多项式微分系统的不变直线的不同斜率的最大个数

本文证明了公式β（ｎ）＝σ（ｎ－１）＋１其中α（ｎ－１）是ｎ－１次多项式微分系统的不为直线的最多条数，βｎ）是ｎ次多项式微分系统的不变直线的不同斜率的最大个数。这里假设所讨论的多项式系统只有限条不变直线。     

Strigolactone inhibition of shoot branching

A carotenoid-derived hormonal signal that inhibits shoot branching in plants has long escaped identification. Strigolactones are compounds thought to be derived from carotenoids and are known to trigger the germination of parasitic plant seeds and stimulate symbiotic fungi. Here we present evidence that carotenoid cleavage dioxygenase 8 shoot branching mutants of pea are strigolactone deficient and that strigolactone application restores the wild-type branching phenotype to ccd8 mutants. Moreover, we show that other branching mutants previously characterized as lacking a response to the branching inhibition signal also lack strigolactone response, and are not deficient in strigolactones. These responses are conserved in Arabidopsis. In agreement with the expected properties of the hormonal signal, exogenous strigolactone can be transported in shoots and act at low concentrations. We suggest that endogenous strigolactones or related compounds inhibit shoot branching in plants. Furthermore, ccd8 mutants demonstrate the diverse effects of strigolactones in shoot branching, mycorrhizal symbiosis and parasitic weed interaction.