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The sum of four squares: An exploration of Lagrange's theorem and its legacy in number theory 四次方之和:探索拉格朗日定理及其在数论中的传承
Pub Date : 2024-07-26 DOI: 10.54254/2755-2721/70/20240576
Yifan Cheng
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.
拉格朗日四次方定理是数论中的一个基本原理,它指出每个正整数都可以表示为四次方的和。该定理最早由希腊数学家亚历山大的 Diophantus 于公元 3 世纪提出。后来,皮埃尔-德-费马在 17 世纪证明了该定理,1770 年约瑟夫-路易-拉格朗日首次公布了该定理的证明。本文全面阐述了数论中的四则运算定理,其重点是寻找多项式方程的整数解。该定理极大地推动了对 Diophantine 方程的研究。本文追溯了拉格朗日四次方定理从其猜想起源到成为当代数学研究基石的过程。本文回顾了该定理的证明及其影响,以及它与现代研究和应用的联系,强调了它在数学中永恒的意义。此外,本文还重申了该定理对 Diophantine 方程的发展所产生的广泛影响,以及它在阐明数论之谜方面的持续意义。这加深了我们对该定理在更广泛的数学进步故事中的地位的理解,证实了它在历史和当代背景下的意义。
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引用次数: 0
Improving the crashworthiness of B-Pillars in side-collisions 提高侧面碰撞时 B 柱的耐撞性
Pub Date : 2024-07-26 DOI: 10.54254/2755-2721/78/20240455
Jiayu Guo, Shuyang Liu, Yu Fu, Ricky Liu, Jincheng Shi
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.
在发生侧面碰撞时,B 柱对保护乘客起着至关重要的作用。然而,目前 B 柱采用的技术不足以提供足够的保护。因此,本研究旨在探讨如何提高 B 柱的耐撞性。由于 2020 年款丰田雅力士的普遍性和较差的侧面耐撞性,本研究使用其右侧车身(尺寸为 80 厘米 60 厘米 40 厘米)来模拟侧面碰撞。结果表明,B 柱上部的速度和加速度均大于 B 柱下部,这表明应将焊点置于 B 柱下端,并增加 B 柱厚度,以提高侧面耐撞性。此外,研究还发现,与纳米材料结合的 PVC、物理混合的 ABS 树脂和 SMC 材料在碰撞时不会产生明显变形,同时密度极低。因此,研究建议使用这些强度更高的材料来替代钢材。研究还分析了使用这些材料进行大规模生产的成本和可行性。
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引用次数: 0
Design and implementation of scrambling and decoding circuits 加扰和解码电路的设计与实现
Pub Date : 2024-07-26 DOI: 10.54254/2755-2721/72/20241032
Peixiang Sun, Zefeng Yan, Ye Zhang
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.
目前,加扰解码技术已广泛应用于数字信号的传输。电路设计是实现加解扰的重要基础。因此,研究人员将加解扰电路的设计与实现作为本文的研究课题。本研究根据需求设计电路,使电路能够完成伪随机序列的构建,然后进行模块划分,确定不同模块完成的具体工作。最后,根据设计的电路和模块设计仿真,验证前期设计的准确性。结果表明,原始数据输入后,经过电路加扰运算,输出数据可以与输入数据一致,达到设计加扰电路的目的。通过此次实验,研究人员希望研究内容能更好地促进数据传输的安全性和准确性。同时,通过对现有编码技术的优化,研究人员期望能够拥有更高效的解码过程,减少错误,提高数据恢复率。
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引用次数: 0
Study on the optimization process and application of FIR digital filter FIR 数字滤波器的优化过程和应用研究
Pub Date : 2024-07-26 DOI: 10.54254/2755-2721/72/20241033
Zhenyu Hao, Chenyang Liu, Shaowei Ouyang
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.
作为数字信号处理技术的组成部分之一,FIR 数字滤波器以其系统稳定、易于线性相位等优点,在现实生活中得到了广泛的应用,并发挥着越来越重要的作用。本文将总结分析以往一些科研团队对 FIR 数字滤波器的研究成果,并展示该技术的优化过程和在实际生活中的应用实例。本文重点研究了 FIR 数字滤波器的降噪性能、延迟和尺寸以及能耗优化的优化过程。本研究总结了其在医疗、音频处理和雷达领域的三个应用实例。医疗领域是心电图(ECG)信号的处理,音频处理领域是音频信号的频率整形、噪声去除和信号增强,雷达领域是接收信号的精确滤波和处理。本文最后指出,FIR 数字滤波器在全球各个领域都有着不可替代的作用,未来将逐步向小型化和低功耗方向发展。
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引用次数: 0
An in-depth study of the principles and technologies of wind-solar complementary systems: Optimization strategies and future development trends 深入研究风光互补系统的原理和技术:优化策略和未来发展趋势
Pub Date : 2024-07-26 DOI: 10.54254/2755-2721/70/20240980
Xianzhi Liu
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.
面对 21 世纪全球能源危机和气候变化的挑战,迫切需要转向可持续能源解决方案。风光互补系统是风能和太阳能相结合的可再生能源技术,它能提高能源供应的稳定性和效率,因此显得尤为重要。本研究通过对技术创新和系统优化策略的分析,依托风能和太阳能技术发展的最新研究,以及不同应用场景下风光互补系统的实证研究,探索提高系统性能和经济性的途径。研究结果表明,风光互补系统可以有效降低对化石燃料的依赖,减少环境污染,在全球能源结构转型中发挥着越来越重要的作用。持续的技术创新和政策支持是推进该系统广泛部署的关键。
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引用次数: 0
Enhancing radio signal classification under low SNR conditions using deep residual networks with channel attention mechanisms 利用具有信道关注机制的深度残差网络加强低信噪比条件下的无线电信号分类
Pub Date : 2024-07-26 DOI: 10.54254/2755-2721/72/20241016
Bingxu Zhang
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.
本文深入探讨了深度残差网络(ResNets)与信道关注机制的结合,以在低信噪比(SNR)条件下对无线电信号进行分类。本文利用广泛的无线电信号数据集,介绍了一种新型架构 MyResNet1,该架构将残差学习与信道关注相结合,使模型能够专注于精确分类的基本特征。研究表明,MyResNet1 的分类准确率有了显著提高,尤其是在具有挑战性的低信噪比场景中,这凸显了注意力增强型深度残差网络在无线电信号处理中的潜力。此外,这项研究还探索了各种优化策略,包括数据增强和正则化技术,以提高模型的性能和鲁棒性。我的研究成果极大地促进了认知无线电技术的发展,并阐明了深度学习在复杂信号分类任务中的潜力,这与最近通过深度学习和基于自动编码器的方法在自动调制识别(AMR)方面进行的探索相一致,从而增强了 I/Q 信道交互。
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引用次数: 0
Indoor positioning systems based on visible light communication 基于可见光通信的室内定位系统
Pub Date : 2024-07-26 DOI: 10.54254/2755-2721/78/20240460
Runze Kong, Ruiteng Li, Zhengyang Ma, Yixiang Yu
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.
室内定位系统(IPS)在不断扩展的无线通信系统中至关重要。根据基本定位技术,这些系统一般可分为四类。其中之一是基于使用发光二极管(LED)的可见光技术。在本文中,我们首先介绍了可见光系统中从发送方到接收方的简单传输模型。随后,我们基于 Epsilon 提出的技术,构建了一个精度更高、成本效益更高的模型。接下来,我们介绍了可见光室内定位中最常用的指纹识别方法和三角测量方法。传统的指纹识别方法存在误差较大等问题。最近的研究根据不同的问题提出了各种改进方法。针对位置误差大的问题,新的研究提出了一种基于位置指纹识别和元启发式的精确可见光定位(VLP)方法。本文介绍的方法解决了特殊情况下位置误差受影响的问题。典型的 IPS 是利用双音多频 (DTMF) 技术的室内定位系统。系统设计包括将 LED 灯布置成矩形网格状,并使用一个基本定位单元。本文讨论的研究还探讨了信道增益的计算和定位误差的模拟结果。在所提出的定位系统中,粗定位是通过 ID 采集过程获得的。当移动装置接收到一个或多个 LED 信号时,ID 获取过程用于根据最高接收信号强度指示(RSSI)获取最近的 LED ID。模拟结果表明,在信噪比(SNR)为 10 dB 时,平均定位误差为 18 毫米。通过研究结果,我们得出结论:VLC 技术的广泛适用性使其成为许多领域的基石。在我们的日常生活中,光通信定位技术在不断改进,有望在未来得到更广泛的应用。
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引用次数: 0
Research on the intelligent fatigue detection of metal components in vehicles 车辆金属部件智能疲劳检测研究
Pub Date : 2024-07-26 DOI: 10.54254/2755-2721/78/20240414
Zhaoran Xue, Qiren Chen, Hongde Du, Esu Xian
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.
随着运输速度的加快,重载卡车对轮轴的质量提出了更高的要求,卡车轮轴的检测已成为纠正性维护的重点。汽车行业要求对车辆部件进行及时检测。无损检测(NDT)技术提供了一种在不造成损坏的情况下检测和分析物体内表面物理量的方法。它可以确定是否存在缺陷或异常情况。无损检测(NDT)在汽车行业的应用对于保证汽车的安全性和可靠性至关重要。本文概述了相控阵超声成像和涡流检测的原理和应用,重点介绍了车桥的智能监测解决方案。本文提出了一种增强型智能监测方法,利用现有的检测方法为车主提供有关单个汽车零件疲劳强度的实时反馈。该方法旨在当疲劳趋势接近预定的警告阈值时,提示更换汽车零件。
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引用次数: 0
Application prospects of graphene in environmental science 石墨烯在环境科学中的应用前景
Pub Date : 2024-07-26 DOI: 10.54254/2755-2721/72/20240987
Chenglin Song
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.
纳米材料和石墨烯作为前沿材料,在环境治理中发挥着至关重要的作用。纳米材料的引入为环境治理带来了新的希望。石墨烯不仅能提高水处理的效率和成本效益,还能推动环境技术的创新和发展。本文从纳米材料和石墨烯的特点出发,进行了总结和分析综述,全面回顾了石墨烯在环境技术方面的优势,并发现了其在该领域的应用。研究总结认为,石墨烯的特性使其适合解决水污染等环境问题,其复合材料通过不同的制备方法和反应机理,可在水处理过程中发挥重要作用,包括水净化、重金属吸附、有机化合物吸附和去除等。通过在石墨烯膜上引入纳米孔结构和人工设计的堆叠结构,可以调节和改善其渗透性能。通过物理和化学吸附、离子交换、电化学和光催化等方法,石墨烯及其氧化物可用于去除污染水体中的重金属离子和有机物。文章还介绍了石墨烯的主要制备方法及其潜在的二次污染问题。这篇文章为环境保护和可持续发展领域的科学研究和工程实践提供了宝贵的启示。
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引用次数: 0
A review of applications of deployable structure 可部署结构应用综述
Pub Date : 2024-07-26 DOI: 10.54254/2755-2721/78/20240404
Mingzhao Wen, Linghao Ye, Hongrui Pu, Yuanqi Ye
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.
从购物袋和婴儿车到阳台和体育场屋顶等大型建筑,简单可靠的可展开结构已经在我们日常生活的方方面面发挥着作用。近几十年来,人们对可展开结构的各种应用越来越感兴趣,例如航空航天工程。本文回顾了可展开结构领域的一些实例,包括从基本要素到平面双链连杆和可展开天线等更复杂的组合。可展开结构具有成本低、体积小、用途多等特点,已被广泛应用于卫星和其他空间活动装置的设计和制造。可展开空间天线是目前为空间探测器开发的一项关键技术,本文通过公式解释其功能和突出能力,对其进行了综述。由于抛物面缆网系统的一些优点,本文也对其进行了评述。我们讨论并总结了应用可部署结构所面临的一些挑战,以及潜在的解决策略。
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引用次数: 0
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Applied and Computational Engineering
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