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。     

Nuclear genetic control of mitochondrial DNA segregation

Mammalian mitochondrial DNA (mtDNA) is a high copy-number, maternally inherited genome that codes for a small number of essential proteins involved in oxidative phosphorylation. Mutations in mtDNA are responsible for a broad spectrum of clinical disorders. The segregation pattern of pathogenic mtDNA mutants is an important determinant of the nature and severity of mitochondrial disease, but it varies with the specific mutation, cell type and nuclear background and generally does not correlate well with mitochondrial dysfunction. To identify nuclear genes that modify the segregation behavior of mtDNA, we used a heteroplasmic mouse model derived from two inbred strains (BALB/c and NZB; ref. 12), in which we had previously demonstrated tissue-specific and age-dependent directional selection for different mtDNA genotypes in the same mouse. Here we show that this phenotype segregates in F2 mice from a genetic cross (BALB/c x CAST/Ei) and that it maps to at least three quantitative-trait loci (QTLs). Genome-wide scans showed linkage of the trait to loci on Chromosomes 2, 5 and 6, accounting for 16-35% of the variance in the trait, depending on the tissue and age of the mouse. This is the first genetic evidence for nuclear control of mammalian mtDNA segregation.     

Epistasis between mouse Klra and major histocompatibility complex class I loci is associated with a new mechanism of natural killer cell-mediated innate resistance to cytomegalovirus infection

Experimental infection with mouse cytomegalovirus (MCMV) has been used to elucidate the intricate host-pathogen mechanisms that determine innate resistance to infection. Linkage analyses in F(2) progeny from MCMV-resistant MA/My (H2 (k)) and MCMV-susceptible BALB/c (H2 (d)) and BALB.K (H2 (k)) mouse strains indicated that only the combination of alleles encoded by a gene in the Klra (also called Ly49) cluster on chromosome 6, and one in the major histocompatibility complex (H2) on chromosome 17, is associated with virus resistance. We found that natural killer cell-activating receptor Ly49P specifically recognized MCMV-infected cells, dependent on the presence of the H2 (k) haplotype. This binding was blocked using antibodies to H-2D(k) but not antibodies to H-2K(k). These results are suggestive of a new natural killer cell mechanism implicated in MCMV resistance, which depends on the functional interaction of the Ly49P receptor and the major histocompatibility complex class I molecule H-2D(k) on MCMV-infected cells.