Eucommia ulmoides, also called hardy rubber tree, is an economically important tree; however, the lack of its genome sequence restricts the fundamental biological research and applied studies of this plant species. Here, we present a high-quality assembly of its ∼1.2-Gb genome (scaffold N50 = 1.88 Mb) with at least 26 723 predicted genes for E. ulmoides, the first sequenced genome of the order Garryales, which was obtained using an integrated strategy combining Illumina sequencing, PacBio sequencing, and BioNano mapping. As a sister taxon to lamiids and campanulids, E. ulmoides underwent an ancient genome triplication shared by core eudicots but no further whole-genome duplication in the last ∼125 million years. E. ulmoides exhibits high expression levels and/or gene number expansion for multiple genes involved in stress responses and the biosynthesis of secondary metabolites, which may account for its considerable environmental adaptability. In contrast to the rubber tree (Hevea brasiliensis), which produces cis-polyisoprene, E. ulmoides has evolved to synthesize long-chain trans-polyisoprene via farnesyl diphosphate synthases (FPSs). Moreover, FPS and rubber elongation factor/small rubber particle protein gene families were expanded independently from the H. brasiliensis lineage. These results provide new insights into the biology of E. ulmoides and the origin of polyisoprene biosynthesis.
In this paper, we investigate a splitting algorithm for treating monotone operators. Strong convergence theorems are established in the framework of Hilbert spaces.
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