Melon Fusarium wilt disease caused by the soil-borne pathogen Fusarium oxysporum f. sp. melonis (Fom) is one of the most devastating melon diseases worldwide. Recently, the Fom-1 gene responsible for resistance against Fom races 0 and 2 was cloned. In this study we amplified, cloned and sequenced full genomic DNA and cDNA of Fom-1 from several melon resistant and susceptible accessions using three pairs of primers designed within this gene. Sequence analyses showed that this gene contains four exons interrupted by three introns. The comparative sequence analysis of the cloned cDNA amplicons from resistant and susceptible genotypes revealed eight nucleotide substitutions, within Fom-1 coding regions, among which four were non-synonymous. RT-PCR revealed that the Fom-1 expression is induced by Fom race 2 inoculation. The Fom-1 predicted protein (FOM-1) exhibits a tripartite modular structure composed of an N-terminal TIR domain, a central NB-ARC domain and a C-terminal LRR domain. FOM-1 from resistant melon accessions share four amino acid differences relative to the FOM-1 protein in susceptible ones. Two amino acid substitutions N56K and R103H were located at the FOM-1 TIR domain and the substitution E385K in the NB-ARC domain. Based on single nucleotide polymorphisms within the coding region of the Fom-1 locus, we have generated two CAPS markers, Fom-1R and Fom-1S. Results from screening various melon accessions clearly demonstrated the usefulness of both functional CAPS markers in the marker-assisted selection for melon breeding programs.
We study the solution of one-dimensional generalized backward stochastic differential
equation driven by Teugels martingales and an independent Brownian motion. We prove existence and uniqueness of the solution when the coefficient verifies some conditions of Lipschitz. If the coefficient is left continuous, increasing,
and bounded, we prove the existence of a solution.
This paper proves the existence and uniqueness of a solution to reflected backward stochastic differential equations with a lower obstacle, which is assumed to be right upper-semicontinuous. The result is established where the coefficient is stochastic Lipschitz by using some tools from the general theory of processes such as Mertens decomposition of optional strong supermartingales and other tools from optimal stopping theory.
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