Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: a Review and Extensions of Tests for the Painlev\'e Property

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable equations have the Painlev\'e property, that is, all solutions are single-valued around all movable singularities. In this expository article, we review methods for analysing such singularity structure. In particular, we describe well known techniques of nonlinear regular-singular-type analysis, i.e. the Painlev\'e tests for ordinary and partial differential equations. Then we discuss methods of obtaining sufficiency conditions for the Painlev\'e property. Recently, extensions of \textit{irregular} singularity analysis to nonlinear equations have been achieved. Also, new asymptotic limits of differential equations preserving the Painlev\'e property have been found. We discuss these also.Comment: 40 pages in LaTeX2e. To appear in the Proceedings of the CIMPA Summer School on "Nonlinear Systems," Pondicherry, India, January 1996, (eds) B. Grammaticos and K. Tamizhman

Novel Cropping Technologies and Management Applied to Energy Crops

Dedicated energy crops are undergoing a rapid development. Progress is not only sought in increasing crop surface and biomass utilization, but also in advanced techniques for increasing the efficiency in the agricultural phase while restraining the drawbacks in energy cropping. The use of traditional food crops as an energy source only needs minor changes, whereas novel energy crops often necessitate starting from scratch in laying out their husbandry. Therefore, continuous improvement in large-scale food crops such as cereals and oilseeds also benefits their energy uses, whereas a variable gap remains to be filled in novel crops such as perennial rhizomatous grasses to keep abreast of current agricultural progress. Energy crops are aimed for a high efficiency in converting subsidiary energy, and are devised to originate positive externalities in environmental sustainability and global warming abatement. The ongoing progress in crop techniques is therefore confronted with these two delicate topics. Water footprint and land use are two other foremost issues related to energy crops at present. The fears for the depletions of specific resources such as fertilizer phosphates and for negative externalities such as land grabbing will likely be new issues to be discussed as regards energy crops. All these issues increase the pressure to improve the efficiencies per unit land cultivated and per unit input of energy, seed, fertilizer, etc. in energy crop production. The agricultural practices reviewed in the five categories of planting, nutrition, water management, protection and harvest are equally involved in the process. The potential echoed in several scientific sources is the best premise for optimistic prospects; the commitment in pursuing the current efforts is the best assurance to achieve them