A New Kind of Graded Lie Algebra and Parastatistical Supersymmetry

In this paper the usual $Z_2$ graded Lie algebra is generalized to a new form, which may be called $Z_{2,2}$ graded Lie algebra. It is shown that there exists close connections between the $Z_{2,2}$ graded Lie algebra and parastatistics, so the $Z_{2,2}$ can be used to study and analyse various symmetries and supersymmetries of the paraparticle systems

Differential responses of roots for varying tolerance to salinity stress in wheat with special reference to elasticity

Two salt-sensitive (Yongliang-15, GS-6058) and two salt-tolerant (JS-7, Xinchun-31) wheat cultivars were used to investigate the extension, extensibility (viscoelastic parameters), and chemical composition of the cell walls in their root elongation regions (apical 10 mm-long root segments), under salinity stress. The elasticity of the root cell wall, indicated by E0, significantly decreased in the salt-sensitive cultivars, whereas the E0 in the salt-tolerant cultivars was maintained at the same level as that in the non-saline condition. Root extension and the differences among cultivars were largely dependent on elastic extension, which accounts for one-half to two-thirds of the total extension. Viscosity, indicated by η0, and the plastic extension of the root cell walls did not change across the treatments and cultivars. The significant decrease in cell wall elasticity in the root elongation region was one of the factors that depressed root growth in salt-sensitive cultivars under the saline condition. The well-maintained elasticity of salt-tolerant cultivars alleviated the depression of root growth by NaCl. Cell wall elasticity was positively correlated with the relative pectin and hemicellulose I contents and negatively correlated with the relative cellulose content. Under saline conditions, the relative hemicellulose II content did not change in the salt-sensitive cultivars; however, it decreased in the salt-tolerant ones. Thus, changes in chemical composition of the cell wall were correspond with the cell wall extensibility and root growth in wheat cultivars with different degrees of salt tolerance

Asymptotic distributions of non-central studentized statistics

Let X (1), ..., X (n) be independent and identically distributed random variables and W (n) = W (n) (X (1), ..., X (n) ) be an estimator of parameter I. Denote T (n) = (W (n) - I (0))/s (n) , where s (n) (2) is a variance estimator of W (n) . In this paper a general result on the limiting distributions of the non-central studentized statistic T (n) is given. Especially, when s (n) (2) is the jacknife estimate of variance, it is shown that the limit could be normal, a weighted chi (2) distribution, a stable distribution, or a mixture of normal and stable distribution. Applications to the power of the studentized U- and L- tests are also discussed