The root is the below-ground organ of a plant, and it has evolved multiple signaling pathways that allow adaptation of architecture, growth rate, and direction to an ever-changing environment. Roots ...grow along the gravitropic vector towards beneficial areas in the soil to provide the plant with proper nutrients to ensure its survival and productivity. In addition, roots have developed escape mechanisms to avoid adverse environments, which include direct illumination. Standard laboratory growth conditions for basic research of plant development and stress adaptation include growing seedlings in Petri dishes on medium with roots exposed to light. Several studies have shown that direct illumination of roots alters their morphology, cellular and biochemical responses, which results in reduced nutrient uptake and adaptability upon additive stress stimuli. In this review, we summarize recent methods that allow the study of shaded roots under controlled laboratory conditions and discuss the observed changes in the results depending on the root illumination status.
Let Φ be a root system in a finite dimensional Euclidean space F and S be a subset of Φ. Let the smallest in the collection of all root systems in F which contain S—i.e., the intersection of all such ...root systems—be denoted by R(S). It can be easily shown that Φ has linearly independent subsets X such that R(X)=Φ—e.g., for any base Δ of Φ, R(Δ)=Φ. We prove a result that generalizes the preceding fact: If Ψ is any subset of Φ, then there exists a linearly independent subset S of Ψ such that R(S)⊇Ψ. In the process of deriving the above one, we find a sufficient condition for a root system to be isomorphic to one of the root systems in {An,Dn+3:n∈N} and obtain a simple proof of the following known result on exceptional root systems: Let k,ℓ be integers such that 6⩽k⩽ℓ⩽8; if X is a subset of the exceptional root system E8 such that R(X) is isomorphic to Eℓ, then for some linearly independent subset Y of X, R(Y) is isomorphic to Ek.
Rootsytems of nonclassical simple Lie algebras L=Σ
a∈R
L
a
such that a(e
f)≠0 for some
for each a∈R-{0} either contain T
2
-sections or are irreducible witt rootsystem. In 9 D. winter introduced the ...following conjecture: The transitive irreducible Witt rootsystems are those of the form W
m
S
n
, or W
m
⊕S
n
(R
′
) for m≥1,n≥2, and R
′
a transitive irreducible Witt rootsystem of prime rank less than n. In this paper we prove the validity of Winter's conjecture and therefore, give a complete classification of all transitive Witt rootssystems.
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