From January to March 2005, the effects of group size on the vigilance behavior of wintering Common Cranes Grus grus were studied at Lashihai Lake, Yunnan Province, China. We used scan sampling to record the group siz...From January to March 2005, the effects of group size on the vigilance behavior of wintering Common Cranes Grus grus were studied at Lashihai Lake, Yunnan Province, China. We used scan sampling to record the group sizes and the number of vigilant individuals in each group, and focal sampling to record the frequency and duration of individual vigilance behavior. Both the vigilance efforts of groups and individuals significantly decreased as group size increased, but when the group size exceeded 30 individuals, the decrease of group vigilance became not significant （P 〉 0. 05）, and the vigilance duration of adult cranes increased （P 〈 0.01 ）. The vigilance frequency of adults increased （P 〈 0.05） when the size exceeded 50 individuals. Presumably, the maximal group size allowing the lowest vigilance for juvenile cranes was larger than that for adults, and the flocks composed of 20 to 30 individuals represented the optimal group size of wintering Common Cranes by considering only the vigilance behavior. Further research should focus on the synthesized effects of various factors.展开更多
It is one of the oldest research topics in computer algebra to determine the equivalence of Riemann tensor indexed polynomials. However, it remains to be a challenging problem since Grbner basis theory is not yet powe...It is one of the oldest research topics in computer algebra to determine the equivalence of Riemann tensor indexed polynomials. However, it remains to be a challenging problem since Grbner basis theory is not yet powerful enough to deal with ideals that cannot be finitely generated. This paper solves the problem by extending Grbner basis theory. First, the polynomials are described via an infinitely generated free commutative monoid ring. The authors then provide a decomposed form of the Grbner basis of the defining syzygy set in each restricted ring. The canonical form proves to be the normal form with respect to the Grbner basis in the fundamental restricted ring, which allows one to determine the equivalence of polynomials. Finally, in order to simplify the computation of canonical form, the authors find the minimal restricted ring.展开更多
Let (?, ?) be a linear matrix problem induced from a finite dimensional algebra ∧. Then an? ×? matrix M in R(?, ?) is indecomposable if and only if the number of links in the canonical formM (∞) of M is equal t...Let (?, ?) be a linear matrix problem induced from a finite dimensional algebra ∧. Then an? ×? matrix M in R(?, ?) is indecomposable if and only if the number of links in the canonical formM (∞) of M is equal to. ?-dim? ? 1. On the other hand, the dimension of the endomorphism ring of M is equal to ?-dim? ? σ(M).展开更多
文摘From January to March 2005, the effects of group size on the vigilance behavior of wintering Common Cranes Grus grus were studied at Lashihai Lake, Yunnan Province, China. We used scan sampling to record the group sizes and the number of vigilant individuals in each group, and focal sampling to record the frequency and duration of individual vigilance behavior. Both the vigilance efforts of groups and individuals significantly decreased as group size increased, but when the group size exceeded 30 individuals, the decrease of group vigilance became not significant （P 〉 0. 05）, and the vigilance duration of adult cranes increased （P 〈 0.01 ）. The vigilance frequency of adults increased （P 〈 0.05） when the size exceeded 50 individuals. Presumably, the maximal group size allowing the lowest vigilance for juvenile cranes was larger than that for adults, and the flocks composed of 20 to 30 individuals represented the optimal group size of wintering Common Cranes by considering only the vigilance behavior. Further research should focus on the synthesized effects of various factors.
基金supported by the National Natural Science Foundation of China under Grant No.11701370the Natural Science Foundation of Shanghai under Grant No.15ZR1401600
文摘It is one of the oldest research topics in computer algebra to determine the equivalence of Riemann tensor indexed polynomials. However, it remains to be a challenging problem since Grbner basis theory is not yet powerful enough to deal with ideals that cannot be finitely generated. This paper solves the problem by extending Grbner basis theory. First, the polynomials are described via an infinitely generated free commutative monoid ring. The authors then provide a decomposed form of the Grbner basis of the defining syzygy set in each restricted ring. The canonical form proves to be the normal form with respect to the Grbner basis in the fundamental restricted ring, which allows one to determine the equivalence of polynomials. Finally, in order to simplify the computation of canonical form, the authors find the minimal restricted ring.
基金the National Natural Science Foundation of China (Grant No. 19831070) and the Doctoral Foundation of Institution of Higher Education.
文摘Let (?, ?) be a linear matrix problem induced from a finite dimensional algebra ∧. Then an? ×? matrix M in R(?, ?) is indecomposable if and only if the number of links in the canonical formM (∞) of M is equal to. ?-dim? ? 1. On the other hand, the dimension of the endomorphism ring of M is equal to ?-dim? ? σ(M).
