The Navier-Stocks equation (NSE) was derived based on Newton’s second law and Euler’s equation with the viscosity effect. The continuity of mass, conservation of momentum and energy contribute to the motion of fluid. This paper discusses the hypothesis and theories of the solution of the 3D NSE corresponding to the boundary and initial conditions from previous research. Meanwhile, this paper focuses on the study of solutions and turbulence models of NSE contributed to the applications of aerodynamics. Machine Learning and Neural Networks are applied to the solution of the NSE to improve the accuracy of prediction of fluid motion. Aerodynamics applications on airfoil, turbulence model, design of propeller and ejection seats are discussed with analysis of solutions of Navier-Stocks equation. With the contribution of Machine learning, accurate and global solutions are expected to be computed for the NSE in the future.

This comprehensive article explores the transformative impact of technological innovations in the field of astronomical physics. It delves into key advancements in precision optics, spectroscopy, high-resolution imaging, radio and infrared technologies, space-based observatories, and the exciting prospects that lie ahead. The discussion covers the role of emerging technologies, international collaboration, and ethical considerations in shaping the future of astronomical research. By examining these facets, this article highlights the pivotal synergy between technology and astronomy, driving profound discoveries and enriching our understanding of the cosmos.

Number Theory, the investigation of natural numbers, is a time-honored discipline within Mathematics that has captivated mathematicians over numerous centuries due to its inherent purity. In today's world, a thorough understanding of Number Theory is essential for the advancement of cutting-edge technology, as it is extensively applied in domains such as software engineering and cryptography. The objective of this study is to elucidate the understanding of Number Theory that underlies several composite encryption systems and analyze the advantages and disadvantages of each encryption system through a comprehensive examination of existing literature. The discipline of Number Theory has extensive practical implications in cryptography and holds the promise of being increasingly employed in various domains in the future. By elucidating the role of Number Theory in various encryption systems, the fundamental nature of encryption can be enhanced, hence fostering the emergence of novel methodologies or approaches in information security.

The background of the research field on the design of assessment algorithms and models for Chinese spoken language teaching based on natural language processing and knowledge graph mainly involves two aspects: one is the growing global demand for learning Chinese, and the other is the potential application of advanced computing technology in language learning. The significance of this research lies in providing a more scientific and systematic assessment method for Chinese teaching through this system, and, on a macro level, paving the way for the future development of language learning technologies. Through this study, not only can teachers better guide students’ learning, but students can also receive more effective learning feedback and guidance. Experimental data shows that the accuracy rate of the Chinese spoken language teaching assessment algorithm system based on natural language processing and knowledge graph is 98.05%, and the satisfaction rate for personalized teaching evaluation reaches 98.12%. In summary, this research provides new methods and approaches for the personalization and technologization of Chinese spoken language teaching, thus having a profound impact on the field of language education.

This paper provides a comprehensive overview of the fundamental principles and implications of quantum mechanics, general relativity, and string theory, focusing on their role in shaping our understanding of the universe. We delve into quantum mechanics through wave-particle duality, quantum entanglement, and the measurement problem, highlighting the probabilistic nature of reality and the challenges of observer-dependent phenomena. In exploring general relativity, we examine the curvature of space-time, black holes, singularities, and gravitational waves, showcasing the theory's impact on our perception of gravity and the cosmos. String theory is discussed as a unifying framework, with emphasis on its basics, the necessity of extra dimensions, and the landscape of possible universes it predicts. This paper aims to bridge complex theoretical concepts with observational evidence and technological advancements, offering insights into the ongoing quest to understand the fabric of the universe

Recently, the Japanese government unilaterally discharged tens of thousands of tons of contaminated nuclear water into the ocean. Analyzing the spread of nuclear-contaminated water to determine its impact on the environment is a top priority. In this paper, a nuclear wastewater diffusion model is established by using cellular automata, which can be used to simulate the process of nuclear wastewater diffusion in a specific sea area. The proliferation of nuclear contaminated water off the coast of Japan is predicted and visualized. For complex sea states, the quasi-true reliability of cellular automata is improved by dividing the sea area. At the same time, the algorithm of the model is optimized to predict the time of nuclear sewage pollution in the main sea area and the most polluted sea area in the world.

This paper examines the intricate relationship between economic theories, trade policies, and diplomatic engagements in the context of international relations. Utilizing theoretical frameworks such as the theory of comparative advantage and the Heckscher-Ohlin model, we analyze the foundational principles guiding global trade and policy-making. We explore the role of probabilistic models, including Bayesian statistics and regression analysis, in forecasting economic trends and their implications for international relations. Furthermore, we investigate the impact of trade policies, including tariffs, non-tariff barriers, and global trade agreements, on economic dynamics and diplomatic interactions. Through case studies of economic sanctions, we assess the effectiveness of sanctions as a diplomatic tool and propose policy recommendations for their optimal implementation. Our analysis highlights the complexity of economic diplomacy and underscores the importance of quantitative analysis in informing policy decisions and fostering international cooperation.

This study employs molecular simulation techniques, particularly the Brownian motion model, to investigate the influence of temperature on diffusion coefficients. Leveraging Einstein’s relationship for calculating diffusion coefficients and a one-dimensional random walk model, we systematically explore the impact of simulation direction, particle quantity, and simulation duration on diffusion behavior. The research extends its scope to three-dimensional Brownian motion simulations, offering insights into the stochastic motion of particles in a fluid. The primary objective is to analyze the relationship between temperature and diffusion coefficients. Through rigorous linear regression analysis, a significant and strong linear association is identified, demonstrating that an increase in temperature correlates with an increase in the diffusion coefficient. The research not only contributes to the fundamental understanding of molecular motion but also provides practical recommendations for simulation parameters, especially in resource-constrained computational environments. The study acknowledges certain limitations in the current Brownian motion algorithm and proposes avenues for future research to enhance computational efficiency and precision. This abstract encapsulates the key methodologies, findings, and implications of the research, laying the foundation for a comprehensive exploration of temperature-dependent diffusion coefficients in molecular systems.

Industry 4.0 technology has transformed human-robot interaction in robot-assisted rehabilitation therapy. However, most current studies focus on the patient’s perceived “motor participation”. Few studies have systematically reviewed the patient’s experience, including their psychological involvement, perception, experience, and judgment of the rehabilitation environment, therapist, and robot, as well as examining the coupling of “mental participation” and “motor participation”. This paper presents a systematic study and literature review from the perspective of the embodied experience of patients, utilizing a combination of the scoping review, performance analysis, science mapping, and bibliometrics analysis to examine relevant literature. The result emphasizes the significance and necessity of the patient’s embodied experience in robot-assisted rehabilitation training therapy. Most research in this field is founded on embodied theory and embodied technology. This study provides an essential theoretical reference for the study of embodied experience in robot-assisted rehabilitation therapy, helping to improve theoretical and practical approaches to improve the users’ embodied experience and aid user experience research and design in related research institutions and businesses.

The revolutionary influence of wearable electronics on health monitoring is highlighted in this research. It explores the critical dimensions and components of wearable electronics. It investigates how sensors may be integrated for noninvasive techniques like sweat analysis to analyze biochemical indicators like glucose and electrolyte levels and vital signs in real-time. The research emphasizes how crucial it is to consider user comfort, data security, device sensitivity, and stability while creating wearable health monitoring. It concludes with the promise of these devices to support large-scale health research and individualized health management. It also addresses the difficulties in sensor integration, data accuracy, and power management.