With the continuous practice of the “Belt and Road” initiative, the countries along the “Belt and Road” have achieved rapid social and economic development. However, environmental problems have become increasingly prominent. Around the world, there are comments that China’s “Belt and Road” initiative is a result of resource plundering, transfer of backward production capacity, and environmental degradation of countries along the line. This study quantitatively evaluated the static, dynamic, linear, and non-linear effects of China’s foreign direct investment on the carbon emissions of countries along the line. The results showed that: (1) The direct effect of China’s foreign direct investment on the carbon emissions of countries along the route was significantly negative. (2) The economic scale and industrial structure effects of China’s foreign direct investment increased the carbon emissions of countries along the route. The production technology effect suppressed the carbon emissions of countries along the route and played a leading role. (3) The estimation results of the system generalized method of moments showed that the carbon emissions of countries along the route were significantly affected by the lag period, but the impact was small. (4) The results of the threshold regressive model showed that the GDP and proportion of industrial added value had significant threshold effects on the carbon emissions effect of China’s outward foreign direct investment. When the GDP of countries along the route exceeded 7.2696, China’s outward foreign direct investment carbon emissions reduction effect could not be realized; when the proportion of the industrial added value of countries along the route was lower than 4.0106, China’s outward foreign direct investment carbon emission reduction effect could not be realized. Based on the research conclusion, we concluded that China and countries along the “Belt and Road” should strengthen cooperation on carbon emissions reduction, jointly promote low-carbon construction of industrial parks, accelerate cooperation on green energy projects, and establish a green development fund to achieve sustainable development of the countries along the “Belt and Road”.

There is a large gap between China’s urban and rural income. The urban rural income disparity (URID) is particularly prominent. This paper deeply studies the interaction between sustainable urbanization (SU) and the URID in China by taking the construction of a new urbanization plan with Chinese characteristics suggested in China’s 14th Five-Year Plan as the research background. Firstly, the paper puts forward the hypothesis of an inverted U-shape between SU and the URID through impact path analysis. Secondly, a nonlinear panel regression model (NPRM) and a threshold regression model (TRM) are constructed to test the hypothesis. Research findings: (1) The NPRM shows that the quadratic coefficient is significant and negative, so the assumption is true, and an inverted U-shaped relationship exists. (2) The result of the TRM shows that SU passes the single threshold test, and the hypothesis of a U-shaped relationship is tenable. (3) Economic development has narrowed the URID; economic openness and road network construction have increased the URID; education has no significant impact on the URID.

This article is concerned with the bipartite flocking problem in multi-agent systems. Our contributions can be summarized as follows. Firstly, a class of preassigned-time consensus protocols is proposed to solve the issue of multi-agent systems. Secondly, with the aid of the symmetric properties of the graph theory and the Lyapunov stability theorem, we prove that agents can be divided into two disjointed clusters in a finite time, and they move to opposite directions at the same magnitude and speed. The protocol is novel among existing fixed/finite-time protocols in that the associated settling time is a preassigned constant and a parameter of the protocol. Moreover, it is proven that the diameters of the clusters are bounded and independent of other the protocol parameters. These results are demonstrated through both theoretical analysis and simulation examples.