Mehler Integral Transforms Associated with Jacobi Functions with Respect to the Dual Variable

AbstractWe prove a Mehler representation for Jacobi functions ϕλ(α,β)(t) with respect to the dual variable λ. We exploit this representation to define a pair of dual integral transforms χα,βand its transposedtχα,β. We define two second order difference operatorsPα,βandQsuch that ϕλ(α,β)(t) is an eigenfunction ofPα,βwith respect to the dual variable λ, and χα,βandtχα,βare permutation operators betweenPα,βandQ. Next we give some spaces of functions on which χα,βandtχα,βare isomorphisms and we establish inversion formulas for these transforms

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

Effects of crop sequences on soil population dynamics of Monosporascus cannonballus ascopsores and Monosporascus root rot and vine decline incidence

[EN] Crop sequences effect on the soil population dynamics of Monosporascus cannonballus ascospores and the incidence of Monosporascus root rot and vine decline (MRRVD), was investigated in a field in which three different cucurbit crops: melon, watermelon, and watermelon grafted onto Cucurbita rootstock, and tomato, were grown during two consecutive growing seasons. Cultivation of melon or watermelon crops in the first growing season resulted in an increase of soil ascopore densities. But, on the contrary, the soil ascospore densities in the second growing season were lower when grafted watermelon or tomatos were cultivated in the first growing season. In the second growing season, MRRVD incidence for each cucurbit crop was significantly different depending on the previous crop, being in general higher when melon or watermelon were the previous crops, slightly lower when the previous crop was grafted watermelon and the lowest when the previous crop was tomato. Disease incidence corresponded with the percentage of isolation of M. cannonballus from the roots, being always significantly lower when the previous crop was tomato. These results demonstrate the potential of crop rotation as a management strategy to reduce infection and reproduction of M. cannonballus, ascospore densities in soil and disease incidence in cucurbits.Ben Salem, I.; M'hamdi, M.; Armengol Fortí, J.; Boughalleb-Mhamdi, N. (2015). Effects of crop sequences on soil population dynamics of Monosporascus cannonballus ascopsores and Monosporascus root rot and vine decline incidence. International Journal of Current Microbiology and Applied Sciences (Online). 4(9):482-500. http://hdl.handle.net/10251/89413S4825004

Fungitoxicity of some fungicides against to pathogens responsible of olive trees decline in the Chebika’s area in Tunisia

The incidence of the disease seems very important on young trees and tends to bemoderate with the aging of the tree. In fact, olive trees have a shallow root system and arestill vulnerable to pathogens especially the irrigated varieties. Chemical and biological control against Fusarium solani, Fusarium oxysporum, Rhizoctonia solani and Verticillium dahliae have revealed that the application in vitro of Prodazim and of Methyl-thiophanatehave showed a very good efficacy up to 100%. Ridomil and Tachigaren have indicated aregular efficiency, while the two bio-fungicides Fungstop and the compost juice havedemonstrated a low efficiency. The two bio-control agents Trichoderma harzianum and Gliocladium virens have showed a relatively high effectiveness in vitro. In vivo, obtainedresults have revealed that the nature of the product, the doses applied and the condition ofthe olive trees are highly correlated factors. The treatment doesn’t appear to have apositive effect on the beginning of stage 1 and on plots presented a good structured soil.Going beyond this stage, whatever the product and the doses used, the attack isirreversible

Development of a screening test for resistance of cucurbits and Cucurbita hybrid rootstocks to Monosporascus cannonballus

[EN] Screening test resistance of cucurbit plants to Monosporascus cannonballus, responsible of Monosporascus root rot and vine decline was developed. Inocula of two isolates were grown in wheat seeds medium and served for pathogenicity test on watermelon (cv. Charleston gray) using 5 inoculum densities (50, 100, 150, 200 and 250 g of infected wheat seeds/kg of peat). Disease severity was evaluated based on root disease index (RDI), plant height (PH), shoot and root fresh and dry weights (SFW, RFW, SDW, and RDW). Significant differences in RDI records were noted among the 5 inoculum densities tested as compared to the non-inoculated control, and they were negatively correlated with PH, TDW and RDW. Pathogenicity tests on Armenian cucumber (Fakous), muskmelon (cvs. Flamengo and Dziria), watermelon (cv. Charleston gray), and two Cucurbita maxima x C. moschata rootstocks (cvs. Strongtoza and Emphasis), were conducted at the inoculum density of 200 g of inoculum/kg of peat. Characteristic symptoms of the disease were reproduced and the range of responses to M. cannonballus corresponded to those reported by previous research. Watermelon was susceptible to the pathogen, while Cucurbita hybrid rootstocks were the most tolerant. Evaluation of the resistance to M. cannonballus of eight Cucurbita hybrid rootstocks was conducted in a greenhouse experiment with 200 g of inoculum/kg of peat. All rootstocks evaluated seemed to response similarly for the RDI. However, no significant difference was noted for the other evaluated parameters.[FR] Un test de criblage de la résistance des plants de cucurbitacées à Monosporascus cannonballus, responsable du dépérissement a été développé. Deux isolats ont été cultivés sur des grains de blé et ont servi pour le test de la pathogénie sur la pastèque (cv. Charleston gray) selon 5 densités d¿inoculum (50, 100, 150, 200 et 250 g de grains de blé infectés/kg de tourbe). La sévérité de la maladie a été évaluée selon un indice de maladie racinaire (RDI), la hauteur de la plante (HP), les poids frais (SFW et RFW) et secs (SDW et RDW) des parties aérienne et racinaire. Une différence significative a été notée selon l¿indice RDI entre les 5 densités d'inoculum par rapport au témoin, et une corrélation négative avec la réduction des paramètres HP, SDW et RDW a été obtenue. Les tests de pathogénie sur trois espèces de cucurbitacées: concombre arménien (Fakous), melon (cvs. Flamengo et Dziria), pastèque (cv. Charleston gris) et deux porte-greffes Cucurbita maxima x C. moschata (cvs. Strongtoza et Emphasis), ont été effectuées à la densité de 200 g d'inoculum/kg de tourbe. Les symptômes caractéristiques de la maladie ont été reproduits et la gamme des réponses à M. cannonballus correspondaient à ceux rapportés dans la littérature. La pastèque s¿est montrée sensible à cet agent pathogène, tandis que les porte-greffes hybrides du genre Cucurbita étaient les plus tolérants. Un autre essai de la résistance à M. cannonballus a été réalisé sur huit porte-greffes hybrides du genre Cucurbita en culture sous serre avec 200 g d¿inoculum/kg de tourbe. Tous les porte-greffes paraissent réagir de la même façon concernant l¿indice RDI et des différences non significatives pour les autres paramètres évalués ont été notées.Ben Salem, I.; Armengol Fortí, J.; Berbegal Martinez, M.; Boughalleb-Mhamdi, N. (2015). Development of a screening test for resistance of cucurbits and Cucurbita hybrid rootstocks to Monosporascus cannonballus. Tunisian Journal of Plant Protection. 10(1):23-33. http://hdl.handle.net/10251/101851S233310

Quantitative Trait Locus (QTL) involved in the resistance of barley (Hordeum vulgare L.) to the mildew under different water treatments, in semi-arid Mediterranean region

In the present study we evaluated the contribution of molecular marking to the breeding of barley ( Hordeum vulgare L.) for resistance to the mildew ( Erysiphe graminis sp L. hordei ) in semi-arid Mediterranean region. For this study a F8 progeny of 167 recombinants inbred lines (RILs) from two row barley was cultivated at the experimental station of the National Institute of Agronomic Research of Tunisia (INRAT), at Kef during the cropping season of 1999/2000. The trials, in a completely randomized design, were conducted under three water treatments: (1) irrigation at seedling emergence, (2) no water addition and (3) irrigation at first observation of water stress symptoms. Assessment of natural infection by mildew of was made every fifteen days starting from the day when water treatments were setup. Statistical analyses of data showed a high among progeny variation within the progeny of RILs regardless a water treatments; however plants of treatment 1 (irrigation since seedling emergence) appeared to be the most susceptible. A combination of data on susceptibility of barley to natural infection by mildew and data from the genetic map generated from the crossing of Er/Apm vs Tadmor (parents of the 167RILs) allowed the detection and localization of several QTLs on chromosomes 3(3H), 4(4H) and 7(5H) of the barley. The most significant QTLs were located on the longer arm of chromosome 4(4H); on a portion where several authors have located reaction genes of barley to E. graminis. Overall, our results showed that the detection of QTL responsible of the expression of the resistance to E. graminis seemed to be intimately linked to the initial cropping conditions (e.g. temperature and optimum humidity). Indeed, no primary QTL were observed for dry conditions treatment (no irrigation). Moreover, the available literature reports did not allow us to confirm the relative situations of the secondary QTLs found for these treatments. Thus, genes of resistance to E. graminis would express themselves only in conditions that are favorable for the development of the pathogen. Improving the resistance of barley to mildew infection requires therefore, by a good knowledge on the process that governs expression of these genes

Morphological and Biological Characterization of Monosporascus cannonballus isolates, responsible of watermelon decline in Kairouan's area

Watermelon grown in Kairouan's region is infected by vine decline disease caused by M. cannonballus. In vitro tests showed that this pathogen produces perithecia with a diameter of 495 μm releasing ascospores with a diameter of 44 μm. The mycelium is very fine, rarely visible in the media KOMADA and TANAKA. The colony of different isolates on substrate culture such as Malt, MS and S, appears very dense. On PDA, the grayish brown color characteristic of this ascomycete was observed. The perithecia production in vitro test for this fungus requires relatively long period of incubation (45 days). The effect of culture media showed that the PDA, MS and Malt are the best for the mycelia development of M. cannonballus. The most favorable culture media for fructification arein descending order MS, S, PDA, Malt. M. cannonballus isolates tested in this study showed an optimum temperature of mycelial growth and reproduction of 30°C. MT15 andMT12 isolates originated from Chebika (Kairouan government) showed a significantmycelial growth at all temperatures of incubation. MT7 and MT14 isolates from the sameregion were the most fertile. The results of pH effect on M. cannonballus developmenthave revealed that the maximum mycelial growth occurred at pH 6 for most of isolates andfor the fructification occurred at pH 4 and pH 8. For the osmotic pression with the addition of NaCl and KCl, the optimal development for majority of isolates is registeredat -0.5 MPa and -2 MPa, with a minimum at -4MPa. The inhibition of the fructification of the M. cannonballus isolates occurred beyond -2MPa

Screening of fungi implicated in the dieback of olive trees (Olea europea) in Chebika’s area

Several surveys were conducted during spring 2008 in Chebika’s area in Tunisia. Samples were collected from infected plants showed different types of symptoms and they have been the subject of mycological analysis. The morphological identification of fungal colonies isolated from roots, crown and stems of two olive varieties Koroneiki and Chemlali Sfax, revealed the presence of a fungi complex including Fusarium oxysporum, Fusarium solani, Rhizoctonia solani, Verticillium dahliae, Cladosporium fulvum, Alternaria solani, Alternaria tenuis, Bispora punctata. and Cylindrocarpon .sp; Although,those fungi Fusarium oxysporum, Fusarium solani, Rhizoctonia solani and Verticillium dahliae are ubiquitous and the predominant one. Pathogenicity results revealed that the fungi isolated from olive trees exhibited typical symptoms on Koroneiki variety incontrolled conditions