We find all the inequivalent simple root systems for the complex reflection groups G12, G24, G25 and G26. Then we give all the non-congruent essential presentations of these groups by generators and relations. The methed used in the paper is applicable to any finite (complex) reflection groups. Introduction. Shephard and Todd classified all the finite complex reflection groups in paper [5]. Lat...

The fluorescent compound trisodium, 3-hydroxy-5,8,10-pyrenetrisulfonate (PTS) was used to quantify the apoplastic flux through red pine (Pinus resinosa Ait.) root systems-that portion of the total water flux reaching the xylem without ever crossing a semipermeable membrane. Flow was induced by pressure through detopped root systems, and by transpiration through intact seedlings. Apoplastic flux...

Starting from Borcherds’ fake monster Lie algebra we construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for...

When crop plants are subjected to soil waterlogging, or an anaerobic condition, their root and shoot systems respond differently. A variety of morphological and anatomical alterations develop in the root system. Reduction of the root respiration rate has been reported in both flooding-tolerant and intolerant species. Besides alcoholic fermentation, several diverse fermentative bypasses take pla...

Plant root is an organ composed of multiple cell types with different functions. This multicellular complexity limits our understanding of root biology because -omics studies performed at the level of the entire root reflect the average responses of all cells composing the organ. To overcome this difficulty and allow a more comprehensive understanding of root cell biology, an approach is needed...