Currently, there is a significant gap between the training objectives and the actual situation of electromechanical talents in higher vocational colleges. Many teachers in electromechanical departments do not meet the required qualifications and are unable to adapt to the developments of the new era. The talent training mode is insufficiently comprehensive, and the criteria for talent assessment are not unified. In response to these issues, it is necessary to promptly change the mindset, innovate educational ideas, focus on the present while planning for the future, clarify training objectives, adopt a dual education model that integrates production and education, strengthen the faculty, utilize their potential, and improve the overall educational quality to provide guarantees for talent development.

The work is devoted to the numerical solution of the initial boundary value problem for the heat equation with a fractional Riesz derivative. Explicit and implicit difference schemes are constructed that approximate the boundary value problem for the heat equation with a fractional Riesz derivative with respect to the coordinate. In the case of an explicit difference scheme, a condition is obtained for the time step at which the difference scheme converges. For an implicit difference scheme, a theorem on unconditional convergence is proved. An example of a numerical calculation using an implicit difference scheme is given. It has been established that when passing to a fractional derivative, the process of heat propagation slows down.

The cultivation of sugar beet (Beta vulgaris L.) for table or horticultural purposes is largely carried out in the conventional way which is characterized by intense mechanization causing soil degradation and high labor costs. New cultivation techniques are being employed in the production of vegetables aiming to ensure improvements in environmental and economic conditions, such as the no-till farming system. Thus, the objective of this work was to evaluate the vegetable classification and physicochemical characteristics of beets from different corn planting densities. The experiment was conducted in the period from October 2018 to June 2019 in the municipality of Nova Laranjeiras (PR). Corn was used as a cover plant and the vegetable used was beet cultivar Early Wonder Tall Top. The experimental design used was in interspersed blocks in unifactorial scheme (corn densities 40, 60, 80, 100 thousand plants/ha and control) with four blocks, with plots 3.60 m long and 1.20 m wide. The parameters evaluated 60 days after planting were: commercial classification (class, group, subgroup, category), length, diameter, mass, pulp firmness, soluble solids, titratable acidity, pH and ratio, phenolic compounds. Of which the variables that were not significant at 0.5 probability were length, category (defects), firmness, subgroup (flesh color), soluble solids and phenolic compounds. It is concluded that high densities of corn as mulch for SPDH of sugar beet crop negatively affect the grade and physicochemical characterization of the products.

This study investigated the influence of infrastructure spending, government debt, and inflation on GDP in South Africa from 1995 to 2023. Motivated by the need for sustainable growth amid fiscal and inflationary pressures, this research addresses gaps in understanding how these factors shape economic performance. The primary objective was to assess these variables’ individual and combined effects on GDP and offer policy recommendations. Using an ARDL model, the study explored long- and short-term relationships among the variables. Results indicate that infrastructure spending positively impacts GDP, promoting long-term growth, while government debt hinders GDP in both short and long runs. Moderate inflation supports growth, but excessive inflation poses risks. These findings imply the need for targeted infrastructure investments, strict debt management practices, and inflation control measures to sustain economic stability and growth. Policy recommendations include expanding public investment in productive infrastructure, implementing fiscal rules to prevent unsustainable debt levels, and maintaining inflation within a controlled range. Ultimately, these policies could help South Africa build a resilient, balanced economy that addresses both immediate growth needs and long-term stability.

This article scrutinizes the multifaceted challenges inherent in intergovernmental coordination across various sectors, with a particular emphasis on sustainable development and entrepreneurial activity within the Republic of Moldova. It argues that despite the existence of intergovernmental cooperation, it often manifests as deficient, contradictory, incomplete, and inefficient. Through a meticulous analysis, this study delineates the roles of pertinent authorities and institutions in fostering the sustainable development of entrepreneurial activities, identifying critical inter-institutional coordination issues and challenges. The discourse extends to examining institutional processes and the extent to which policies, laws, and international standards are implemented to nurture and sustain business activities. Moreover, the paper explores various strategies to cultivate responsible, transparent, and effective dialogue between institutions, thereby promoting innovative practices, expanding cooperation, and fostering partnerships with national and civil society organizations, including international bodies.

The "chain length system" is a breakthrough attempt made to adapt to the needs of industrial management under the new development pattern of dual circulation and its industrial policy form. The cultivation of cross-border e-commerce talents in vocational colleges has received much attention. Currently, there are still many problems in the construction and teaching mode of cross-border e-commerce courses in vocational colleges, which are highlighted as the disconnection between course offerings and industry needs, low practical value of course content, low professional literacy of graduates, and inability of graduates to handle practical work. Therefore, it is crucial to construct and innovate a golden course for the development of cross-border e-commerce careers in the new era, focus on strengthening and supplementing the cross-border e-commerce talent chain, and open up the "last mile" of the cross-border e-commerce talent chain, so as to  improve the specifications and quality of talent cultivation. Starting from the pain points and difficulties of industry enterprise demand, curriculum teaching patterns, characteristics, and main contradictions as breakthrough points, we will carry out the construction of golden courses, using "task driven", "module teaching", "project teaching", "project incubation", "achievement recognition", and "point exchange" throughout the entire teaching process, in order to enhance the core competitiveness of cross-border e-commerce talents and serve the chain leader system in the Guangdong Hong Kong Macao Greater Bay Area.