Root canal morphology and configuration of 123 maxillary second molars by means of micro-CT

The aim of this study was to investigate the root canal configuration, accessory canals and number of main foramina of 123 maxillary second molars by means of micro-computed tomography. The teeth were scanned and reproduced with 3D software imaging. The root canal configuration and number of main foramina were evaluated by means of a four-digit system. The morphological complexity of human maxillary second molars is depicted by the number of accessory and connecting canals. The most frequently observed root canal configurations in the mesiobuccal root were 2-2-2/2 （19.5%）, 2-2-1/1 （14.6%） and 2-1-1/1 （13.0%）. A 1-1-1/1 configuration was observed in 93.5% and in 96.7% in the distobuccal and palatal roots, respectively. The MB1 mot canal had one accessory canal （18.7%）, and 8.9% of the MB2 root canal had one or two accessory canals. The distobuccal （11.3%） and palatal （14.6%） root canals had at least one accessory canal, and connecting canals were observed in 16.3% of mesiobuccal roots. The MB1, MB2, distobuccal and palatal root canals had one main foramen in 99.2%, 43.1%, 98.4% and 99.2% of samples, respectively. In the mesiobuccal root, one accessory foramen was detected in 14.6%, two were detected in 7.3%, and three were detected in 5.7%. The distobuccal root showed one or two accessory foramina in 9.1% of samples. The root canal configuration of maxillary second molars is quite heterogeneous; the mesiobuccal root has predominantly two root canal entrances （58.4%, 1 in 41.1%） with one main foramen （54.4%）. Two main foramina were observed in 43.0%. Morphological variations, connecting and accessory canals were observed in all apical thirds.

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

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.

The second discriminant of a univariate polynomial

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 i<j and j≠k,k≠i.D_(2)vanishes if and only if f has at least one root which is equal to the average of two other roots.We 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 f.We prove several notable properties and present an application of D_(2).