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.