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In Section 2 the results of Section 1 are used to prove that all representations of finite flag length of a vector group, realized in a vector bundle over a submanifold of the dual, act by endomorphisms of the bundle.
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(2) We used a recombinant inbred line (RIL) from an interspecific cross between S. bicolor and S. propinquum (BTxSP), the widest cross that can be made with S. bicolor using conventional techniques, containing 141 loci on 10 linkage groups collectively spanning 773.1 cM to map the confidence intervals for base-flag length, flowering time, nodes and total plant height [ 29] for 2010 and 2011 data.
Flag leaf length was measured as the length of leaf-bearing primary panicle from leaf base to the tip.
In addition, a long genome region covering ~1.6 Mb on chromosome 11 was identified, which may be critical for rice leaf architecture because of a high association with flag leaf length and the ratio of flag leaf length and width.
A black ribbon needs to be placed at the top of the flag; the length of the ribbon should be equal to the length of the flag.
Maximum number of novel QTLs were found for flag leaf length (10) followed by 1000-grain weight, spikelet setting density (6 each), plant height (5), panicle length (4), flag leaf width, spikelets per panicle, grain yield per plant (3 each), filled grains per panicle (2) and panicles per plant, per cent sterility (1 each).
A flag's length (also called the fly) usually exceeds its width (hoist).
Likewise, the population averages of flag leaf length (FLL) and flag leaf width (FLW) were only slightly reduced.
The flag leaf length (FLL, cm) and flag leaf width (FLW, cm) were measured on three tillers.
The best five BC2F3 plants showing the maximum phenotypic similarity with the RP were used for measuring plant height, flag leaf length, flag leaf width, tiller number and number of grain per panicle.
Four QTLs were identified for flag leaf length under SF on chromosomes 4, 5, 6, and 9 (Table 3, Fig. 1).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com