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The second discriminant of a univariate polynomial

Science China Mathematics 2021年第6期64卷 1157-1180页

作者： Dongming Wang Jing Yang BDBC LMIB and School of Mathematics and Systems ScienceBeihang UniversityBeijing 100191China SMS HCICGuangxi University for NationalitiesNanning 530006China Centre National de la Recherche Scientifique Paris 75794France

We define the second discriminant D_(2)of a univariate polynomial f of degree greater than 2 as the product of the linear forms 2r_(k)-r_(i)-r_(j)for all triples of roots r_(i),r_(k),r_(j)of f with iroot which is equal to the average of two other *** show that D_(2)can be expressed as the resultant of f and a determinant formed with the derivatives of f,establishing a new relation between the roots and the coefficients of *** prove several notable properties and present an application of D_(2).

关键词： determinant discriminant polynomial ideal resultant root configuration

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Morphological plasticity and phosphorus uptake mechanisms of hybrid Eucalyptus roots under spatially heterogeneous phosphorus stress

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Journal of Forestry Research 2017年第4期28卷 713-724页

作者： Chuifan Zhou Wuya Jiang Ying Li Xiaolong Hou Aiqin Liu Liping Cai College of Forestry Fujian Agriculture and Forestry UniversityFuzhou 350002China

In this study, we subjected the root systems of eight Eucalyptus hybrids currently cultivated in southern China to heterogeneous phosphorus stress to provide a scientific basis for the selection of a highly phosphorus-efficient Eucalyptus variety. When the ability of these hybrids to locate phosphorus under different experimental conditions (phosphorus supply in a homogeneous or heterogeneous manner vs. no phosphorus supply) was compared, the main growth characteristics of Eucalyptus, such as plant height, diameter, dry mass, and phosphorus content, significantly improved when the phosphorus supply was increased from no phosphorus or heterogeneous phosphorus (half of the phosphorus amount) to homogeneous phosphorus. Across these three conditions, the growth traits of different Eucalyptus hybrids differed significantly, indicating different adaptabilities of the hybrids to various phosphorus conditions. The growth traits of the aboveground tissues of Eucalyptus under different phosphorus conditions were largely influenced by the morphology of the underground root system. In addition, the root morphology of Eucalyptus under heterogeneous phosphorus treatment suggested that there were two mechanisms for locating nutrients. Eucalyptus hybrids such as Urophylla 3229, Grandis 9, Guanglin 3, 201-2, and Dunn produced more roots proximal to the phosphorus supply; the other hybrids, Urophylla 3216, Grandis 5, and Guanglin 9, relied mainly on the growth of roots opposite the phosphorus supply to obtain adequate nutrients for growth. With these two strategies, a wide range of nutrients was obtained, root distribution was greater, more soil volume was covered, the contact area of the roots with soil phosphorus was increased, and the uptake of phosphorus by the root system was increased. These results demonstrate that Eucalyptus relies on changes to morphological characteristics of the root system to increase accessibility to phosphorus resources.

关键词： Eucalyptus hybrid Phosphorus Growth traits root configuration

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