Long time behavior of the Schroedinger group associated with a potential aximum

We give a semiclassical expansion of the Schrödinger group in terms of the resonances created by a non-degenerate potential maximum. This formula implies that the imaginary part of the resonances gives the decay rate of states for large time of order of the logarithm of the semiclassical parameter.グローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryMRIT 6th Workshop Math-for-Industry Tutorial : Spectral theories of non-Hermitian operators and their applicatio

Seduced by the dark side: integrating molecular and ecological perspectives on the influence of light on plant defence against pests and pathogens.

Plants frequently suffer attack from herbivores and microbial pathogens, and have evolved a complex array of defence mechanisms to resist defoliation and disease. These include both preformed defences, ranging from structural features to stores of toxic secondary metabolites, and inducible defences, which are activated only after an attack is detected. It is well known that plant defences against pests and pathogens are commonly affected by environmental conditions, but the mechanisms by which responses to the biotic and abiotic environments interact are only poorly understood. In this review, we consider the impact of light on plant defence, in terms of both plant life histories and rapid scale molecular responses to biotic attack. We bring together evidence that illustrates that light not only modulates defence responses via its influence on biochemistry and plant development but, in some cases, is essential for the development of resistance. We suggest that the interaction between the light environment and plant defence is multifaceted, and extends across different temporal and biological scales