Classical R-Matrices and the Feigin-Odesskii Algebra via Hamiltonian and Poisson Reductions

We present a formula for a classical $r$-matrix of an integrable system obtained by Hamiltonian reduction of some free field theories using pure gauge symmetries. The framework of the reduction is restricted only by the assumption that the respective gauge transformations are Lie group ones. Our formula is in terms of Dirac brackets, and some new observations on these brackets are made. We apply our method to derive a classical $r$-matrix for the elliptic Calogero-Moser system with spin starting from the Higgs bundle over an elliptic curve with marked points. In the paper we also derive a classical Feigin-Odesskii algebra by a Poisson reduction of some modification of the Higgs bundle over an elliptic curve. This allows us to include integrable lattice models in a Hitchin type construction.Comment: 27 pages LaTe

Response of rice cultivars to phosphorus supply on an oxisol.

Genotypic differences in absorption or utilization of P might be exploited to improve efficiency of fertilizer use or to obtain higher productivity on P-deficient soils. The objective of this study was to evaluate responses by 75 genotypes of upland rice (Oryza sativa L.) to two soil P levels in two field experiments. In the first experiment, soil P levels (Mehlich 1) were 1.5 mg kg-1 and 5 mg kg-1, and in the second experiment, 3 mg kg-1 and 4.7 mg kg-1 of soil, respectively. Rice cultivars differed significantly in shoot dry matter production at flowering, grain yield, and plant P status. Based on a grain yield efficiency index, cultivars were classified as P-efficient or P-inefficient. Shoot dry matter was more sensitive to P-deficiency but was not related to grain yield. Phosphorus use efficiency was higher under the low P treatment. Phosphorus uptake was significantly correlated with dry matter, P concentration and P-efficiency ratio. Results of this study indicate that genetic differences in P-use efficiency exist among upland rice cultivars and may be exploited in breeding programs

Antimicrobial secondary metabolites from agriculturally important bacteria as next-generation pesticides

The whole organisms can be packaged as biopesticides, but secondary metabolites secreted by microorganisms can also have a wide range of biological activities that either protect the plant against pests and pathogens or act as plant growth promotors which can be beneficial for the agricultural crops. In this review, we have compiled information about the most important secondary metabolites of three important bacterial genera currently used in agriculture pest and disease management