Competency-based education is one of the many important educational objectives in the cultivation of senior vocational talents. In the past education model, the importance of achievement is greater than ability. Teachers rely on the scores of test papers to classify students' grades. Competency-based education has changed this situation very well, paying special attention to students' ability training. This paper mainly studies how to better promote the reform and innovation of English teaching in higher vocational colleges and strengthen students' learning ability and vocational skills while ensuring students' ability development.

Since the proposal of the low-carbon economy plan, all countries have deeply realized that the economic model of high energy and high emission poses a threat to human life. Therefore, in order to enable the economy to have a longer-term development and comply with international low-carbon policies, enterprises need to speed up the transformation from a high-carbon to a low-carbon economy. Unfortunately, due to the massive volume of data, developing a low-carbon economic enterprise management model might be challenging, and there is no way to get more precise forecast data. This study tackles the challenge of developing a low-carbon enterprise management mode based on the grey digital paradigm, with the aim of finding solutions to these issues. This paper adopts the method of grey digital model, analyzes the strategy of the enterprise to build the model, and makes a comparative experiment on the accuracy and performance of the model in this paper. The results show that the values of MAPE, MSE and MAE of the model in this paper are the lowest. And the r^2 of the model in this paper is also the highest. The MAPE value of the model in this paper is 0.275, the MSE is 0.001, and the MAE is 0.003. These three indicators are much lower than other models, indicating that the model has high prediction accuracy. r² is 0.9997, which is much higher than other models, indicating that the performance of this model is superior. With the support of this model, the efficiency of building an enterprise model has been effectively improved. As a result, developing an enterprise management model for the low-carbon economy based on the gray numerical model can offer businesses new perspectives into how to quicken the shift to the low-carbon economy.

The implementation of the "the Belt and Road" requires the common development of the "five links" of policies, facilities, trade, finance and popular support, among which "people to people connectivity" is the premise of the coordinated promotion of the "five links", and cultural communication, exchange and cooperation are the foundation and guarantee of the popular support project. The "the Belt and Road" cultural communication, exchange and cooperation are diverse in content and form. We need to identify the opportunities and challenges we face, make long-term strategic plans, and take practical countermeasures and implementation paths according to the characteristics of cultural communication diversity. Some domestic scholars have conducted research on cultural communication strategies and analyzed the opportunities and challenges they face, but there is a lack of diversity analysis on the forms of communication that should be adopted. This paper explores and studies the "the Belt and Road" cultural communication strategy, implementation path and safeguard measures, constructs a new model of diversified cultural communication and exchange cooperation, and tries to play a certain role in promoting the actual effect of cultural communication and exchange cooperation and better safeguarding the "the Belt and Road" community of interests.