{"title":"The sum of four squares: An exploration of Lagrange's theorem and its legacy in number theory","authors":"Yifan Cheng","doi":"10.54254/2755-2721/70/20240576","DOIUrl":"https://doi.org/10.54254/2755-2721/70/20240576","url":null,"abstract":"Lagranges Four-square Theorem is a fundamental principle in number theory, which states that every positive integer can be expressed as the sum of four squares. The theorem was first conjectured by the Greek mathematician Diophantus of Alexandria in the 3rd century CE. It was later proved by Pierre de Fermat in the 17th century, and the first published proof was attributed to Joseph-Louis Lagrange in 1770. This paper presents a comprehensive account of the four-square theorem in number theory, which focuses on finding integer solutions to polynomial equations. The theorem has significantly advanced the study of Diophantine equations. It traces Lagranges Four-square Theorem from its conjectural origins to its emergence as a cornerstone of contemporary mathematical research. This paper reviews the proof of the theorem and its implications, as well as its connection to modern research and applications, highlighting its timeless relevance in mathematics. In addition, the paper reaffirms the extensive influence of the theorem on the advancement of Diophantine equations and its ongoing significance in elucidating the enigmas of number theory. This enhances our comprehension of the theorems position in the wider story of mathematical progress, confirming its significance in both historical and contemporary contexts.","PeriodicalId":502253,"journal":{"name":"Applied and Computational Engineering","volume":"22 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141801060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jiayu Guo, Shuyang Liu, Yu Fu, Ricky Liu, Jincheng Shi
{"title":"Improving the crashworthiness of B-Pillars in side-collisions","authors":"Jiayu Guo, Shuyang Liu, Yu Fu, Ricky Liu, Jincheng Shi","doi":"10.54254/2755-2721/78/20240455","DOIUrl":"https://doi.org/10.54254/2755-2721/78/20240455","url":null,"abstract":"The B-pillar plays a crucial element in protecting passengers during side collisions. However, the current technology used in B-pillars is insufficient in providing adequate protection. Therefore, this research aims to investigate ways to improve the crashworthiness of the B-pillars. The study utilizes a 2020 Toyota Yaris due to its prevalence and poor side-crashworthiness and a right body measuring 80cm 60cm 40cm to simulate side collision. The results show that the velocity and acceleration of the upper B-pillar are greater than that of the lower B-pillar, indicating that the welding spot should be placed at the lower end of B-pillars, and the pillars thickness should be increased to enhance side crashworthiness. Furthermore, the study discovers that PVC, when combined with nano-materials, ABS resin, when combined through physical mixing, and SMC materials experience no significant deformation during collision while possessing an incomparably low density. Therefore, the study proposes the use of these stronger materials as an alternative to steel. The cost and feasibility of using these materials in mass production is also analyzed.","PeriodicalId":502253,"journal":{"name":"Applied and Computational Engineering","volume":"20 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141801456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Design and implementation of scrambling and decoding circuits","authors":"Peixiang Sun, Zefeng Yan, Ye Zhang","doi":"10.54254/2755-2721/72/20241032","DOIUrl":"https://doi.org/10.54254/2755-2721/72/20241032","url":null,"abstract":"Scrambling decoding technology is now widely used in the transmission of digital signals. The circuit design is an important basis for the realization of adding and de-scrambling. So the researchers take the design and implementation of scrambling and decoding circuit as the research topic of this paper. In this study, the circuit is designed according to the demand, so that the circuit can complete the construction of pseudo-random sequences, and then the module division is carried out to determine the specific work completed by different modules. Finally, according to the designed circuit and module design simulation, the accuracy of the early design is verified. The results show that after the original data is input, the output data can be the same as the input data after the circuits scrambling operation to achieve the purpose of designing the scrambling circuit. Through this experiment, the researchers hope that the research content can better promote the security and accuracy of data transmission. At the same time, with the optimization of the existing coding technology, researchers expect to have a more efficient decoding process, reduce errors, and improve the data recovery rate.","PeriodicalId":502253,"journal":{"name":"Applied and Computational Engineering","volume":"39 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141798753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Study on the optimization process and application of FIR digital filter","authors":"Zhenyu Hao, Chenyang Liu, Shaowei Ouyang","doi":"10.54254/2755-2721/72/20241033","DOIUrl":"https://doi.org/10.54254/2755-2721/72/20241033","url":null,"abstract":"As one of the components of digital signal processing technology, the FIR digital filter has been widely used in real life and played an increasingly important role due to its advantages of system stability and ease of linear phase. This paper will summarize and analyze the research results of some past scientific research teams on FIR digital filters, and show the optimization process of this technology and the application examples in real life. This paper focuses on the optimization process of noise reduction performance, delay and size, and energy consumption optimization of FIR digital filters. This study summarizes three examples of its applications in medical, audio processing, and radar. In the medical field, the processing of electrocardiogram (ECG) signals, the audio processing fields are the frequency shaping, noise removal, and signal enhancement of audio signals, and the precise filtering and processing of received signals in the radar field. At the end of this paper, the FIR digital filter has an irreplaceable role in all fields in the world and gradually develops in the direction of miniaturization and low power consumption in the future.","PeriodicalId":502253,"journal":{"name":"Applied and Computational Engineering","volume":"9 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141799369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An in-depth study of the principles and technologies of wind-solar complementary systems: Optimization strategies and future development trends","authors":"Xianzhi Liu","doi":"10.54254/2755-2721/70/20240980","DOIUrl":"https://doi.org/10.54254/2755-2721/70/20240980","url":null,"abstract":"In the face of the global energy crisis and the challenges of climate change in the 21st century, there is an urgent need to shift to sustainable energy solutions. Wind-solar hybrid systems, renewable energy technologies that combine wind and solar energy, are particularly important because they improve the stability and efficiency of energy supply. Through the analysis of technological innovation and system optimization strategies, this study explores ways to enhance system performance and economy by relying on the latest research on wind and solar energy technology development as well as empirical studies of wind-solar complementary systems in different application scenarios. The results of the study show that wind-solar hybrid systems can effectively reduce the dependence on fossil fuels and reduce environmental pollution, and they play an increasingly important role in the transformation of the global energy structure. Continued technological innovation and policy support are key to advancing the widespread deployment of the system.","PeriodicalId":502253,"journal":{"name":"Applied and Computational Engineering","volume":"49 43","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141799548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Enhancing radio signal classification under low SNR conditions using deep residual networks with channel attention mechanisms","authors":"Bingxu Zhang","doi":"10.54254/2755-2721/72/20241016","DOIUrl":"https://doi.org/10.54254/2755-2721/72/20241016","url":null,"abstract":"This paper delves into the advancement of deep residual networks (ResNets) integrated with channel attention mechanisms for the classification of radio signals under conditions of low Signal-to-Noise Ratio (SNR). Utilizing an expansive dataset of radio signals, this paper introduces a novel architecture, MyResNet1, that combines residual learning with channel-wise attention, allowing the model to concentrate on essential features for precise classification. My, investigations exhibit notable improvements in classification accuracy, especially in challenging low SNR scenarios, highlighting the potential of attention-augmented deep residual networks in radio signal processing. Furthermore, this studyexplores various optimization strategies, including data augmentation and regularization techniques, to enhance the models performance and robustness. My findings contribute significantly to cognitive radio technologies and illuminate the potential of deep learning in sophisticated signal classification tasks, aligned with recent explorations in automatic modulation recognition (AMR) through deep learning and autoencoder-based methodologies for enhancing I/Q channel interactions.","PeriodicalId":502253,"journal":{"name":"Applied and Computational Engineering","volume":"54 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141799586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Indoor positioning systems based on visible light communication","authors":"Runze Kong, Ruiteng Li, Zhengyang Ma, Yixiang Yu","doi":"10.54254/2755-2721/78/20240460","DOIUrl":"https://doi.org/10.54254/2755-2721/78/20240460","url":null,"abstract":"Indoor positioning systems (IPS) are crucial in the ever-expanding landscape of wireless communication systems. These systems can generally be classified into four categories based on the underlying positioning technologies. One of them is based on visible light technology using Light Emitting Diodes (LEDs). In this paper, we first present a simple transmission model from the sender to the receiver in a visible light system. Subsequently, we construct a higher-precision, cost-effective model based on the technology proposed by Epsilon. Next, we introduce the most commonly used fingerprint recognition method and triangulation method in visible light indoor positioning. Traditional fingerprint recognition methods have issues such as significant errors. Recent studies have proposed various improvements based on different problems. To address the problem of high position errors, new research introduces an accurate Visible Light Positioning (VLP) method based on location fingerprinting and meta-heuristic. The method presented in this paper addresses the issue of position errors being affected in special cases. A typical IPS is an indoor positioning system utilizing dual-tone multi-frequency (DTMF) technology. The system design involves arranging LED lamps in a rectangular grid shape and using a basic positioning unit. The research discussed in this paper also explores the calculation of channel gains and simulation results of positioning errors. In the proposed positioning system, the coarse position is obtained through the ID acquisition process. When the mobile unit receives one or more LED signals, the ID acquisition process is used to obtain the nearest LEDs ID based on the highest Received Signal Strength Indication (RSSI). Simulation results indicate an average positioning error of 18 millimeters at a Signal-to-Noise Ratio (SNR) of 10 dB. Through the results of our research, we conclude that the wide applicability of VLC technology makes it a cornerstone in many fields. In our daily lives, optical communication positioning technology continues to improve, promising broader applications in the future.","PeriodicalId":502253,"journal":{"name":"Applied and Computational Engineering","volume":"22 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141801051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Research on the intelligent fatigue detection of metal components in vehicles","authors":"Zhaoran Xue, Qiren Chen, Hongde Du, Esu Xian","doi":"10.54254/2755-2721/78/20240414","DOIUrl":"https://doi.org/10.54254/2755-2721/78/20240414","url":null,"abstract":"With the acceleration of transportation speed, heavy loading of trucks has higher requirements for the quality of wheel axles, and the detection of wheel axles on trucks has become a key focus in corrective maintenance. The automotive industry requires timely detection of vehicle components. Nondestructive testing (NDT) technology provides a method of detecting and analyzing physical quantities on the internal surface of an object without causing damage. It can determine the presence of defects or abnormal conditions. The application of nondestructive testing (NDT) is essential in the automotive industry to guarantee the safety and dependability of vehicles. This article provides an overview of the principles and applications of phased array ultrasound imaging and eddy current testing, focusing on intelligent monitoring solutions for axles. This article proposes an enhanced intelligent monitoring approach that utilizes existing detection methodologies to provide vehicle owners with real-time feedback regarding the fatigue strength of individual automotive parts. This approach aims to prompt the replacement of auto parts when the fatigue trend approaches predetermined warning thresholds.","PeriodicalId":502253,"journal":{"name":"Applied and Computational Engineering","volume":"62 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141798966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Application prospects of graphene in environmental science","authors":"Chenglin Song","doi":"10.54254/2755-2721/72/20240987","DOIUrl":"https://doi.org/10.54254/2755-2721/72/20240987","url":null,"abstract":"Nanomaterials and graphene, as cutting-edge materials, have play a crucial role in environmental governance. The introduction of nanomaterials brings new hope to environmental governance. Graphene not only improves the efficiency and cost-effectiveness of water treatment but also drives innovation and development in environmental technologies. This article provides a summary and analysis review starting from the characteristics of nanomaterials and Graphene, comprehensively reviewing Graphenes advantage in environmental technologies and discovered its application in this area. The research summarized the conclusion that Graphenes characteristics make it suitable for addressing environmental issues such as water pollution, its composites can play an important role in water treatment process including water purification, heavy metal adsorption, organic compound adsorption and removal through different preparation and reaction mechanisms. By introducing Nanopore structures and artificially designed stacking structures on graphene membranes, the permeation performance could be modulated and improved. By the way of physical and chemical adsorption, ion exchange, electrochemical and photocatalysis, Graphene and its oxide could be applied to remove heavy metal ion and organic substances from polluted water. The article also introduced the main preparation methods of Graphene and its potential secondary pollution problem. This article provides valuable insights for scientific research and engineering practices in environmental protection and sustainable development.","PeriodicalId":502253,"journal":{"name":"Applied and Computational Engineering","volume":"21 21","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141801285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A review of applications of deployable structure","authors":"Mingzhao Wen, Linghao Ye, Hongrui Pu, Yuanqi Ye","doi":"10.54254/2755-2721/78/20240404","DOIUrl":"https://doi.org/10.54254/2755-2721/78/20240404","url":null,"abstract":"Simple and reliable deployable structures already play a role in every aspect of our daily lives, from shopping bags and baby carriages to large buildings such as balconies and stadium roofs. In recent decades, people have been more interested in the various applications of deployable structures, for example, aerospace engineering. This paper reviews some examples in the field of deployable structures, including from the basic elements to more complex ensembles such as planar double-chain linkages and deployable antennas. Due to its properties including lower cost, smaller volume, and multiple usages, deployable structures have been extensively applied to the design and manufacture of satellites and other devices for space activities. Sizeable space antennas, as a key technology currently developed for space probes, are reviewed in this paper by using formulas to explain their functions and highlight abilities. The system of paraboloid cable net is also reviewed due to some benefits. We have discussed and summarized some challenges in applying deployable structures, along with strategies for potential solutions.","PeriodicalId":502253,"journal":{"name":"Applied and Computational Engineering","volume":"7 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141801389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}