Group motion exists widely in nature. Physicists use abstract models, such as the Vicsek model, to simplify group motion to obtain universal laws. However, the order parameters and phase transition types that describe the characteristics of the Vicsek model system are still controversial. For example, how to characterize the order parameters and types of phase transitions that characterize the system. This paper starts with the eigen microstate method and studies the Vicsek model. First, the continuous phase transition in the system is deeply studied through scaling analysis, and two critical exponents about the noise are obtained. Second, considering the density effect, similar to the noise study, three eigen microstates in the Vicsek model are revealed through scaling analysis, showing discontinuous and continuous phase transitions. Moreover, it is proved that in the actual infinite system, continuous phase transition and discontinuous phase transition still exist. Finally, the experimental data under different noises and densities are obtained through a large number of numerical simulations, and the phase diagram of the Vicsek model is depicted.

The commercial launch of 5G has already begun globally, in the meantime, academia and industry have carried out research on 6G as planned. 6G will bring a new perspective of communication technology, incredible technological innovation, fulfilling coverage technology application, and massive scale of in-depth technology integration. This paper describes technological vision on 6G based on the current situation of mobile communication technological development, and then considers the future directions of technological development from the perspective of 6G, this paper introduces new value offered in the 6G era to support the potential use cases put forward in Chapter 4. Requirements of 6G reveal the goals of mobile development—smarter, faster and greener, which provide reference for industry and society in the 2030s.

Nowadays, more than one million people die due to heart problems annually. Detecting the Electrocardiogram curve is an effective way to evaluate heart condition. Compared with large devices in the hospital, wearable devices are showing their advantage in detecting people’s Electrocardiogram whenever and wherever possible. However, in traditional amplifier circuit design, there is less attention to the bandwidth. The noise is negatively correlated with the current while the power consumption is positively correlated with the current, so it is challenging to balance the noise and power. Therefore, a design of a high bandwidth Electrocardiogram signal low noise amplifier circuit for wearable devices is proposed in this paper. The improved circuit is based on a conventional instrumentation amplifier and consists of two stages. The op-amps were replaced with Operational Transconductance Amplifier. The circuit also has a Driven-Right-Leg circuit part, which can tremendously reduce the effect of common-mode noise. The simulation result shows that the circuit has a high bandwidth and stable gain. Meanwhile, the circuit consumes less power and has a low integrated input-referred noise. This study is extremely helpful in expanding the application of wearable Electrocardiogram signal-detecting devices.

The Axiom of Choice (AC), a cardinal principle in set theory, postulates that for any assortment of disjoint non-empty sets, it’s possible to construct a new set by selecting one element from each set in the collection. Using choice functions, this idea suggests that every collection of nonempty sets can be associated with a choice function. In the mathematical landscape, AC’s significance is accentuated by its extensive application in a myriad of mathematical deductions, marking it as a cornerstone among mathematical axioms. This study delves into the practical implications and applications of AC, employing rigorous analytical methods to investigate its vast and multifaceted influence on the broader mathematical domain. Key findings indicate that AC has facilitated the proof of various theorems, some of which, on the surface, appear unrelated. While its inception sparked considerable debates due to concerns over its intuitive validity, its impact on contemporary mathematics is profound. This research underscores AC’s central role in advancing mathematical thought, highlighting its contributions to both foundational theories and intricate proofs.

Cryptography holds a significant place in the realm of information technology, safeguarding sensitive information from unauthorized access. This discourse centers on two prevalent cryptographic algorithms: AES (Advanced Encryption Standard) and RSA (Rivest-Shamir-Adleman). While AES falls under the category of symmetric cryptography, RSA is a part of asymmetric cryptography. The paper’s objective lies in furnishing readers with an insightful exploration of both algorithms, delving into their respective strengths and weaknesses. A comprehensive examination reveals the intricate details of their operation, highlighting the security aspects and potential vulnerabilities. Understanding the fundamental distinctions and the operational mechanics of AES and RSA contributes to an enhanced perception of their application in diverse cryptographic contexts. Beyond this, the paper delves into the synergistic utilization of AES and RSA, presenting an innovative approach to reinforcing information security. This integration leverages the unique advantages of both algorithms, mitigating their individual limitations and bolstering the security framework. In essence, a balanced perspective on AES and RSA, along with their collaborative application, furnishes a robust foundation for informed cryptographic choices, fortifying the safeguarding of sensitive data against emerging security threats.

In this age marked by a wealth of information, the relevance of social networks has increased in a manner that is analogous to an exponential growth curve. Notably, the content that is shared on these platforms has the potential to act as a reflection of the emotional states that people are now experiencing. The importance of emotions is brought to light in the research presented here, which makes use of a technique based on a review of the relevant literature to analyze the problem of random sample bias and the effects that it has on sentiment analysis. It is possible to draw the conclusion, on the basis of the findings of the research, that the problem of random sample propensity is not a sporadic or insignificant one. In addition, the findings of the study indicate the presence of multiple types of prejudice. Because of the potential repercussions that could result from doing a distorted sentiment analysis, it is really necessary to keep your method focused.

China, as a major economic power, has been increasing its carbon emissions year after year. Effectively controlling carbon emissions and finding suitable and effective methods to reduce emissions have become the main research themes of current research. The Stochastic Impacts by Regression on Population, Affluence, and Technology (STIRPAT) model is used in this work to analyze the impact of GDP, population, urbanization, and energy intensity on China’s carbon emissions from 2003 to 2020. From the output by the SPSS software, it can be illustrated that GDP and energy intensity have more obvious contribution on carbon emission, while urbanization level and population don’t. Additionally, as the GDP index increases by a value of one, a 1.220 change will be seen by the carbon emission. Similarly, every one unit change for energy intensity is associated with 0.897 change in carbon emission. Therefore, this paper can consider effective ways to conserve energy and mitigate greenhouse gas emissions from these two aspects, and in this way attain the objective of carbon peaking and carbon neutrality.

This paper will discuss the analysis of Chinese football performance data over the past five years to predict future trends. The study will be analysed in three parts, firstly we will present the performance of the Chinese national team and the national teams of each echelon in the last five years of international matches. Secondly, we will discuss the main body, the main body of the author mainly using the last five years of the Chinese national team and the U23 national team U19 national team World Cup and the Asian Cup results for the results of the conversion, and statistics on the performance of the other two national teams in East Asia, will be China’s national team, the national team of South Korea, the national team of Japan for the comparison, the use of authors on the conversion to compare the last five years of the results of the results of the results. Chinese football has been at a low ebb in recent years, and the public opinion environment has been unfavourable for a long time. The reason for this is that the competitive performance of football has not met expect addition, the author will process the data to make a linear regression equation to predict the future trend of Chinese football performance. Finally, the author will summary and analyse the shortcomings of Chinese football development and make some recommendations.

The conic section is a crucial part of high school mathematics and usually plays the role of tough problem in examinations. Hence, this dissertation will use the literature analysis method to introduce the mathematical background of the conic section to enable students to know about the conic section more clearly and explain the basic concept of the conic section such as the first and second definitions of conic section, then introduce some second level conclusions such as focus length formula and average property of parabola. After that, this dissertation will provide some conic section problems in past exam papers and corresponding problem-solving processes to show how to use the basic concept and these common second-level conclusions of the conic section, then summarize the train of thought of the conic section. For choice questions and fill-in-the-blank questions, combining the condition given by questions with the first definition and second common level is important, and for questions that need to write the complete process, setting parameters and Vieta theorem is essential, and for extremely complicated problems, special methods such as homogenization can be considered to reduce the calculation.

A digital electronic clock stands as a pinnacle of modern timing technology, built on digital circuits that offer precise hour, minute, and second tracking and display capabilities. The evolution of integrated circuits, combined with the ubiquitous application of quartz crystal oscillators, has propelled the digital electronic clock into myriad sectors including science, transportation, and finance. These clocks, appreciated for their precision, clarity, stability, and other attributes, vastly differ from their mechanical predecessors. Absent of mechanical transmission devices, they promise longevity and exact timekeeping. Such digitization serves as the foundational technological support for crafting large machinery and precision tools. Delving into the intricacies of digital electronic clocks and broadening their utilization holds substantial real-world relevance. This discourse employs a top-down hierarchical circuit design approach, segmenting the comprehensive circuit into distinct modules. This method not only streamlines its configuration, rendering it user-friendly and legible, but also ensures that each segmented circuit operates as an autonomous entity. This modularity facilitates smoother simulations and circuit modifications, enhancing adaptability and efficiency.

Stemming from the need to formalize the divisibility of rational numbers, p-adics provide a unique mathematical perspective rooted in prime number theory. This article provides a comprehensive discussion of p-adic numbers, including their research background, definition, properties, theory, and extensions. This study first elucidates the historical background and significance of p-adic numbers, emphasizing their key role in number theory and its applications. At the heart of this research is a deep dive into the precise definition of p-radical numbers, revealing their unique, often counterintuitive, distance measure. We look at their fundamental characteristics, demonstrate their illogical characteristics, and discuss how they affect transcendental number theory, Diophantine equations, and algebraic number theory. Furthermore, this article explores the theoretical foundations of p-radical numbers and their extensions, emphasizing their integral role in advanced mathematical structures such as p-radical analysis and p-radical geometry. By covering these aspects, this study aims to highlight the lasting impact of p-adic on modern mathematics, reshape our understanding of divisibility, and advance mathematical inquiry into new and uncharted territory.

Nowadays, more and more people are looking for a faster and safer way of encryption. Fractal coding and chaos encryption fit those two points. This article discussed the usage of Fractal and Chaos Theory in photo processing. For example, Fractals and chaos theory are usually used in picture encrypting and picture processing to make the object in the target picture much more clearly. And currently, the method become advanced. The current method can provide great defense from hacking. Meanwhile, in terms of compression performance, it achieves a higher compression ratio than other solutions while meeting the reconstruction visual quality. In this article, the writer analyses the future of Fractal coding by talking about the advantages and disadvantages of this method which came from different articles. Furthermore, in this paper, the author discusses the definition of Fractal and the properties of Fractal. The Iterated Function System (IFS) is also a key point in photo processing.

Today, greenhouse gas emissions caused by human activities have led to rising global temperatures, increasing extreme weather events, and rising sea levels, posing a threat to human society and ecosystems. People are also taking some active measures to mitigate these impacts. Therefore, in order to make a positive response in the aviation industry, this paper studies how to reduce greenhouse gas emissions brought by aircraft engines under the environment of energy conservation and emission reduction, mainly from two aspects of improving large bypass ratio engines and adopting new environmentally friendly fuels. Then the two major aspects, respectively, the origin and advantages and disadvantages of their analysis, for the current needs of the theory and the problems encountered in the actual production, how to solve and apply. After synthesizing the previous studies and reorganizing the previous studies, this paper expounds these two aspects in more detail.

The aviation sector has undergone substantial growth, leading to a corresponding increase in emissions attributed to this industry. This escalation in emissions has notably contributed to the intensification of global warming. This research provides a comprehensive examination of various prospective solutions to mitigate these emissions. Among the proposed solutions is the adoption of an intercooled turbofan engine. This specific engine type holds the promise of realizing a 3.1% reduction in fuel consumption compared to traditional engines. Furthermore, the incorporation of a recuperator in an intercooled turbofan engine could potentially lead to a significant decrease in fuel consumption by up to 30%, alongside a remarkable 20% improvement in engine efficiency. The discourse also extends to the subject of hydrogen-powered aviation, underscoring its substantial potential in achieving emissions reduction goals. However, the associated challenges, especially those related to hydrogen storage, are also explored in this study. The forthcoming era of jet engine technology may witness the amalgamation of intercooled turbofan engines and hydrogen energy sources as a viable pathway for substantial emissions reduction.

Scientifically predicting the annual failure quantity of smart meters is of significant importance for enhancing the economic benefits of smart meters and promoting the stable operation of smart grids. In this paper, traditional Grey Markov prediction models and Grey Markov models with weakened buffering operators are employed to predict smart meter failure data. To improve prediction accuracy, an Induced Ordered Weighted Averaging (IOWA) operator is introduced to construct a combination prediction model. Based on this approach, we predict the annual failure quantity of smart meters for a certain company in Wuhan, China, from 2020 to 2022 using data from 2012 to 2019. Accuracy indicators, such as correlation degree (G) and average relative error (P), have improved from level three to level two, indicating that the combination prediction model based on the IOWA operator effectively enhances prediction accuracy. This method demonstrates the feasibility and effectiveness of predicting smart meter failures.

This essay discusses a potential method of designing a micro-wearable device that can effectively detect human heart conditions and provide real-time feedback. Compared to the traditional method of designing wearable devices, the core innovation in this new approach is the utilization of the DRL circuit for the extraction of common-mode signals. This device can filter out a significant amount of noise due to the low current and low voltage conditions. The low current and low voltage conditions under which this device operates contribute to its remarkable energy efficiency. Consequently, the device boasts a long-lasting battery, reducing the need for frequent recharges, which is often a significant inconvenience associated with wearable technology. In the meantime, the non-invasive nature of the ECG technology integrated into this wearable device ensures that wearers can go about their daily lives comfortably without causing discomfort, making it suitable for continuous heart monitoring without impeding people’s activities or affecting people’s overall comfort.

The use of drones in logistics is steadily becoming more common as drone technology advances. As a result, logistics path planning has become a viable research topic. The majority of previous research has concentrated on low-load vehicle-borne UAVs. DJI recently produced a high payload civilian delivery UAV with a maximum capacity of 30 to 40 kg, paving the path for high payload UAVs and providing the criteria for this research. The goal of this research is to increase the efficiency of UAV delivery while also reducing energy consumption, as well as to investigate the path planning problem for large load UAVs in batches. Prior to choosing the ACO method to determine the best route for a single batch, the genetic algorithm is used to achieve the entire load for express delivery in batches. After this, the whole path is determined and supported. The output of the program is the correlation between the number of iterations and the single optimal route, which is then added to produce the overall path. After showing this, we infer that the sum of single ideal paths is the best total path, which maximizes efficiency and saves energy. The significance of this research is to provide some directions for thinking and help for the research of UAV logistics, and we hope to further develop UAV logistics technology to some extent under the premise of energy saving and time saving.

Drones, also known as unmanned aerial vehicles (hereinafter referred to as “UAV”), are widely used in both military and civilian applications, but agricultural drones have made great strides in recent years. Agricultural drones are often used to detect and evaluate crops, aid crop pollination, and spray fertilizers and disperse seeds. However, in terms of seed seeding, the vast majority of drones can only achieve extensive sowing of seeds, and seeds can only be sown on the surface of the soil, and the sowing accuracy of this method is extremely low, and there is a large waste of seeds. In order to improve the sowing efficiency of UAVs and the sowing effect on hard soil, this paper conducts relevant research on the seeding device carried by UAV and designs a new seeding device. On the basis of the traditional spreading function, the device performs design calculation, three-dimensional dynamic feasibility analysis, and is equipped with a precise interval sowing mechanism, which can also send seeds into the deep soil while accurately sowing seeds, which solves the problem of low efficiency of UAV seeding.

Voltage mode band-gap reference source and current mode band-gap reference source is the basic unit of integrated circuit, which plays an important role in some circuit systems such as low-voltage linear regulator, power control chip and analog-to-digital/analog-to-digital converter. Band-gap reference circuit is divided into voltage mode band-gap reference circuit and current mode band-gap reference circuit, and their basic principles and optimization methods are different. The voltage mode bandgap reference voltage is generated by superimposing voltages with positive and negative temperature coefficients, thereby producing a low-temperature related factor. In contrast, the current mode bandgap reference generates a reference voltage by superimposing currents with positive and negative temperature coefficients, requiring appropriate resistance matching and compensation. This paper analyzes the basic principles of the above two band-gap reference circuits, analyzes the temperature characteristics and mismatch sources of them, compares the research results including the implementation mode, temperature characteristics, application range and optimization scheme of the two, and looks forward to the future development prospect of both types of circuits.

Concerns from both society and the government about the pollutants from automobile exhaust is becoming more and more noticeable in recent years. Compared with the engines mostly used currently, which are gasoline engines and diesel engines, the HCCI engine has ameliorated not only the problem of pollutant emissions but also efficiency to a large extent. This paper provides an in-depth analysis of Homogeneous Charge Compression Ignition (HCCI) engines. It first introduces the fundamental processes governing HCCI combustion and illustrates its working mechanism. While HCCI engines promise heightened efficiency, reduced emissions, and fuel versatility, they also present challenges such as combustion timing and related emissions. Commercial implementations by Nissan and Honda are discussed, shedding light on real-world applicability. Furthermore, the potential amalgamation of biodiesel with HCCI is explored, signaling a promising future for renewable fuels in advanced combustion engines. Despite the rise of hybrid vehicles, the unique benefits of HCCI position it as a significant player in future transportation. This paper emphasizes the necessity of ongoing research to overcome HCCI’s challenges, ensuring it remains at the forefront of green automotive solutions.