This paper undertakes a historical investigation of the separate and independent development of calculus by Isaac Newton and Gottfried Leibniz in the late 17th century. Through analysis of primary sources and historiographical perspectives, it explores the differences in notation, methods, and applications used by each mathematician to formulate foundational concepts of calculus. The research demonstrates that Newton relied more on geometric intuition, developing calculus concepts like fluxions and fluents rooted in kinematic problems. His 1687 Philosophiae Naturalis Principia Mathematica synthesized many calculus innovations. Meanwhile, Leibniz approached calculus from an algebraic mindset, utilizing infinitesimal differentials and comprehensively explaining integral and differential calculus in publications like Nova Methodus pro Maximis et Minimis. Evaluation of letters and documents from the 1670s and 1680s shows no direct collaboration or communication about calculus between Newton and Leibniz. This lack of transmission, coupled with the disparities in their notation and calculus techniques, provides evidence for independent creation. However, Newton and Leibniz shared key insights regarding rates of change, derivatives and integrals, hinting at a broader zeitgeist in early modern mathematics and science. Thus, this dual achievement illustrates how the Scientific Revolution facilitated conceptual convergence despite geographic separation between great thinkers. Investigating this case study offers perspective on the interplay between individual genius and wider social contexts in driving scientific progress. This paper concludes by assessing the legacy of the Newton-Leibniz debate over priority and analyzing work that paved the way for modern unified calculus notation and applications.

In the vast cosmos, the enigmatic interplay of black holes and gravitational waves unfolds as a mesmerizing narrative, offering profound insights into the universe’s deepest mysteries. This paper delves into the intricate relationship between these cosmic phenomena, exploring their formation, properties, and their transformative implications in the realm of astrophysics. As colossal black holes merge, they generate gravitational waves that carry signatures of their masses, spins, and orientations. These waves, harnessed through advanced detectors like LIGO and Virgo, present a new dimension of cosmic exploration, unveiling the intricate dynamics of the universe’s most energetic events. Through the lens of gravitational wave astronomy, the author embarks on a journey to decipher gravity’s elegant dance with spacetime, testing the fundamental principles of general relativity and pushing the boundaries of people’s understanding. This paper weaves an intricate tapestry from the cosmic threads of black holes and gravitational waves, inviting people to unravel the universe’s most profound enigmas and redefine people’s cosmic narrative.

Natural resources are becoming more and more scarce while pollution continues to increase. It is imperative to reduce emissions and improve energy efficiency. As an efficient, low-emission machine, the Stirling engine may be an answer on the road to emission reduction and improved efficiency. Stirling engine has been used in some areas, such as nuclear-powered submarine engines, combined heat and power and Stirling cryocoolers. However, there are still several problems that cannot be ignored in Sterling generators themselves. Stirling generators, characterized by high efficiency and potential for reducing greenhouse gas emissions, face challenges, including high material and assembly costs, complex waste heat treatment processes, and the need for durable, high-temperature resistant materials. Despite current limitations, ongoing research aims to enhance conversion efficiency, minimize size, and lower manufacturing costs, with promising applications in various sectors, including transportation and household energy, representing a significant stride towards green energy power generation in the future.

Due to the rapid development of semiconductor technology, the edges of electronic devices are getting smaller and the power consumption is getting lower and lower 3-op-amp instrumentation amplifier. However, there are still some problems such as excessive power consumption and noise. First, the disadvantages are identified, and then the shortcomings of the specialty are improved. So this design gives a low noise ECG equipment, which shows great performance in reducing noise to 3.94uV and the highest differential gain reaches 36.508376dB. It can be used in watches and other wearable devices for ECG signal detection. At the same time, this project can complete the required requirements and is suitable for some wearable devices. Its successful research could lead to more accurate ECG monitoring and consume less power in wearable devices. More importantly, its emergence brings new development ideas and development directions to ECG equipment, making ECG monitoring convenient and mobile.

In this paper, we delve deeply into the intricacies of linear algebra, with a focus on the progression from finite to infinite-dimensional vector spaces. Starting with the foundational concepts, we define vectors, vector spaces, linear combinations, and basis. The importance of infinite-dimensional vector spaces is emphasized, particularly their role in better understanding and modeling complex mathematical phenomena. Through well-illustrated examples, we guide the reader on how to validate if a given set can be classified as a vector space. Additionally, the methodology to identify bases for these vast spaces is discussed in detail. Reduction methods also play an important role in determining bases for infinite-dimensional spaces. In our conclusion, we reflect on the evolution from basic vector concepts to the more nuanced understanding of infinite dimensions. This progression not only deepens our understanding of vectors but also sets the stage for advanced investigations into linear relationships and transformations. By bridging the gap between elementary vector knowledge and advanced infinite-dimensional spaces, this paper makes a notable contribution to the ever-evolving field of linear algebra, serving as a valuable resource for both students and practitioners.

This research delves into an analysis of lung, bronchus, and trachea cancer rates in the United States across genders. Employing the data spanning seven decades (1950-2020) sourced from the Our World in Data website, the study leverages time series modeling techniques, ARIMA and ETS models. The ARIMA methodology initiates with an assessment of data stationarity, followed by differencing procedures to transform the dataset into a non-stationary data. Subsequently, Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots are examined. Last, the ARIMA model is fitted to dissect the mortality rates among males and females. Simultaneously, the ETS model is directly applied to the mortality data of both genders. The components of the ETS model and the check residuals for ETS are delineated. The outcomes reveal the trends: both genders exhibit a discernible decline in lung, bronchus, and trachea cancer death rates over the period. Despite this downward trajectory, the persistent mortality rates underscore the gravity of the issue. This paper advocates for a heightened focus on lung-related cancers. Understanding and addressing these mortality rates are imperative.

Dynamic models have been widely cited in predicting criminal population, residential electricity consumption, food prices and other objects. However, for total population predictions, dynamic models are rarely used. In this study, we will analyse the relationship between 13 variables such as CPI, grain prices, and medical expenditures and the total population of the United States, then combine it with the ARIMA model to generate a time series dynamic regression model. The conclusion is that, according to the parameters of the final model, two predictors (CPI and the number of crimes) and one interaction term (the product of the poverty rate and unemployment rate) are significantly related to changes in the population. Ultimately, the model performed well on the test set and was remarkably accurate for population prediction five years later. This report screens various factors influencing the total population and provides a broader background for applying dynamic models. In addition, this study also provides directions for subsequent research on more efficient dynamic models.

Immigration is a very important link in the current international society. This paper will study and predict the net immigration of the United States and the Central African Republic through two different models- drift model and ARIMA model, and to further explore the trends and influencing factors of migration between these countries. The results show that from 1960 to 2021, net migration from the United States and the Central African Republic showed very different trends. The United States, as a developed country, attracts a large number of immigrants from all over the world, while the Central African Republic, as a developing country, the flow of immigrants is mainly affected by economic, political and social factors in the region. Therefore, it can be seen that developing countries and developed countries have different impacts on the number of immigrants. This study provides a basis for further understanding of population migration and net migration of United States and Central African Republic.

Cancer is not only a highly detrimental disease but also a particularly grave health concern. Moreover, the current incidence and mortality rates in our country are far from encouraging, making the prevention and control situation very challenging. Therefore, identifying the most scientific and effective treatment methods has become one of our primary research focuses. This paper, building upon previous models and incorporating resistance factors, categorizes tumor cells into those that are sensitive to chemotherapy drugs and those that become resistant. Using MATLAB, we have adjusted various sensitivity parameters in the model to simulate the number of tumor cells over 40 days. This simulation aims to analyze the sensitivity levels of tumor cells to different parameters upon the inclusion of resistance factors. The initial data used for the simulation were derived from the original paper. Ultimately, our findings indicate that tumor cells are most sensitive to the chemotherapy drug’s killing rate for normal tumor cells and the decay rate of the chemotherapy drug. Due to the drug resistance factor, the sensitivity of different parameters is influenced. For parameters related to chemotherapy drugs, the final results, when incorporating this factor, may deviate significantly from those of previous models without this factor. For instance, the decay rate of chemotherapy drugs might result in a larger total number of tumor cells or a steeper trend compared to previous findings.

Predicting stock prices has long been a subject of keen interest due to its financial implications and inherent complexity. The examination of existing literature suggests the need for a focused study encompassing a diverse spectrum of stocks within a specific sector. In this research, the author evaluates the efficacy of the AutoRegressive Integrated Moving Average (ARIMA) model in forecasting Google’s stock performance. The data used in this paper comes from the Chinese corn market price of 2018 to October 2023. The selection of the ARIMA model is based on its widespread acceptance and straightforward nature. This paper also explores how the accuracy of predictions is influenced by various historical data points. Simultaneously, the projections indicate that Google’s stock is poised for continued growth in the upcoming weeks. This investigation aims to provide valuable insights into the stock market’s behaviour, particularly within the context of Google, by leveraging the ARIMA model’s capabilities.

In recent years, face recognition technology has become a significant advance in the area of biometrics and machine vision. It paves the way for a wide range of applications, including security systems, access control, surveillance, and user authentication. These applications are undoubtedly a major innovation in the field of UAV, which will greatly expand and extend its application scenarios. This paper shows a compositive review of UAV facial identification technology, including its basic principles, techniques, challenges, and ethical considerations. According to the different stages, this paper focuses on RCNN and YOLO, two more widely used target detection technologies and their respective technical iterations, and through the comparison of the two in terms of technical characteristics and application scenarios, the advantages of the two are obtained, and combined with the current UAV workflow. Get the stage in which they play a specific role. This paper reviews the existing literature and research on face recognition, aiming to help people better understand the current process of this technology and its wider social application and impact.

Most recently, the technology of unmanned vehicles/systems (UVs/USs) has experienced substantial growth. These vehicles can operate on land, in water as well as and even through the air. They have become increasingly important in various civil applications, incorporating surveillance, precise farming, imagery collection, and search and rescue operations, surpassing manned systems in many aspects. Increased mission safety and cheaper operating expenses are provided by unmanned vehicles. UAVs, often known as unmanned aerial vehicles, are one of them that are widely utilized in construction projects because of its benefits including low costs for upkeep, simple deployment, the capacity to hover, and outstanding mobility. The most significant challenge facing the application of drones is their endurance, especially in harsh and windy weather conditions where drones consume power at a faster rate. In this paper, this work explores improvements in drone endurance through lightweight material design, battery enhancements, and path planning by studying and organizing relevant literature from various authors. These advancements aim to effectively extend the flight time of drones, thereby enabling them to successfully complete missions.

First-person shooter games are experiencing a surge in popularity. As more players join, advanced AI-based cheats have emerged. These cheats simulate human gameplay, sending mouse inputs, making them hard to detect and counter. Therefore, this research presents a novel approach that utilizes telemetry data analysis to identify and counteract cheating in FPS games. The main objective of this study is to develop an innovative anti-cheating system that can effectively detect and prevent players from exploiting AI-based cheats to gain unfair advantages. To achieve this, extensive telemetry data is collected during gameplay. The data contains the real-time cursor position when the player is playing the game. Besides, Machine learning and deep algorithms are applied to analyse the telemetry data and distinguish between human player behaviour and AI-driven cheating patterns. Decision Tree, Random Forest, LSTM, and CNN are applied for this research. And in the final evaluation, CNN’s accuracy reached around 80% which proves it is a possible mode to be used for this problem. The significance of this research lies in its contribution against cheating in FPS games, particularly those exploiting AI technologies to gain unfair advantage. The proposed telemetry-based approach offers a solution to safeguard competitive gaming and insight into the game company based on this novel way for further experiments.

In the financial market, due to various factors, the stock price fluctuation is universal. Therefore, the directional prediction of stock market price based on technical analysis is very important in stock investment. This paper conducted a regression analysis and forecasted the future trends in the close price of Apple stock through recent five years between 2018 and 2023. For the purpose of this specific study, this paper did descriptive statistical analysis of the dataset, and made graphs and analyses of regression and predictions relied on the techniques of the Linear Regression Model and Random Forest Model. Based on the three indices: MSE, RMSE, and MAE, the paper compared the advantages and disadvantages of the two machine learning methods. The result of the experiments indicated that the regression generated through employment of the Linear Regression Model outperforms the result of the Random Forest Model, leading to the conclusion that Linear Regression Model is a more effective method to forecast in this dataset.

Bike sharing has become a much more popular topic nowadays. Not only do the producers in bike-sharing need to provide a relatively accurate number of bikes in each period, but also the consumers need to have a general understanding of the number of bikes in each hour. This study analyses the dataset of bike-sharing rentals in 2011 in Washington, D.C. using machine learning, after training, testing, analyzing, and visualizing the dataset, the author chose the best model-random forest to predict it through the method of cross-test. The research result shows that the number of rentals in bike-sharing is the highest in the morning and evening travel peaks in one day, the highest in working days in one week, and the highest in autumn in one year. This information can help the bike-sharing service to prepare different quantities of bike-sharing at different times, and the customers would have a better overview of the bike demand when they plan to rent one. The whole research process provides valuable information for the service providers and users of bike-sharing.

Scattering is discussed in classical mechanics, quantum mechanics, and quantum field theory, which shows it is an important part of physics subject. From the Rutherford scattering in classical mechanics to the simple case of a potential barrier impeding the propagating wave in quantum mechanics, scattering problems seem trivial initially but get much more complicated with the study. The scattering theory developed along with the improvement and discovery in physics, and it brings lots of benefits and techniques for researchers from different science fields. To understand the scattering, finding the scattering is a good way to build up the connection between the fundamental theory and intuitive understanding. Specifically, the author wants to emphasize the scattering amplitude in the passage, which repeals the fundamental things of scattering, and the article would include some discussion of the properties of the Green function, which is a powerful mathematical tool for physicists. The author tries to show the scattering amplitude’s beauty through the discussion. Then, link them with the quantum field theory of scattering.

Two-dimensional quantum materials are currently a hot research area in the field of materials. These unique materials allow electrons to move freely in only two dimensions and the other dimension is limited within the atom scale. The isolation of Graphene in 2004 showed the advantages of two-dimensional (2D) materials and led a rapid development in this field. Meanwhile, it stimulates the synthesis and research of the materials beyond carbon. 2D materials beyond carbon have different components and structures, showing a broader range of remarkable properties and applications than traditional graphene. This article will pay attention to the phenomenon and mechanism of these exceptional properties, including superconductivity, ferromagnetism, antiferromagnetism, and quantum spin liquid phase. Additionally, potential applications and future prospects of 2D materials beyond carbon will be explored. With the progress of technology, 2D materials beyond carbon are expected to have exciting developments in various fields, leading to significant changes in human life and production

This article aims to establish the comprehensiveness of the Dirac equation as an effective modification of quantum mechanics for the analysis of electrons and atomic fine structure. The Dirac equation is applied to investigate two scenarios involving electron interactions with different potentials. In the case where ϕ=0, the Dirac equation aligns naturally with electron theories and yields an electron gyromagnetic factor of g_s=2. With additional radiative corrections, it is possible to bring this value into closer proximity to experimental results. On the other hand, when considering spin-orbit coupling within a central field of V=(-e^2)⁄r, the spin-orbit Hamiltonian derived from the Dirac equation is shown to match calculations based on Larmor and Thomas interactions. These cases collectively demonstrate the superior utility of Dirac’s theory when dealing with spin-1/2 particles like electrons, underscoring Dirac’s historical success in addressing the complexities of the time. His achievements in elucidating atomic fine structure and spin-orbit coupling hold pivotal significance for advancing technologies rooted in these theories. However, it is important to note that the Dirac equation primarily remains valid in weak external field situations, as observed in electron orbital motion, while challenges persist in unifying it with general relativity in stronger external field contexts.

Against the backdrop of increasing attention to the integration of machine learning and stock analysis, stock prediction models are a hot topic. The question this paper is studying in this study is which stock prediction model is more accurate in predicting stocks. The method of this study is based on the stock prices of new energy vehicle leader Tesla Motors in the past three years as a data set, using a random forest model and an SVR model to predict the stock prices over the next 10 days. Based on the parameter MSE values of the training models of two stock prediction models, compare their sizes to determine the accuracy and stability of the models. This study found that the stock prediction results of the SVR model are more accurate and stable than those of the random forest model. Therefore, it is believed that the stock prediction model using the SVR method will have more market value and occupy an important position in the integration of machine learning and stock trading analysis.

Environmental control and life support systems (ECLSS) are essential for the triumph of human spaceflight missions, furnishing astronauts with crucial resources like breathable air, purified water, nourishment, and protection from radiation. The unique and challenging space environment, coupled with the critical nature of ECLSS components, necessitates a high degree of reliability to prevent catastrophic failures. This paper conducts a comprehensive examination of various ECLSS subsystems, including air revitalization, water processing, food storage, waste management, and radiation shielding. Gaining perspectives from historical missions like Apollo, Skylab, and the International Space Station (ISS), the research outlines strategic approaches to improve the fault tolerance of ECLSS. The implementation of advanced simulation modeling, strategic component redundancy, and improved subsystem interconnectivity are posited as pivotal measures to bolster the reliability of ECLSS. These improvements are vital to guarantee the safety and viability of prolonged space missions to the Moon, Mars, and beyond, thereby facilitating humanity’s ongoing exploration of the universe.