The Generalization of the Decomposition of Functions by Energy Operators

This work starts with the introduction of a family of differential energy operators. Energy operators ($Psi_R^+$, $Psi_R^-$) were defined together with a method to decompose the wave equation in a previous work. Here the energy operators are defined following the order of their derivatives ($Psi_k^+$, $Psi_k^-$, k = {0,1,2,..}). The main part of the work is to demonstrate that for any smooth real-valued function f in the Schwartz space ($S^-(R)$), the successive derivatives of the n-th power of f (n in Z and n not equal to 0) can be decomposed using only $Psi_k^+$ (Lemma) or with $Psi_k^+$, $Psi_k^-$ (k in Z) (Theorem) in a unique way (with more restrictive conditions). Some properties of the Kernel and the Image of the energy operators are given along with the development. Finally, the paper ends with the application to the energy function.Comment: The paper was accepted for publication at Acta Applicandae Mathematicae (15/05/2013) based on v3. v4 is very similar to v3 except that we modified slightly Definition 1 to make it more readable when showing the decomposition with the families of energy operator of the derivatives of the n-th power of

Active oxygen species production in tobacco cells elicited by cryptogein

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Active oxygen species production in tobacco cells elicited by cryptogein

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Lipoxygenase-mediated production of fatty acid hydroperoxides is a specific signature of the hypersensitive reaction in plants

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Apoplastic peroxidase generates superoxide anions in cells of cotton cotyledons undergoing the hypersensitive reaction to Xanthomonas campestris pv. malvacearum race 18

Cotton cotyledons displayed a hypersensitive reaction (HR) in the resistant cultivar Reba B50 after infiltration with the avirulent race 18 of #Xanthomonas campestris pv. #malvacearum (Xcm). Generation of active oxygen species during the HR was studied biochemically and cytochemically. O2(-) was detected in cotyledon disks by the cytochrome c reduction assay 3 h after inoculation. This activity was inhibited by superoxide dismutase (SOD) and by the peroxidase inhibitors salicylhydroxamic acid (SHAM) and KCN but not by the NADPH oxidase inhibitor diphenyleneiodonium chloride (DPI). Strong NADH oxidation activity also was found 3 h after inoculation in crude extracts or in apoplastic washing fluid and was dramatically decreased after treatment with SHAM or KCN. NADH oxidation was activated by 2,4-dichlorophenol and MnCl2, indicating the involvement of a peroxidase. Activity of cationic peroxidase isoforms (pI 9 to 9.5) constitutively expressed in cotyledons was found to be enhanced 3 h after inoculation in the resistant cultivar. Activities of apoplastic peroxidase(s) and H2O2 accumulation were observed cytochemically, 3 and 4 h post inoculation, respectively. When digitonin, a O2(-) elicitor, was infiltrated into cotyledons of resistant and susceptible cultivars, generation of O2(-) radicals was shown to be reduced by SOD and inhibited by SHAM and KCN as observed after infection, and also by DPI. Our results strongly suggest that cotton cotyledons contain two O2(-) generating systems and that cells undergoing the HR in response to an avirulent race of Xcm produce O2(-) through the activation of an apoplastic peroxidase. (Résumé d'auteur

Are elicitins cryptograms in plant-oomycete communications?

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