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。     

Lagged effects of ocean climate change on fulmar population dynamics

Environmental variation reflected by the North Atlantic Oscillation affects breeding and survival in terrestrial vertebrates, and climate change is predicted to have an impact on population dynamics by influencing food quality or availability. The North Atlantic Oscillation also affects the abundance of marine fish and zooplankton, but it is unclear whether this filters up trophic levels to long-lived marine top predators. Here we show by analysis of data from a 50-year study of the fulmar that two different indices of ocean climate variation may have lagged effects on population dynamics in this procellariiform seabird. Annual variability in breeding performance is influenced by the North Atlantic Oscillation, whereas cohort differences in recruitment are related to temperature changes in the summer growing season in the year of birth. Because fulmars exhibit delayed reproduction, there is a 5-year lag in the population's response to these effects of environmental change. These data show how interactions between different climatic factors result in complex dynamics, and that the effects of climate change may take many years to become apparent in long-lived marine top predators.