寻找四元域上n维线性空间中n/2维自对偶子空间的方法

本文讨论F4上n维线性空间的k维子空间W，这些子空间都有特定的自同构群(实际上是典型群GLn(F4)的一个子群)，根据群中元素形式的不同可将子空间W分为两类，并对寻找n维空间中形如这两类的n／2维自对偶子空间提供了一种采用降低维数寻找的方法。     

Deletion of steroid 5 alpha-reductase 2 gene in male pseudohermaphroditism

The conversion of testosterone into dihydrotestosterone by steroid 5 alpha-reductase is a key reaction in androgen action, and is essential both for the formation of the male phenotype during embryogenesis and for androgen-mediated growth of tissues such as the prostate. Single gene defects that impair this conversion lead to pseudohermaphroditism in which 46X,Y males have male internal urogenital tracts, but female external genitalia. We have described the isolation of a human 5 alpha-reductase complementary DNA from prostate. Subsequent cloning and genetic studies showed that this gene (designated 5 alpha-reductase 1) was normal in patients with 5 alpha-reductase deficiency. We report here the isolation of a second 5 alpha-reductase cDNA by expression cloning and the polymerase chain reaction. The biochemical and pharmacological properties of this cDNA-encoded enzyme (designated 5 alpha-reductase 2) are consistent with it being the major isozyme in genital tissue. A deletion in this gene is present in two related individuals with male pseudohermaphroditism caused by 5 alpha-reductase deficiency. These results verify the existence of at least two 5 alpha-reductases in man and provide insight into a fundamental hormone-mediated event in male sexual differentiation.