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.

As the fastest means of transportation in the globe for people, airplanes are receiving more and more attention in the fields of science and engineering. Experts around the world try to figure out methods of increasing safety for airplanes, while it may elicit an ongoing debate on how to explain wing aerodynamics. This essay delves into the intricate world of wing aerodynamics, first presenting an analysis of forces acting on the airplane which could help provide basic knowledge and serve as background information. Three main theories, Bernoulli’s equation, Newton’s third law, and the Coanda effect are analyzed and compared here to get a relatively accurate explanation. By figuring out how wings work to make a plane uplift in the air, the results help improve the design of traditional airliners and increase their stability.

Dynamical systems are crucial for defining our comprehension of the physical world, offering a robust structure for examining and representing intricate occurrences. The exploration of dynamical systems in physics traces back to the initial developments of classical mechanics by Newton and Lagrange. Over time, this framework has developed and grown to encompass a broad array of physical phenomena, ranging from the movement of astronomical objects to the actions of subatomic particles. The close relationship between dynamical systems and physical principles has inspired the study and improvement of this mathematical field. This paper delves into the diverse applications of dynamical systems in physics, emphasizing the research background, methodology, main discoveries, and wider ramifications. This study tries to offer a thorough summary of the diverse impacts of dynamical systems on the area of physics by combining several research papers. By utilizing dynamical systems, researchers have gained a deeper understanding of the fundamental order that governs complex dynamics, paving the way for improved predictions, innovative technologies, and a deeper understanding of the underlying principles that govern the universe.

Thermal management is pivotal in robotics engineering, ensuring optimal performance and reliability of robotic systems. This comprehensive review explores various heat dissipation mechanisms, cooling techniques, and thermal modeling approaches employed in robotics engineering. Key topics include conduction-based, convection-based, and radiation-based heat transfer mechanisms, alongside liquid cooling, air cooling, and phase-change cooling techniques. Analytical thermal models, computational fluid dynamics (CFD) simulations, and finite element analysis (FEA) modeling are discussed for their roles in predicting thermal behaviors and optimizing heat dissipation strategies. By synthesizing these advancements, this review provides valuable insights into enhancing thermal management efficiency and ensuring the longevity of robotic systems.

Taking the joint membership system carried out by two cross-market bilateral platforms as the background, this paper studies how to achieve the optimal cooperation between two cross-market platforms, and analyzes the various influences brought by platform differences. Considering two cross-market two-sided platforms with differences basic services, we establish a horizontal cooperation model for cross-market bilateral platforms based on the joint membership system. Taking cross-network externalities as the starting point of the research, we compare and analyze the platform strategies under decentralized decision making and joint centralized decision making to obtain the benchmark for joint membership cooperation. Finally, we propose a two-part pricing mechanism that can make joint membership cooperation achieve the best, and analyze the impact of basic service differences on platform pricing, user participation, platform profits and coordination mechanism.

Previous studies have analyzed the factors affecting academic performance and concluded that the length of study is related to academic performance. However, there are other factors worth investigating. Data from 500 students were analyzed using the Binary Logistic Regression model. This paper studies the influence of Study Hours and Previous Exam Scores on pass or fail the exam. The results of the likelihood ratio test of the binary Logit regression model show the validity of the model and the significance of the construction of the model. In the Hosmer-Lemeshow fit test, the p-value is greater than 0.05, the model is considered to have good goodness of fit and passes the HL test. Through research, the author finally concludes that Study Hours and Previous exam Scores have a positive impact on passing the exam. Therefore, this paper argues that people can improve the likelihood of passing the exam by increasing their study time before the exam and getting better grades in the previous exam.

As an important parameter of the Earth's ecosystem, ocean temperature has always been a hot research field for scholars, and the rise in ocean temperature caused by global warming is a topic related to the fate of humanity. The prediction of future ocean temperature is of great significance. The ARIMA model, as a typical prediction model, is highly favored by scholars from various countries due to its accuracy and adaptability. In this paper, the ARIMA multiplication model with seasonal effect is used to forecast the trend of ocean temperature change in the next year, and to prediction graph as well as specific reference values are given. The conclusion is as follows: The global average monthly ocean temperature will continue to rise in the next year. Therefore, this article believes that the government should promptly introduce relevant policies to address the rise in ocean temperature caused by global warming, and people should also fulfill their obligations to protect the environment.

The theoretical existence of magnetic monopoles within the framework of electroweak unification and quantum field theories presents one of the most intriguing puzzles in modern physics. This article explores the formation, theoretical implications, and potential experimental signatures of magnetic monopoles emerging from electroweak symmetry breaking. Through a detailed analysis of their theoretical foundation, including Dirac's quantization, monopole solutions in non-Abelian gauge theories, and their role in Grand Unified Theories (GUTs), we delve into the profound implications these entities have for the Standard Model and beyond. We further examine the challenges and prospects of detecting magnetic monopoles through particle accelerator experiments, cosmic ray observations, and their significance in the quest for a unified theory of quantum gravity. Our investigation not only highlights the current state of theoretical and experimental efforts but also underscores the pivotal role magnetic monopoles play in bridging the gap between quantum mechanics and cosmological phenomena, offering insights into the early universe's symmetry-breaking events and the fundamental forces that shape our universe.

This study uses a multiple linear regression model to analyze the key factors affecting second-hand car prices. Using data exploration and regression analysis, 945 samples spanning the years 2019-2024 were analyzed, and four variables were chosen for further examination. In terms of price, these factors include the impact of mileage, the year the vehicle was manufactured, the brand category, and the color. According to the findings, the most important factors that influence price are the number of miles driven and the year the vehicle was manufactured. Additionally, the category of the brand has a significant impact, while the color has a negligible effect on the price. In addition to assisting customers in making more informed choices, the findings of this study can also provide car dealers with valuable insights regarding pricing strategies and inventory management. The findings of this study also revealed that the market for used automobiles is characterized by a significant circulation and a multitude of factors that have an impact. To further refine the existing model, further research could be conducted to take into consideration additional potential influencing factors.

Rare-earth doped fibers are an important means of expanding the wavelength band of optical fibers. Currently, researchers aim to broaden the working wavelength band of optical fibers by doping with different rare-earth elements, thereby increasing the amount of information that can be transmitted. In this paper, a bismuth-doped fiber laser operating around 1300nm was designed. A basic physical model for implementing a bismuth-doped fiber laser was proposed based on the energy levels and transition processes of bismuth, rate, and power propagation equations. It was possible to determine the link between pump power and laser power at a wavelength of 1300 nm by modeling tests using the physical model. Additionally, the relationship between pump light and laser power in bismuth-doped fiber at different positions and propagation directions was analyzed. Suggestions for the future large-scale application of bismuth-doped fiber lasers around the 1300nm wavelength band were provided.

In recent years, laser emitters have developed rapidly, been used in many fields, and have also brought great development to many industries such as communications and medical treatment. Thulium as a rare earth ion has a long service life and laser conversion efficiency, so the study of thulium-doped fiber lasers is of great significance for the development of the laser industry, but there is still a gap in the research in the field of 1900nm thulium-doped fiber lasers, Therefore, this experiment uses the physical model and quantum electric model to study 1900nm thulium-doped fiber lasers. The conclusion that the pump optical power decreases with the increase of distance and the pump optical power increases with the increase of laser power is processed, and the relationship between the pump optical power and the laser power, the relationship between the distance length and the pump optical power and the lasing optical power is shown with images.