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.

In China, ideological and political education is currently the hot direction of teaching reform in various colleges and universities, yet the development of appropriate teaching evaluation methods needs to catch up. This study addresses the pressing need for a preliminary investigation into the complex relationships among ideological and political education, the students’ learning satisfaction and teaching quality. This research examines the influence of teaching and ideological and political education quality on students’ satisfactions by designing a set of scales, collecting about 3800 questionnaires. Utilizing Structural Equation Modeling (SEM) and qualitative interviews, this study reveals that the teaching quality directly affects students’ learning satisfaction and ideological and political education. Notably, ideological and political education can also affect students’ learning satisfaction. The findings underscore the importance of including ideological and political education assessments in evaluating courses. This research contributes to the ongoing dialogue on effective teaching evaluation methods in the context of evolving educational practices.

This research explores the implementation of streamlined licensing frameworks and consolidated procedures for promoting renewable energy generation worldwide. An in-depth analysis of the challenges faced by renewable energy developers and the corresponding solutions was identified through a series of industry interviews. The study aims to shed light on the key barriers encountered during project development and implementation, as well as the strategies employed to overcome these obstacles. By conducting interviews with professionals from the renewable energy sector, the research uncovers a range of common challenges, including complex permitting processes, regulatory uncertainties, grid integration issues, and financial barriers. These challenges often lead to project delays, increased costs, and limited investment opportunities, thereby hindering the growth of renewable energy generation. However, the interviews also reveal various solutions and best practices employed by industry stakeholders to address these challenges effectively. These solutions encompass the implementation of streamlined licensing procedures, such as single licenses and one-stop services, to simplify and expedite the permitting process. Additionally, the development of clear and stable regulatory frameworks, collaboration between public and private entities, and improved grid infrastructure were identified as key strategies to overcome regulatory and grid integration challenges. The research findings highlight the importance of collaborative efforts between policymakers, industry players, and other relevant stakeholders to create an enabling environment for renewable energy development. By incorporating the identified solutions and best practices, policymakers can streamline regulatory processes, foster public-private partnerships, and enhance grid infrastructure, thus catalyzing the growth of renewable energy projects.

The aim of the present study was to determine the effects of single and mixed infections of nematode (Meloidogyne javanica), fungus (Fusarium oxysporum) and bacterium (Xanthomonas axonopodis) on nodulation and pathological parameters of Bambara groundnut (Vigna subterrenea (L.) Verdc.) in field condition. Nematode infested field was used while other pathogens were obtained from diseased plants. The Randomized Complete Block Design (RCBD) was adopted in a 5 × 9 × 5 factorial design (5 blocks, 9 treatments and 5 replicates per treatments) resulting in 225 experimental units. In each experimental unit, three seeds were sown to a depth of 5cm and thinned to one plant per planting hole after germination at day 7. Treatments were inoculated into test plant following standard methods. As a result, the control treatment recorded the highest number of nodules (64.0 ± 6.91), followed by bacterium (45.2 ± 5.11) while N + F + B had the lowest number of root nodules (23.4 ± 2.42). Simultaneous treatment (N + F + B) gave the highest percentage reduction in nodulation (63.44%), followed by treatment N + F7 (56.25%). Fungus treatment recorded the highest mean wilted plants (3.8 + 0.20) followed by N + F7 treatment (3.40 + 0.40). Gall formation in the nematode treatment increased proportionately by 56.33% as the highest recorded, followed by treatment N + F7 with 50.0%. Treatment N + F7 had the highest reproduction factor (Rf) value of 9.30 followed by nematode (8.30), N + B7 (7.40), N + F + B (6.80) and N + F14 (6.50). Zero (0) Rf value was recorded in fungus, bacterium and control treatments. The observed differences in nodulation and pathological parameters among the treatments are significant (P < 0.05). The data provided in this work is important in the control of the three pathogens affecting the productivity of Bambara nut. Formulation of a single protectant should be designed to have potent effects on the three pathogens to achieve effective protection and good production of Bambara nut.

This study explores the intricate relationship between family functioning, emotional bonding, parent-child contact, and academic success among students through a serial mediation analysis. The research, conducted on a sample of 200 participants, sheds light on the indirect pathways through which family dynamics influence academic achievements, emphasizing the significance of emotional connections and parent-child interactions. The findings affirm the positive association between family functioning and academic achievement, in alignment with prior research. Additionally, the study identifies parent-child bonds and contact as partial mediators in this relationship, reinforcing previous findings. A noteworthy discovery is the full complementary sequential mediation effect, revealing that family functioning’s influence on academic success becomes substantial when emotional bonds foster increased parent-child contact. In conclusion, this research underscores the importance of emotional bonds and parent-child contact as sequential mediators, emphasizing their role in translating family dynamics into academic achievements among students. While providing valuable insights, the study acknowledges limitations such as sample size, potential sampling bias, self-reported measures, and a cross-sectional design. Addressing these limitations and expanding the scope of outcomes in future research will contribute to a more comprehensive understanding of the complex dynamics within family and educational institutions relationships and their profound impacts on students’ academic success.

In contemporary English teaching in primary and secondary schools, good use of modern educational technology can greatly improve the efficiency of teachers' teaching and students' learning, especially during the epidemic period, the application of educational technology in teaching has become an indispensable topic. As the guider of students, teachers should have more mature modern education concepts, master various advanced teaching technologies, prevent the use of "formalism" in educational technology, and ensure that network resources can have a positive impact on students' learning efficiency and effect. This paper adopts the methods of field investigation, interview and literature analysis to investigate and study the current situation of the application of modern educational technology in English teaching in Jinhe Middle School in Genhe City, analyze the existing problems, and propose targeted solutions, in order to effectively apply modern educational technology in Jinhe Middle School and improve its English teaching efficiency and effect.