In order to study the soil nitrogen (N) distribution pattern in the root zone of chili peppers under aerated drip irrigation (ADI) conditions and analyze the relationship between soil N distribution and crop growth, two irrigation methods (conventional drip irrigation and ADI) and three N levels (0, 140, and 210 kg hm⁻²) were set up in this experiment. Soil samples were collected by the soil auger method at the end of different reproductive periods, and the uniformity coefficient of soil N in the spatial distribution was calculated by the method of Christiansen’s coefficient. The growth status and soil-related indices of pepper were determined at each sampling period, and the relationships between soil N distribution and chili pepper growth were obtained based on principal component analysis (PCA). The results showed that the spatial content of soil nitrate-N (NO₃⁻-N) fluctuated little during the whole reproductive period of chili peppers under ADI conditions, and the coefficient of uniformity of soil NO₃⁻-N content distribution increased by 5.29~37.63% compared with that of conventional drip irrigation. The aerated treatment increased the root length and surface area of chili peppers. In addition, the ADI treatments increased the plant height, stem diameter, root vigor, and leaf chlorophyll content to some extent compared with the nonaerated treatment. The results of PCA showed that the yield of chili peppers was positively correlated with the uniformity coefficient of soil NO₃⁻-N, root vigor, and root length. ADI can significantly improve the distribution uniformity of soil NO₃⁻-N and enhance the absorption and utilization of N by the root system, which in turn is conducive to the growth of the crop, the formation of yields, and the improvement of fruit quality.

In order to provide a theoretical basis for the rational application of nitrogen fertilizer for tomatoes under aerated drip irrigation, a model of the critical nitrogen dilution curve was established in this study, and the feasibility of the nitrogen nutrition index (NNI) for the real-time diagnosis and evaluation of the nitrogen nutrient status was explored. The tomato variety “FENOUYA” was used as the test crop, and aerated drip irrigation was adopted by setting three levels of aeration rates, namely, A1 (dissolved oxygen concentration of irrigation water is 5 mg L⁻¹), A2 (dissolved oxygen concentration of irrigation water is 15 mg L⁻¹), and A3 (dissolved oxygen concentration of irrigation water is 40 mg L⁻¹), and three levels of nitrogen rates, namely, N1 (120 kg ha⁻¹), N2 (180 kg ha⁻¹) and N3 (240 kg ha⁻¹). The model of the critical nitrogen concentration dilution of tomatoes under different aerated treatments was established. The results showed that (1) the dry matter accumulation of tomatoes increased with the increase in the nitrogen application rate in a certain range and it showed a trend of first increase and then decrease with the increase in aeration rate. (2) As the reproductive period progressed, the nitrogen concentration in tomato plants showed a decreasing trend. (3) There was a power exponential relationship between the critical nitrogen concentration of tomato plant growth and above-ground biomass under different levels of aeration and nitrogen application rate, but the power exponential curves were characterized by A1 (Nc = 15.674DM^−0.658), A2 (Nc = 101.116DM^−0.455), A3 (Nc = 119.527DM^−0.535), N1 (Nc = 33.819DM^−0.153), N2 (Nc = 127.759DM^−0.555) and N3 (Nc = 209.696DM^−0.683). The standardized root mean square error (n-RMSE) values were 0.08%, 3.68%, 3.79% 0.50%, 1.08%, and 0.55%, which were less than 10%, and the model has good stability. (4) The effect of an increased nitrogen application rate on the critical nitrogen concentration dilution curve was more significant than that of the increase in aeration rate. (5) A nitrogen nutrition index model was built based on the critical nitrogen concentration model to evaluate the nitrogen nutritional status of tomatoes, whereby 180 kg ha⁻¹ was the optimal nitrogen application rate, and 15 mg L⁻¹ dissolved oxygen of irrigation water was the optimal aeration rate for tomatoes.

In this paper, we establish the existence of global-in-time solutions to the compressible micropolar fluid for a viscous heat-conducting flow with shear viscosity and general large initial data. We prove that the temperature is uniformly bounded from below and above in time and space and the global weak solution is asymptotically stable as the time tends to infinity.

This paper investigates multiple solutions for super-linear symmetric operator equations by optimization methods like index theory, Mountain pass theorem and mini-max methods. Applying the results to second order Hamiltonian systems with symmetry yields finite or infinitely many solutions.

In this paper, the large time behavior of globally smooth solutions of the Cauchy problem for the three dimensional Euler-Poisson system of compressible fluids coupled to a magnetic field is studied. We prove that the smooth solutions (near a given constant equilibrium state) of the problem converge asymptotically to a stationary solution exponentially fast as $ t $ goes to $ \infty $.