionally rotomolded PA6. Results pointed at lower cycle times and increased tensile properties at weak deformation

Short-term forecasting of GDP using large monthly datasets: a pseudo real-time forecast evaluation exercise.

This paper evaluates different models for the short-term forecasting of real GDP growth in ten selected European countries and the euro area as a whole. Purely quarterly models are compared with models designed to exploit early releases of monthly indicators for the nowcast and forecast of quarterly GDP growth. Amongst the latter, we consider small bridge equations and forecast equations in which the bridging between monthly and quarterly data is achieved through a regression on factors extracted from large monthly datasets. The forecasting exercise is performed in a simulated real-time context, which takes account of publication lags in the individual series. In general, we find that models that exploit monthly information outperform models that use purely quarterly data and, amongst the former, factor models perform best.Bridge models ; Dynamic factor models ; real-time data flow.

Anatomy of the fruit of the halophyte Crithmum maritimum L. with emphasis on the endosperm structure and histochemistry

The halophytes are plants that can survive and reproduce under high salinity. They show high potentiality as new crops plant for biosaline agriculture. Crithmum maritimum L. (Apiaceae) is one of the promising halophytes. In this paper, the endosperm structure of the fruit of this oilseeds halophyte was investigated using scanning electrons microscopy (SEM), light microscopy (LM) and fluorescence microscopy (FM). The fruit was composed of a spongy outer coat, a secretory envelope, a thin endocarp reduced to a unicellular layer delimiting the endosperm and an embryo. The endosperm cell appeared limited by thick cell wall and filled with numerous reserve globoids. The histochemical test showed that the cell wall of the endosperm was rich of carbohydrates as revealed by PAS (periodic acid-schiffs). Within the endosperm cells, there were mainly lipid bodies and protein bodies. The starch grains were less abundant. The protein bodies enclose crystal globoids. The x-ray microanalysis revealed that the reserve globoids accumulated mostly Mg, K, Ca, S and P. Taken together, these results highlight the structural features, the biochemical composition and confirm the nutritional quality of C. maritimum L. fruit.Keys words: C. maritimum L., crystal globoids, the endosperm cells, histochemical test, protein bodies, x-ray microanalysis