The Method of Discretization in Time (MDT) is a hybrid numerical technique intended to alleviate upfront the computational procedure of timedependent partial differential equations of parabolic type upfront. The MDT engenders a sequence of adjoint second order ordinary differential equations, wherein the space coordinate is the independent variable and time becomes an embedded parameter. Essentially, the adjoint second order ordinary differential equations are considered of “quasistationary” nature. In this work, the MDT is used for the analysis of unsteady heat conduction in regular bodies (large wall, long cylinder and sphere) accounting for nearly constant thermophysical properties, uniform initial temperature and surface heat flux. In engineering applications, the surface heat flux is customarily provided by electrical heating, radiative heating and pool fire heating. It is demonstrated that the approximate, semianalytical temperature solutions of the first adjoint “quasistationary” heat conduction equations using the first time jump are easily obtainable for each regular body. For enhanced acccuracy, regression analysis is applied to the deviations of the dimensionless surface temperature as a function of the dimensionless time for each regular body.

Three-dimensionally cross-linked polymer nanocomposite networks coated nano sand light-weight proppants (LWPs) were successfully prepared via ball-milling the macro sand and subsequently modifying the resultant nano sand with sequential polymer nanocomposite coating. The modified nano sand proppants had good sphericity and roundness. Thermal analyses showed that the samples can withstand up to 411 ℃. Moreover, the proppant samples’ specific gravity (S.G.) was 1.02–1.10 g/cm³ with excellent water dispersibility. Therefore, cross-linked polymer nanocomposite networks coated nano sand particles can act as potential candidates as water-carrying proppants for hydraulic fracturing operations.

In the dynamic landscape of modern education, it is essential to understand and recognize the psychological habits that underpin students’ learning processes. These habits play a crucial role in shaping students’ learning outcomes, motivation, and overall educational experiences. This paper shifts the focus towards a more nuanced exploration of these psychological habits in learning, particularly among secondary school students. We propose an innovative assessment model that integrates multimodal data analysis with the quality function deployment theory and the subjective-objective assignment method. This model employs the G-1-entropy value method for an objective evaluation of students’ psychological learning habits. The G-1-entropy method stands out for its comprehensive, objective, and practical approach, offering valuable insights into students’ learning behaviors. By applying this method to assess the psychological aspects of learning, this study contributes to educational research and informs educational reforms. It provides a robust framework for understanding students’ learning habits, thereby aiding in the development of targeted educational strategies. The findings of this study offer strategic directions for educational management, teacher training, and curriculum development. This research not only advances theoretical knowledge in the field of educational psychology but also has practical implications for enhancing the quality of education. It serves as a scientific foundation for educators, administrators, and policymakers in shaping effective educational practices.

The effective allocation of resources within police patrol departments is crucial for maintaining public safety and operational efficiency. Traditional methods often fail to account for uncertainties and variabilities in police operations, such as fluctuating crime rates and dynamic response requirements. This study introduces a fuzzy multi-state network (FMSN) model to evaluate the reliability of resource allocation in police patrol departments. The model captures the complexities and uncertainties of patrol operations using fuzzy logic, providing a nuanced assessment of system reliability. Virtual data were generated to simulate various patrol scenarios. The model’s performance was analyzed under different configurations and parameter settings. Results show that resource sharing and redundancy significantly enhance system reliability. Sensitivity analysis highlights critical factors affecting reliability, offering valuable insights for optimizing resource management strategies in police organizations. This research provides a robust framework for improving the effectiveness and efficiency of police patrol operations under conditions of uncertainty.

Healthcare mobile applications satisfy different aims by frequently exploiting the built-in features found in smart devices. The accessibility of cloud computing upgrades the extra room, whereby substances can be stored on external servers and obtained directly from mobile devices. In this study, we use cloud computing in the mobile healthcare model to reduce the waste of time in crisis healthcare once an accident occurs and the patient operates the application. Then, the mobile application determines the patient’s location and allows him to book the closest medical center or expert in some crisis cases. Once the patient makes a reservation, he will request help from the medical center. This process includes pre-registering a patient online at a medical center to save time on patient registration. The E-Health model allows patients to review their data and the experiences of each specialist or medical center, book appointments, and seek medical advice.

The profound impact of China's concept of healthy development on various fields of society has influenced the mode of university education, and has gradually undergone changes in actual teaching modes, ways of thinking, and technologies. As one of the important educational courses in universities and sports departments, the reasonable introduction and implementation of functional training models in practical guidance can deepen students' learning of basic dance and skills, and further improve the performance of the dance stage. As a mentor, teachers should play the role of functional guidance essentials based on students' differentiated training abilities, optimize educational content from students' physical function training, and make adjustments. The professional functional training method is adopted to establish the practical application and promotion of functional training in university physical education.