Gorenstein平坦预包络和预解式

我们在［７］中引进了Ｇｏｒｅｎｓｔｅｉｎ平坦模。本文将这类模的刻画推广到任意ｎ－Ｇｏｒｅｎｓｔｅｉｎ环上，并利用这类模刻画了ｎ－Ｇｏｒｅｓｔｅｉｎ环。而且，我们证明了任意ｎ－Ｇｏｒｅｎｓｔｅｉｎ环上Ｇｏｒｅｎｓｔｅｉｎ平坦预包络的存在性，并证得得这种环关于Ｇｏｒｅｎｓｔｅｉｎ平坦模的内射类的整体维数至多为ｎ－２，当ｎ≤１时，该整体维数为零。     

Sex-specific volatile compounds influence microarthropod-mediated fertilization of moss

Sexual reproduction in non-vascular plants requires unicellular free-motile sperm to travel from male to female reproductive structures across the terrestrial landscape. Recent data suggest that microarthropods can disperse sperm in mosses. However, little is known about the chemical communication, if any, that is involved in this interaction or the relative importance of microarthropod dispersal compared to abiotic dispersal agents in mosses. Here we show that tissues of the cosmopolitan moss Ceratodon purpureus emit complex volatile scents, similar in chemical diversity to those described in pollination mutualisms between flowering plants and insects, that the chemical composition of C. purpureus volatiles are sex-specific, and that moss-dwelling microarthropods are differentially attracted to these sex-specific moss volatile cues. Furthermore, using experimental microcosms, we show that microarthropods significantly increase moss fertilization rates, even in the presence of water spray, highlighting the important role of microarthropod dispersal in contributing to moss mating success. Taken together, our results indicate the presence of a scent-based 'plant-pollinator-like' relationship that has evolved between two of Earth's most ancient terrestrial lineages, mosses and microarthropods.