ON SOME RESULTS RELATED TO SOBER SPACES

This paper investigates sober spaces and their related structures from different perspectives.First,we extend the descriptive set theory of second countable sober spaces to first countable sober spaces.We prove that a first countable T_(0) space is sober if and only if it does not contain a∏_(2)^(0)-subspace homeomorphic either to S_(D),the natural number set equipped with the Scott topology,or to S_(1),the natural number set equipped with the cofinite topology,and it does not contain any directed closed subset without maximal elements either.Second,we show that if Y is sober,the function space TOP(X,Y)equipped with the Isbell topology(respectively,Scott topology)may be a non-sober space.Furthermore,we provide a uniform construction to d-spaces and well-filtered spaces via irreducible subset systems introduced in[9];we called this an H-well-filtered space.We obtain that,for a T_(0) space X and an H-well-filtered space Y,the function space TOP(X,Y)equipped with the Isbell topology is H-well-filtered.Going beyond the aforementioned work,we solve several open problems concerning strong d-spaces posed by Xu and Zhao in[11].

Simulation and visualization of spraying droplets behavior and deposition within virtual rice canopy

Models for accurately simulating pesticide droplet deposition and transmission mechanism in rice canopies can provide an effective and economic tool to optimize methods for spraying pesticides,adjuvant formulation,and spray parameters.However,the current studies on the modeling of spray droplet deposition within rice plants are still very limited.Aiming at this problem,a method to model and visualize spray transmission and deposition within the canopy of rice plants was proposed.Firstly,a particle system was used to simulate the spraying scene of droplets.Then an improved method to determine the behavior of rebound and shatter of the droplets in the virtual scene was proposed.The deposition of spraying droplets on a leaf was calculated according to the inclination angles of the leaf,the characteristics of the leaf surface,and the physical and spatial characteristics of the droplets.The experiment shows that the method can simulate the behavior of the spraying droplets within a virtual scene of a rice plant,which may provide a reference for the study of spray deposition in the canopy of the crop.