RESUMEN
We study the extreme value statistics of a one-dimensional resetting Brownian motion (RBM) till its first passage through the origin starting from the position x_{0} (>0). By deriving the exit probability of RBM in an interval [0,M] from the origin, we obtain the distribution P_{r}(M|x_{0}) of the maximum displacement M and thus gives the expected value ãMã of M as functions of the resetting rate r and x_{0}. We find that ãMã decreases monotonically as r increases, and tends to 2x_{0} as râ∞. In the opposite limit, ãMã diverges logarithmically as râ0. Moreover, we derive the propagator of RBM in the Laplace domain in the presence of both absorbing ends, and then leads to the joint distribution P_{r}(M,t_{m}|x_{0}) of M and the time t_{m} at which this maximum is achieved in the Laplace domain by using a path decomposition technique, from which the expected value ãt_{m}ã of t_{m} is obtained explicitly. Interestingly, ãt_{m}ã shows a nonmonotonic dependence on r, and attains its minimum at an optimal r^{*}≈2.71691D/x_{0}^{2}, where D is the diffusion coefficient. Finally, we perform extensive simulations to validate our theoretical results.
RESUMEN
In order to improve the photodegradation ability of fertilizer coating material and realize the sustainability of fertilizers, in this study, the commercially available photosensitive iron stearate (FeSt3) was wet-ground into submicrometer FeSt3 (SFeSt3) particles and used in preparation of a SFeSt3-modified bio-based polyurethane (PU)-coated controlled release urea (PU-SFe-CRU). The results showed that after 1 month photodegradation, the coating material had significant yellowing, the oxygen content of SFeSt3-modified PU (PU-SFe) increased by 56.89%, and its structure became more porous and looser than PU. The thermal stability of PU-SFe decreased, and more intermediate products were produced after exposure to UV light. The germination experiment showed that PU-SFe before and after photodegradation (up to 60 mg/L) had no adverse effect on the seed germination and bud growth of rice. Additionally, PU-SFe had a significantly higher Cr adsorption capacity after photodegradation due to the increase of the oxygen-containing group and specific surface. This study provides a theoretical basis for the research and development of photodegradable environment-friendly controlled release urea.