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This paper firstly calculates the weights of each system and indicator in the index system through the gray correlation method and comprehensively evaluates the status of the regional rural tourism development and the level of human habitat environment as well as the characteristics of temporal and spatial evolution. Constructing the spatio-temporal coupling and coordination relationship between rural tourism and the human habitat environment reveals the obstacle factors of rural tourism development and human habitat environment development level and the coupling mechanism of the two. Finally, the development process of the rural tourism industry in Kaili, Xingyi, and Zunyi, as well as the improvement and optimization process of the rural habitat environment, are empirically studied. The results show that the coupling coordination degree between the rural tourism development level and the optimization level of human habitat environment in the three regions increased from 0.06 in 2012 to about 0.48 in 2021, indicating that the overall coordination level between the rural tourism development and the optimization of the human habitat environment is continuously improving during the period. This paper is significant for the new path of economic development and habitat-environment coordination in rural areas.

In the context of the new dual-cycle development model, the Long Triangle, as the main development pillar of China's economic development, aims to enhance the quality development level of the digitization and industrialization, and achieve the deep development of the two. Based on the differential equation, this paper presents the problems of the linkage and coordination between digitization and sustainable development of manufacturing in Long Triangle. The countermeasures based on panel data of three provinces and a city in Long Triangle from 2011 to 2019, an index system of quality of digitization and productivity has been established, and spatio-temporal evolution characteristics of joint level and problems in the process of joint coupling are analyzed. The results show that from 2011 to 2019, the level of linkage and coordination between economic digitization and sustainable development of production in Long Triangle region is increasing, but the overall level is not high and the spatial difference is large. There are also significant differences between rank and benign cooperation; The key obstacle factors in each province are both relatively concentrated and different.

The interaction between financial assistance and enterprise development is examined in this paper by constructing a coupled coordination degree model. The weights of the secondary indicators in the financial assistance and enterprise development system are calculated using the entropy weighting method. By calculating the coupling degree between financial assistance and enterprise development, we can judge the strength of the coupling effect between them and the time interval. The financial system and enterprise development evaluation indexes were constructed to explore the factors affecting financial assistance for enterprise development. Under certain conditions, financial support and enterprise development can positively affect each other, as shown in the results. The development support weights in the financial support system are 0.1979 and 0.2231, and the total weight is 0.421. The enterprise development system has a technical weight of 0.5806 for technological innovation.

In this paper, the transfer matrix model was first applied, and the eigenvalues of the matrix were calculated to clarify the cultural nature of tourist attractions. The concatenated form is introduced into the transfer matrix, successfully calculating the matrix’s matching function. The coupled coordinated time-series evolution was then used to derive the comprehensive evaluation index of tourist attractions and cultural and educational properties, and the weights of the indexes’ correlation and difference were analyzed to derive the index entropy value. Finally, the original data are processed by the dimensionless standard, the degree of coupling coordination is evaluated with the help of the coupling concept, and the relative level of coupling is dealt with after the matrix transfer. The analysis found that the highest coupling degree of cultural and educational attributes of tourist attractions in 10 years is 0.7. Therefore, the integration and development of cultural and educational attributes of tourist attractions is the inherent requirement and inevitable result of cultural construction and tourism development and must adhere to the principle of coordinated development of promoting tourism with culture and manifesting culture with tourism.