Root Systems Lie Algebras

A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclidean vector space that possesses some remarkable symmetries and completely defines the Lie algebra of g. The purpose of this paper is to show the essentiality of the root system on the Lie algebra. In addition, the paper will mention the connection between the root system and Ways chambers. In addition, we will show Dynkin diagrams, which are an integral part of the root system.

Dye tracer infiltration technique to investigate macropore flow paths in Maka Mountain, Yunnan Province, China

In order to investigate the differences of macropores vertical distribution under different surface plants, and to assess the influences of root systems, organic matter and texture on macropore flow paths, two dye tracer infiltration experiments were performed in slopes under two different plants(Campylotropis polyantha(Franch.) Schindl vs. Cynodon dactylon(Linn.) Pers). Dye tracer infiltration experiments with field observations and measurements of soil properties were combined. Results show that the discrepancy in macropores distribution between two slopes under different plants is significant. Root systems have significant effects on macropore flow paths distribution and the effect become more pronounced as the diameter of roots become larger. Organic matter and stone are important factors to affect macropores distribution. Root-soil interface, inter-aggregate macropore and stone-soil interface are important macropore flow paths in well vegetated slopes.

A NEW TYPE OF PRONORMAT SUBGROUPS IN CHEVALLEY GROUPS

Let L be a simple Lie algebra with irreducible root system. having roots of different length, F be a field of charaCteristic different from 2, G = L(F) be a Chevalley group of type L over F. Denote by Φl the set of all long roots in Φl Set Gl = <xr (t); f∈EΦl,t∈F>. It is a subgroup of G generated by all the long root subgroups. This paper determines the pronormality of Gl in G when L is not of type G2.

Long-distance nitrate signaling displays cytokinin dependent and independent branches

The long-distance signaling network allowing a plant to properly develop its root system is crucial to optimize root foraging in areas where nutrients are available. Cytokinin is an essential element of the systemic signaling network leading to the enhancement of lateral root proliferation in areas where nitrate is available. Here,we explore more precisely：（i） which particular traits of lateral root growth（density and length of emerged lateral roots） are the targets of systemic signaling in a context of heterogeneous nitrate supply; and（ii） if the systemic signaling depends only on cytokinin or on a combination of several signalings.