Differential Equation Model of Carbon, Nitrogen and Zinc Components in Growing Tomatoes

Tomato is a common food on the human table. Up to now, the research on the growth and development model of tomato has been about 50 years. There are many researches on the main nutrients of tomato, such as carbon and nitrogen, but few on the trace element zinc. In this paper, taking plant nutrient C, N and Zn as variables, the differential equation model of C, N and Zn in tomato growth and development was established. According to the research of tomato as a whole and divided into root and leaf, the one-compartment and two-compartment models of tomato growth and development were established. The model was analyzed by Matlab program, and the existing experimental data was used to test the numerical simulation results, which proves that the model conforms to the facts.

Medical X-Ray Image Enhancement Based on Kramer's PDE Model

The purpose of this study is to present an application of a novel enhancement technique for enhancing medical images generated from X-rays. The method presented in this study is based on a nonlinear partial differential equation （PDE） model, Kramer＇s PDE model. The usefulness of this method is investigated by experimental results. We apply this method to a medical X-ray image. For comparison, the X-ray image is also processed using classic Perona-Malik PDE model and Catte PDE model. Although the Perona-Malik model and Catte PDE model could also enhance the image, the quality of the enhanced images is considerably inferior compared with the enhanced image using Kramer＇s PDE model. The study suggests that the Kramer＇s PDE model is capable of enhancing medical X-ray images, which will make the X-ray images more reliable.

Research on China’s Population Structure in the New Situation

To analyze the impact of the“two-child policy”on the population size and structure,first of all,the birth rate,the ratio of men and women,and the ratio of urban and rural population are used as indicators.Before and after the dispersion,then establish a PDE model,and compare it with the population predicted by the gray forecast to analyze the mitigation of the ageing of the second child policy;continue to analyze the impact of changes in the population structure on the national economy,and select the male and female ratio and the labor population The urban-rural population ratio is used as an index to establish a multiple regression equation for analysis,and a related regression equation is obtained.Finally,the future marriage problem is analyzed,considering only the difference in the number of men and women entering the marriageable period at the same time.The difference in the number of marriageable populations is analyzed through the difference in the number of men and women born at birth,focusing on a dynamic perspective.

Dynamical Behavior of SEIR-SVS Epidemic Models with Nonlinear Incidence and Vaccination

For some infectious diseases such as mumps,HBV,there is evidence showing that vaccinated individuals always lose their immunity at different rates depending on the inoculation time.In this paper,we propose an age-structured epidemic model using a step function to describe the rate at which vaccinated individuals lose immunity and reduce the age-structured epidemic model to the delay differential model.For the age-structured model,we consider the positivity,boundedness,and compactness of the semiflow and study global stability of equilibria by constructing appropriate Lyapunov functionals.Moreover,for the reduced delay differential equation model,we study the existence of the endemic equilibrium and prove the global stability of equilibria.Finally,some numerical simulations are provided to support our theoretical results and a brief discussion is given.