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Let G be a simply connected semisimple algebraic groups over ℂ and let ρ:G→GL(Vλ) be an irreducible representation of G of highest weight λ. Suppose that ρ has finite kernel. Springer defined an adjoint-invariant regular map with Zariski dense image from the group to the Lie algebra, 휃λ:G→픤, which depends on λ. This map, 휃λ, takes the maximal torus T of G to its Lie algebra 픱. Thus, for a given simple group G and an irreducible representation Vλ, one may write , where we take the simple coroots as a basis for 픱. We give a complete determination for these coefficients ci(t) for any simple group G as a sum over the weights of the torus action on Vλ. [ABSTRACT FROM AUTHOR]

We analyzed temporal and spatial patterns of water use by a functionally-diverse group of Great Basin plant species and determined their water use rates at the whole-plant and individual-leaf scales under variable summer watering. Species studied were the desert grassesDistichlis spicataandSporobolus airoides, the desert shrubsArtemisia tridentata, Ericameria nauseosa, andAtriplex confertifolia; the wetland/riparian plantsJuncus arcticus, Leymus triticoides, andSalix exigua; and the annual exoticSalsola tragus. Plant species were individually grown in 5.8 m2plots in a common garden in eastern California. Three irrigation treatments in the form of monthly pulses were applied during the summer: low (1.3 cm), medium (2.6 cm), and high (3.9 cm), in addition to a nonirrigated control. Whole-plant water uptake characteristics were determined by soil water depletion at different soil depths, while leaf transpiration was determined by gas exchange. Whole-plant water extraction and leaf transpiration varied similarly among species. Desert shrubs had low water extraction (35 to 395 g m−2 day−1) and were not affected by irrigation. The desert grasses and riparian/wetland species had higher water extraction, increasing with irrigation levels.L. triticoidesandJ. arcticushad the highest water extraction overall (>2,000 g m−2 day−1). Desert shrubs relied 10 times more on deeper water sources than herbaceous species. The average T/ET was 31%, but varied by species. Summer available water in environments such as the Great Basin favors desert grasses and riparian/wetland species, but not desert shrubs. The observed species differences provide alternatives for water and vegetation management. [ABSTRACT FROM PUBLISHER]

We investigate the imaginary cone in hyperbolic Coxeter systems in order to show that any Coxeter system contains universal reflection subgroups of arbitrarily large rank. Furthermore, in the hyperbolic case, the positive spans of the simple roots of the universal reflection subgroups are shown to approximate the imaginary cone (using an appropriate topology on the set of roots), answering a question due to Dyer [9] in the special case of hyperbolic Coxeter systems. Finally, we discuss growth in Coxeter systems and utilize the previous results to extend the results of [16] regarding exponential growth in parabolic quotients in Coxeter groups. [ABSTRACT FROM AUTHOR]

A revised depositional model of predominantly swampy rather than lacustrine conditions is proposed for the upper dark shales and mudstones (Corradigbee Formation) of the Hatchery Creek Group. The whole sequence is interpreted as a humid alluvial fan deposit, conformable on underlying limestones, with a total thickness of about 1800 m. Cyclic sedimentation probably resulted from climatic fluctuations much longer than seasonal events and may reflect Milankovitch cyclicity. The most recent Devonian time-scale calibrations indicate that much of the Hatchery Creek sequence could have been deposited during the Emsian, giving adequate time for subsequent folding during the Middle Devonian Tabberabberan episode. The Corradigbee Formation contains a unique fossil fish assemblage, not represented elsewhere in eastern Australia, but sharing features with Early Devonian faunas from Yunnan, China, and the Middle Devonian Aztec Siltstone fish fauna of Victoria Land, Antarctica. The first invertebrate fossils are recorded from the Hatchery Creek Group (freshwater gastropods, indeterminate arthropods). Abundant plant remains at some localities include lycopsids, some early leaf-like structures, and deep root systems preserved in paleosols, the earliest record of such features from Australia. The new data are inconsistent with Northern Hemisphere fossil evidence linked to a modelled dramatic drop in CO2 levels and rise in O2 during the Devonian Period, but comply with some other evidence that the first forests may have evolved somewhat earlier in East Gondwana than elsewhere. [ABSTRACT FROM AUTHOR]

Metaphors, such as those used in the title of this article, are often useful for the comprehension of specialised topics in plant biology. A brief attempt is made to elucidate one of these metaphors, plant “intelligence”, as it relates to the plastic responses of roots and root systems to their environment. Tropisms and nastic movements of root apices are two expressions of an inherent plasticity of form exhibited by roots. In soil, roots are exposed to multiple stimuli, many of which can potentially elicit such movements. Hence, a key question is how roots respond to and process the different stimuli which simultaneously reach their surfaces. Assuming that roots always use the same site along their length to express their movement responses, and that they also use an auxin-based information-transduction pathway, the most evident choices for the processing of stimuli are that roots either prioritise the various incoming stimuli and respond only to the strongest or they amalgamate stimuli and mount an averaged compromise response to all of them. The proposal that plants may be “intelligent”, especially in respect to their plastic growth responses, is one that draws upon knowledge of this faculty from animal biology. Also implied is that plants and animals are sufficiently similar to share usage of this term “intelligence”. But an alternative view is that plants and animals are sufficiently different and so intelligence is an unfitting term. Following the line of enquiry into creative evolution initiated by Henri Bergson, plants can be viewed differently to animals. The tendency of plants is towards instinctive behaviour rather than intelligent behaviour. [ABSTRACT FROM AUTHOR]

We describe a class of groups with the property that the finite ones among them are precisely the complex reflection groups of rank 2. This situation is reminiscent of Coxeter groups, among which the finite ones are precisely the real reflection groups. We also study braid relations between complex reflections and indicate connections to an axiomatic study of root systems and to the Shephard-Todd “collineation groups.” [ABSTRACT FROM AUTHOR]

This article investigates several convex closure operators on a finite root system. It is shown that a natural closure operator on the positive root system of a finite Weyl group satisfies the anti-exchange condition for all root systems except type F 4 . [ABSTRACT FROM AUTHOR]

In this paper, we generalize the concept of purely imaginary roots of Kac–Moody algebras to generalized Kac–Moody algebras. Also we give a complete classification of those generalized Kac–Moody algebras with the purely imaginary property. We also define a new class of indefinite non-hyperbolic generalized Kac–Moody algebras called extended hyperbolic generalized Kac–Moody algebras and find that it does not always possess the purely imaginary property whereas the extended hyperbolic Kac–Moody algebras possess the purely imaginary property. [ABSTRACT FROM AUTHOR]