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 reform of the training mode for English majors in the context of the new liberal arts is a dynamic process that conforms to social needs, continuously improves and optimizes. After a series of special investigations, this article proposes development ideas for the cultivation of English majors in local applied undergraduate universities based on the analysis of the demand for English majors' abilities in the job market. The aim is to solve the problems of unclear characteristics of English major talent cultivation in local applied undergraduate universities and weak competitiveness of graduates in employment.

Application-oriented universities play a vital role in transporting application-oriented talent to regional industries and industries. In this paper, we discuss the significance and path of building experimental centers for economic management in application-oriented universities and highlight their role in student learning, school-business cooperation and social development. At the same time, it summarizes the problems found during the construction of the experimental center at case University and suggests some improvements, which serve as a reference for the construction of economic management experimental centers at similar universities.