With the development of the society, science and technology innovation becomes the development foundation of the equipment manufacturing industry enterprises. According to the questionnaires of 29 equipment manufacturing industries in Shenyang, the paper summarises the factors that affect the enterprise performance based on grounded theory. In order to study the relationships between the influencing factors and enterprise performance, multiple linear regression analysis is conducted by Statistical Product and Service Solutions (SPSS) software.

This paper constructs a spatial econometric model based on the environmental Kuznets curve to examine the effect of foreign direct investment (FDI) on urban haze pollution in Chinese cities. The evidence from the raster data of PM2.5 concentration in MODIS and MISR shows that there is a significant spatial correlation between haze pollution and FDI in Chinese cities, which is expressed as a spatial spillover effect; FDI in Chinese mainland cities reduces haze pollution, which confirms the “pollution halo hypothesis”; using instrumental variable estimation, the above conclusions are still robust; The total effect of FDI on haze pollution is negative, and the total effect can be decomposed into scale effect, technology effect and structural effect; FDI increases urban haze pollution through scale effects and structural effect, but decreases urban haze pollution through technology effects; the environmental Kuznets curve exists in urban haze pollution in China, i.e., there is an inverted “U” relationship between economic development and haze pollution. This paper proposes that the establishment of inter-city linkage mechanism of haze control and the full play of the technical effect of FDI on haze pollution will help reduce urban haze pollution.

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The Lotka–Volterra model is widely applied in various fields, and parameter estimation is important in its application. In this study, the Lotka–Volterra model with universal applicability is established by introducing the fractional order. Modulation function is multiplied by both sides of the Lotka–Volterra model, and the model is converted into linear equations with parameters to be estimated by the fractional integration method. The parameters are obtained by solving the equations. The state of the system is estimated by shifted Chebyshev polynomial. Last, the implementation program of the model is compiled. The concrete implementation method of the improved model is proposed by an example in this study.

With the development of the society, science and technology innovation becomes the development foundation of the equipment manufacturing industry enterprises. According to the questionnaires of 29 equipment manufacturing industries in Shenyang, the paper summarises the factors that affect the enterprise performance based on grounded theory. In order to study the relationships between the influencing factors and enterprise performance, multiple linear regression analysis is conducted by Statistical Product and Service Solutions (SPSS) software.