Evaluation of a generic agro-hydrological model for water and nitrogen dynamics (SMCR_N) in the soil–wheat system

Agro-hydrological models have widely been used for optimizing resources use in agriculture for maximum crop growth and minimum environmental consequences. The SMCR_N model is a recently developed, process-based, multi-crop and management-oriented agro-hydrological model for water and nitrogen dynamics in the soil–crop system, and has been validated against data from field experiments over a range of vegetable crops. In this study, the model is further tested against the comprehensive measured datasets from field experiments conducted under different circumstances on wheat. It has been found that given the proper parameterization of the simple growth equation, which worked well with vegetable crops, the model was able to simulate wheat growth accurately. The predicted relative root length density distributions at various development stages agreed with the measurements and those modeled by alternative approaches in the literature. The explicit hydrological algorithm for the basic equations governing water and nitrogen transport in soil performed well. Compared with other conventional numerical schemes, the algorithm used in the study was much simpler and easy to implement. The simulated spatial–temporal soil water content was in good agreement with the measurements, given the information of groundwater table was known. The model was also capable of reproducing the data of nitrogen uptake and soil mineral nitrogen concentration measured at depths and at time intervals. This indicates that the key equations for various processes governing water and nitrogen dynamics in the soil–wheat system were correctly formulated, and the model was properly parameterized. The results from this exercise, together with the model's previous validation over 16 vegetable crops, make the model a good candidate to be used for water and nitrogen management for growing diverse crops

On an algebraic formula and applications to group action on manifolds

We consider a purely algebraic result. Then given a circle or cyclic group of prime order action on a manifold, we will use it to estimate the lower bound of the number of fixed points. We also give an obstruction to the existence of $\mathbb{Z}_p$ action on manifolds with isolated fixed points when $p$ is a prime.Comment: 7 pages, revised slightly to update a new reference and reassign the credit of the idea in this not