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。     

Genome-wide association study of quantitative resistance to southern leaf blight in the maize nested association mapping population

Nested association mapping (NAM) offers power to resolve complex, quantitative traits to their causal loci. The maize NAM population, consisting of 5,000 recombinant inbred lines (RILs) from 25 families representing the global diversity of maize, was evaluated for resistance to southern leaf blight (SLB) disease. Joint-linkage analysis identified 32 quantitative trait loci (QTLs) with predominantly small, additive effects on SLB resistance. Genome-wide association tests of maize HapMap SNPs were conducted by imputing founder SNP genotypes onto the NAM RILs. SNPs both within and outside of QTL intervals were associated with variation for SLB resistance. Many of these SNPs were within or near sequences homologous to genes previously shown to be involved in plant disease resistance. Limited linkage disequilibrium was observed around some SNPs associated with SLB resistance, indicating that the maize NAM population enables high-resolution mapping of some genome regions.