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This book presents comprehensive information on genetics, genomics and breeding in Brassica oleracea, an agriculturally important species that includes popular vegetable crops such as cabbage, cauliflower, broccoli, Brussels sprouts, kale, collard greens, savoy, kohlrabi, and gai lan. The content spans whole genome sequencing, assembly and gene annotation for this global vegetable species, along with molecular mapping and cloning of genes, physical genome mapping and analyses of the structure and composition of centromeres in the B. oleracea genome. The book also elaborates on asymmetrical genome evolution and transposable elements in the B. oleracea describes gene family differentiation in comparison to other Brassica species and structural and functional genomic resources and data bases developed for B. oleracea. Useful discussions on the impact of genome sequencing on genetic improvement in the species are also included.
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We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. (i) A typical hypercyclic operator is not topologically mixing, has no eigen-values and admits no non-trivial invariant measure, but is densely distri-butionally chaotic. (ii) A typical upper-triangular operator with coefficients of modulus 1 on the diagonal is ergodic in the Gaussian sense, whereas a typical operator of the form “diagonal with coefficients of modulus 1 on the diagonal plus backward unilateral weighted shift” is ergodic but has only count...
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