In a previous paper published in this journal, it was demonstrated that any bounded, closed interval of the real line can, except for a set of Lebesgue measure 0, be expressed as a union of c pairwise disjoint perfect...In a previous paper published in this journal, it was demonstrated that any bounded, closed interval of the real line can, except for a set of Lebesgue measure 0, be expressed as a union of c pairwise disjoint perfect sets, where c is the cardinality of the continuum. It turns out that the methodology presented there cannot be used to show that such an interval is actually decomposable into c nonoverlapping perfect sets without the exception of a set of Lebesgue measure 0. We shall show, utilizing a Hilbert-type space-filling curve, that such a decomposition is possible. Furthermore, we prove that, in fact, any interval, bounded or not, can be so expressed.展开更多
Heading date in rice is a typical quantitative trait controlled by multiple quantitative trait loci （QTLs）. It is mainly regulated by environmental factors such as photoperiod and temperature （Izawa, 2007）. Many Q...Heading date in rice is a typical quantitative trait controlled by multiple quantitative trait loci （QTLs）. It is mainly regulated by environmental factors such as photoperiod and temperature （Izawa, 2007）. Many QTLs for heading date have been identified using different mapping populations and methods （http：// www.gramene.org/qtl）. Up to date, several major heading date QTLs have been cloned by map-based cloning strategy （Yano et al., 2000; Takahashi et al., 2001; Kojima et al., 2002; Doi et al., 2004; Xue et al., 2008; Wei et al., 2010; Yan et al.,展开更多
文摘In a previous paper published in this journal, it was demonstrated that any bounded, closed interval of the real line can, except for a set of Lebesgue measure 0, be expressed as a union of c pairwise disjoint perfect sets, where c is the cardinality of the continuum. It turns out that the methodology presented there cannot be used to show that such an interval is actually decomposable into c nonoverlapping perfect sets without the exception of a set of Lebesgue measure 0. We shall show, utilizing a Hilbert-type space-filling curve, that such a decomposition is possible. Furthermore, we prove that, in fact, any interval, bounded or not, can be so expressed.
基金supported by grants from the Ministry of Science and Technology of China(No. 2010CB125901)the National Natural Science Foundation of China(No.31271315)the Bill & Melinda Gates Foundation
文摘Heading date in rice is a typical quantitative trait controlled by multiple quantitative trait loci （QTLs）. It is mainly regulated by environmental factors such as photoperiod and temperature （Izawa, 2007）. Many QTLs for heading date have been identified using different mapping populations and methods （http：// www.gramene.org/qtl）. Up to date, several major heading date QTLs have been cloned by map-based cloning strategy （Yano et al., 2000; Takahashi et al., 2001; Kojima et al., 2002; Doi et al., 2004; Xue et al., 2008; Wei et al., 2010; Yan et al.,
