Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R

2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63Using a convolution structure on the real line associated with the Jacobi-Dunkl differential-difference operator Λα,β given by: Λα,βf(x) = f'(x) + ((2α + 1) coth x + (2β + 1) tanh x) { ( f(x) − f(−x) ) / 2 }, α ≥ β ≥ −1/2 , we define mean-periodic functions associated with Λα,β. We characterize these functions as an expansion series intervening appropriate elementary functions expressed in terms of the derivatives of the eigenfunction of Λα,β. Next, we deal with the Pompeiu type problem and convolution equations for this operator

Contribution to the evaluation of the biomass of medicinal and aromatic plants in Mo-rocco: Case of Globularia alypum

Morocco is distinguished by the richness of its flora, including medicinal and aromatic plants (MAPs) which play an important role, particularly in rural populations. Due to pressures often associated with overexploitation, monitoring of MAPs is essential to ensure their sustainability. This study looked to explore the status of Globularia alypum in the Amsittene site of biological and ecological interest (SBEI) in Morocco. A destructive technique was adopted to quantify biomass and productivity of G. alypum at six sites with different ecological characteristics in the Amsisttene SBEI. Linear regression was used to model G. alypum biomass as a function of the normalized difference vegetation index (NDVI). Tree cover had the greatest influence on G. alypum dynamics, showing a significant effect on shrub height, leaf productivity, and total productivity, as did the cutting method, with the highest biomass estimated based on pair matching of similar individuals. NDVI was found to be an adequate indicator of G. alypum biomass, given their high correlation (0.84) with the selected model having an R2 of 0.7. The yield of extracted essential oils ranged from 3.19 to 113.43 L, from which 10 chemical compounds were identified, with ethylvanillin being the most prominent

Downy Mildew of Sunflowers in Tunisia and evaluation of four fungicides

Plasmopara halstedii, the downy mildew pathogen of sunflower (Helianthus annuus L.) causes significant economic losses world-wide, mostly through soilborne systemic infection of seedlings. Natural infection of sunflower with P. halstedii was monitored in sunflower fields cultivated in many regions of Beja, during a survey in the spring of 2010. P. halstedii were obtained from diseased sunflowers seeds in 2010 and characterized by virulence and by reaction to four fungicides: Ridomil MZ 58, Ridomil Gold 48%, Aliette 80% and Triziman 80%. These fungicides have significantly reduced the colony growth of the fungi compared to the control. The significant reduction of mycelia growth were obtained with Ridomil M, Triziman 80% and Aliette 80% with acompletely inhibition

Preservation of endangered Tunisian grapevine cultivars using embryogenic cultures

The preservation of embryogenic lines derived from several endangered local grapevine cultivars was studied. Embryogenic calluses were obtained from immature anthers of eight cultivars, sampled on both fruity-cuttings and field grown vines. Anthers at the 'separated flower' stage, derived from fruity-cuttings, resulted in an increased induction of somatic embryogenesis, compared to those derived from the The preservation of embryogenic lines derived from several endangered local grapevine cultivars was studied. Embryogenic calluses were obtained from immature anthers of eight cultivars, sampled on both fruity-cuttings and field grown vines. Anthers at the 'separated flower' stage, derived from fruity-cuttings, resulted in an increased induction of somatic embryogenesis, compared to those derived from the 15.6% and 34.8% in 'Kahli Kerkennah' and 'Muscat Raf-raf' cultivars, respectively. Although, morphological diversifications of pro-embryogenic calluses (several necrosis and spontaneous maturation) were observed on the induction mediumafter 5 subcultures. The reduction of 2,4-D and TDZ levels to 4.52 \u3bcM and 2.89 \u3bcM respectively, induced granular and yellowish embryogenic material. Thus, Ch\ue9e and Pool (1987) (CP) enriched with 4.52 \u3bcM of 2,4-D and 2.89 \u3bcM of TDZ revealed to be the most appropriate for long-term maintenance. In fact, all the cultivars presented high and regular embryo maturation rates after 12, 24, 36 and 48 months of cultivation on this medium, under light conditions. After 4 years, they still exhibit high germination and regeneration abilities. Germination of somatic embryos was achieved on Murashige and Skoog (1962) basal-medium, with rates ranging from 69% to 96%. Only 5% of somatic embryos were concerned by morphological variations. The regenerated plantlets presented a normal phenotype under controlled greenhouse conditions, compared to mother plants

An Investigation on the Morphological and Mineralogical Characteristics of Posidonius Floor Fractured Lunar Impact Crater Using Lunar Remote Sensing Data

Lunar floor‐fractured craters (FFCs) are a distinguished type of crater found on the surface of the Moon with radial, concentric, and/or polygonal fractures. In the present study, we selected the Posidonius FCC to explore the mineralogy, morphology and tectonic characteristics using remote sensing datasets. The Posidonius crater is vested with a wide moat of lava separating the crater rim inner wall terraces from the fractured central floor. Lunar Reconnaissance Orbiter’s (LRO) images and Digital Elevation Model (DEM) data were used to map the tectonics and morphology of the present study. The Moon Mineralogy Mapper (M3) data of Chandrayaan‐1 were used to inves-tigate the mineralogy of the region through specified techniques such as integrated band depth, band composite and spectral characterization. The detailed mineralogical analysis indicates the nor-itic‐rich materials in one massif among four central peak rings and confirm intrusion (mafic pluton). Spectral analysis from the fresh crater of the Posidonius moat mare unit indicates clinopyroxene pigeonite in nature. Integrated studies of the mineralogy, morphology and tectonics revealed that the study region belongs to the Class‐III category of FFCs. The lithospheric loading by adjacent volcanic load (Serenitatis basin) generates a stress state and distribution of the fracture system

Real time noise and wavelength correlations in octave-spanning supercontinuum generation

We use dispersive Fourier transformation to measure shot-to-shot spectral instabilities in femtosecond supercontinuum generation. We study both the onset phase of supercontinuum generation with distinct dispersive wave generation, as well as a highly-unstable supercontinuum regime spanning an octave in bandwidth. Wavelength correlation maps allow interactions between separated spectral components to be identified, even when such interactions are not apparent in shot-to-shot or average measurements. Experimental results are interpreted using numerical simulations. Our results show the clear advantages of dispersive Fourier transformation for studying spectral noise during supercontinuum generation.Comment: 14 pages, 5 figure