Theoretical and Natural Science

- The Open Access Proceedings Series for Conferences

Volume Info.

  • Title

    Proceedings of the International Conference on Computing Innovation and Applied Physics (CONF-CIAP 2022)

    Conference Date




    The International Conference on Computing Innovation and Applied Physics is an annual academic conference. It aims at building an international platform for the communication and academic exchange among participants from various fields related to mathematics, physics, and computing innovation. Here, researchers are welcomed and encouraged to share their research progress and inspirations. It is a great opportunity to promote academic communication and collaboration worldwide. 


    978-1-915371-13-3 (Print)

    978-1-915371-14-0 (Online)

    Published Date



    Michael Harre, The University of Sydney

    Marwan Omar, Illinois Institute of Technology

    Roman Bauer, University of Surrey


  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220178

    The State-of-art Theorem and Detection Paradigms of Black Holes

    The black hole has been a mystery and a source of detection motivation for the human race ever since our quest of the discovery and research of other space. In general, the black hole can be defined as a special time-space structure where the gravity is strong enough to trap the photons, i.e., the light will be unable to penetrate or escape from it. In this paper, the current theorem and state-of-art detection paradigms are discussed in detail. Primarily, the categories of the black holes are demonstrated. The four different types of black holes all present their unique features. the quest for black hole exploration has never ceased. It has achieved stunning breakthrough with the first ever photo taken of the black hole by NASA in 2019. The future analysis of black hole excavation and research has been brought a bright future, as technology and outer space exploration plans continue to evolve. These results shed light on guiding further exploration of cosmology as well as the astrophysics.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220179

    Ethical Issues of Automatic Driving in the Society

    Autonomous driving is a very hot development direction in the future. With the application of electricity and the development of technology, autonomous driving technology will also be widely adopted. This study discusses the ethical issues of autonomous driving in society from the perspectives of social exclusion and private issues. The results demonstrate that although automatic driving is an excellent technology, it still needs more time to improve the whole systems and hardware facility to provide the best experience for people.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220183

    Python-based Model Optimization Platform

    With the increasing degree of informatization in today's society, the presentation of problems has become more complex, which puts forward higher requirements for people's ability to solve problems. Python is a popular language recently, and it is very popular among developers because of the many mature libraries that are encapsulated in it. People can use related libraries in Python and use open-source related libraries for algorithm research. The main purpose of this paper is to study the optimization platform of the model based on Python. This paper mainly analyzes the characteristics of the Python language and the structure of Python programming, and uses the relevant database of Python to realize the modeling work. The experiment shows that the accuracy of the decision tree model is 96.94 %, the accuracy of the KNN classification model is 89.05%.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220186

    The Importance of Mathematic History Education

    The most fundamental way to comprehend mathematics is through its history. It is becoming more widely acknowledged that studying and teaching mathematics history has important epistemological implications. However, learning about the history of mathematics is also a good way to get a liberal education. This paper, through a method of literature review, introduces the functions of mathematics history education and provides several suggestions for mathematics history education.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220187

    Enigma Machine Structure and The Mathematical Principle of The Introduction and Self-experiment

    The Enigma machine is a kind of advanced mechanical encryption system used by the Nazi German military during World War II, with the rotor structure as the main structure. Cryptographic machines generally take the form of a boxed structure. When encrypting a string of characters, the user enters the information into a machine or system and gets ciphertext. The original information can be obtained by reverse operation of the ciphertext. As the operator enters the message to be encrypted, a sequence of plain-length passwords can be recorded based on the sequence of letters lit up on the lamp board. This article will focus on the simple structure of the Enigma machine and the mathematics behind it, thus illustrating its importance and security in the history of human encryption. Then, to further explore the working principle of the Enigma machine and help to better understand its internal nature, the essay has provided a simple code that can realize the simple function of the Enigma, and also shows a simply equipped Enigma machine.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220188

    The Covid-19 Disinformation Detection on Social Media Using the NLP Approaches

    Artificial intelligence has emerged with big data technologies in natural language processing and been applied to creative solutions for overload information especially around the time of the COVID-19 epidemic. This paper provides a comprehensive review of research dedicated to applications of artificial intelligence in misinformation detection. This work organizes the necessary background material for COVID-19-related misinformation detection in NLP, concentrating on the transfer learning technique. Database, data preparation, and modeling make up the major body of information. In the part of modeling, it will merge the attributes of the pre-trained model with the specifical task scenario to explain and present pertinent comments on the future model's improvement under the task scenario. This research will benefit the decision-making and information screen for people's inability to distinguish truth from fiction during the COVID-19 pandemic.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220192

    A VR Music Learning Application VR-DRUM

    With the explosion of the MetaVerse concept and the burgeoning of VR (Virtual Reality) technology, VR has been applied in diverse scenarios,for example,social networking, games, education, online retail, house inspections, exhibition tours, training, virtual concerts and so on. Learning in the 3D environment of virtual reality can bring people an immersive interactive experience, which can improve the learners’ efficiency and deepen understanding. Music learning mainly includes the cultivation of rhythm (or sense of music, also including intonation), mainly relying on ears, followed by muscle memory, and the immersion of VR games is an optimal solution for music learning. This work proposes a VR-based drum learning game to solve several troubling problems such that when drummers practice real drums at home, the sound gets too loud, and the real drums occupy a large space, going out to practice drums will take much time. But to play drums in VR game, just put on a portable VR glass and pick up the touch controllers, drum players can practice at anytime, anywhere. What's more, it's very easy for novice to get started quickly. Another conspicuous advantage of VR is it provides an immersive experience for users,including a 360-degree panoramic screen, spatial audio, and authentic atmosphere.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220201

    The Basic Structure of Servomotor and The Function of Each Part

    This paper mainly introduces the basic structure and the function of each part of servomotor. At first, it talks about what is servomotor and where does it used for. Three parts are introduced in the article, the integration part, the addition part, and the feedback part. In each part, the article talks what the electronic components that are used in each part and how do these electronic components make the arithmetic come true. At last, the paper will discuss the advantage of the feedback part.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220148

    Predict FTSE100 Stock Movements Using Business News Sentiment and Machine Learning

    In order for investors to maximize their benefit by having better forecasts of the complex dynamics of the stock market, there are many factors that affect the stock market, from a company's financial ratios to investor sentiment and reactions to financial news. This project aims to collect UK business news from the Guardian and uses NLP techniques to transform unstructured text data into usable structured sentiment data to predict the movement of the FTSE100 index. The program uses two different libraries TEXTBLOB and VADER to extract sentiments from both the headlines and main bodies of the business news articles. Four machine learning algorithms including Logistic Regression, Naive Bayes, K-Nearest Neighbours and Support Vector Machines and a voting classifier were used to predict FTSE100 index movement given the business news sentiments of the previous day.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220152

    A Content-based Movie Recommendation System

    In this paper, we describe a content-based movie recommendation system and provide an overview of the movie recommendation systems in today's market. Our findings show 1): Summary-Based and Feature-Based movie recommendation systems will provide different recommendation results. 2) Combined recommendation system’s result is consistent with the Summary-Based recommendation system but different from the Feature-Based recommendation system. Based on our recommendation system, we also made some innovations and fusion and conducted several control tests to improve the quality of our recommendations.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220159

    A SIR Model for the Induction Analysis of a Company

    We notice the situation that when applicants are qualified and have the willingness to seek a job, the appraises of employees already in the company will have a large impact on applicants’ decisions of whether to become a member of this company or not. We believe that positive appraises will encourage the applicants to enter while negative appraises will discourage applicants. On the basis of this fact, in this paper we propose a compartmental model including the applicants population, the employed population and the resignation population. Several differential equations are set up and disease-free equilibrium is calculated. After the calculation of R_0, we complete sensitivity analysis which leads to the conclusion. The conclusion suggests that either decreasing the progression rate from applicants to employees who have negative appraises or increasing the progression rate from employees with negative appraises to employees with positive appraises can decrease the population of negative states.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220166

    Comparisons of Two Types of Astronomical Telescopes: Terrestrial Telescopes and Space Telescopes

    In the field of astrophysics and cosmology, astronomical telescopes are the main and key tool for observing and capturing information of celestial bodies. Generally, there are two types of telescopes, i.e., terrestrial telescopes and space telescopes. This study will be mainly focused on the differences and similarities between the two types mentioned above. According to the analysis, the ground telescope is larger and collect data with processing instead of real picture. The space telescope, on the other hand, is smaller but hard to repair, which is able to send back the real pictures of the space. The research aims of this investigation are helping the further researchers to have better understanding to the two different types of telescopes and offering a guideline for them to choose the more appropriate resources to use for the future research. These results shed light on guiding further exploration of different types of telescopes and pave a path for the future inventions of the telescopes.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220169

    Searching Transits Around Red Dwarfs

    In this research, researchers aim to find the existence of possible new exoplanets within the various red dwarf systems with masses of 0.1 M/Me 0.3 within 15 parsecs of the Earth. In the sample size of 600, the Team Hypothesized the existence of at least 3-5 previously undiscovered exoplanets due to the red dwarf's properties mentioned above combined with technological advancement, allowing for a more effective analysis method of the existing data. The Researchers intended to use python to access Jupyter labs through which the codes analyze to measure the relative flux graph and with the aid of other programs such as NumPy, lightkurve, BLS, and Doppler shift method. The researchers classified all flux patterns into four different types: Ordinary(there’s no worth-noticing feature) flux pattern; Wave pattern, for which the flux distribution in the graph is an approximate adjustment to the sinusoidal mathematical trend with few minimal variations; Transit patterns, graphs which got flux pattern at some specific period ,when researchers find this pattern, they will zoom in the special flux area and employ BLS method to determine whether there exists at least one exo-planet.; Flare patterns, which have a feature of windfall, they have steep and rapid changes in flux as well as patterns. Researchers recorded the fourth type in paper to offer reference materials for later researchers who may be interested in flares. Through analyzing, we found 1 case of unresearched flare and 2 cases of worth-noting patterns, but no new exoplanets were found.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220174

    Stress Analysis and Size Optimization of Suspension Beam Structure of Robot Manipulator

    In this paper, the stress and deformation of a manipulator structure are analyzed, and the structural optimization design is carried out. The initial configuration is a cantilever beam structure with rectangular section, which is fixed at one end and bears a load of 1 ton at the other end. After stress and deformation analysis with ABAQUS software and SolidWorks software, three optimizations were carried out. Geometric configuration optimization, topology optimization and material optimization. After optimization, the overall quality of the structure is reduced by 80%, and there is no great loss of strength and safety.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220175

    Research on Intelligent Dialogue Systems

    Intelligent dialogue systems, as a subfield of artificial intelligence, have very important research significance and application value. Today’s AI dialogue systems are still in a relatively early stage, but they are developing very rapidly. In recent years, intelligent dialogue systems have been applied in many fields, such as intelligent customer service in online transactions, intelligent voice assistants in smartphones, and virtual chatbots. This paper introduces the background of intelligent dialogue systems and the current research status of key technologies and discusses some challenges in this field and some recent research to improve the system. Most of the current intelligent dialogue systems can perform effective human-computer interaction and respond accordingly. But for the next generation of intelligent dialogue system, more human characteristics are needed so that it can better understand and express human language, have its own personality, and maintain the consistency and logic of dialogue.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220058

    Analysis of the Current Situation of Virtual Currency Based on Statistical Data and Prospects for Its Future Model

    Bitcoin is known to the world from its birth to the present, and it only took 13 years. In the past 13 years, countless virtual currencies have flourished. In the rapid development of virtual currencies, many problems have been revealed. This article will mainly discuss (1) energy consumption, (2) miner consolidation, (3) encryption security and finally (4) miner income volatility through different types of virtual currency data. And use Android virtual currency as a case to look forward to virtual currency The direction of development. Readers can learn more about the main challenges faced by virtual currencies through this article, and explore the future development model of virtual currencies.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220076

    Support Vector Machine for Credit System: The Effect of Parameter Optimization and Training Sample

    The credit assessment system is an essential part of modern financial institutions, and most of them have adopted different models to perform the task according to their specific needs. Support Vector Machine has been widespread and proved an efficient classifier, especially for relatively small datasets in recent years. When using SVM, data processing, choosing an appropriate kernel function, and tuning parameters can largely affect its performance. The most popular kernel function of SVM is the Radial basis function (RBF), and its main parameters are the regularization parameter, C, and the kernel coefficient, γ. Our study based on the South German credit dataset demonstrates that parameter optimization and an appropriate ratio of the size of the training dataset to the size of the testing dataset could significantly improve the performance of SVM.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220098

    Comparative Study of RSA Encryption and Quantum Encryption

    Encryption is an important factor during online communication. It is useful to protect users’ privacy and prevent eavesdroppers listening. RSA encryption and quantum encryption are two mainstream encryption methods applied nowadays. This paper focuses on the evaluation and comparison between these two encryptions. It adopts the basic theory of RSA encryption and quantum encryption and provides an analysis of the benefits and shortcomings of these encryptions. It can be concluded that RSA (a type of mathematical encryption) is more popular than quantum encryption (a kind of physical encryption), but is less secure.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220102

    The Workings of a Jet Engine

    This document explains and explores the basics of the jet engine, from basic physical knowledge to the inner workings of the engine, as well as the maintenance aspect. It touches on the mechanical properties that allow the jet engine to function, the design considerations, the mechanisms within the engine, and finally the maintenance of the engine.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220108

    Bionic Soft Robot Review

    Traditional robots are mainly rigid structures. They are complex in structure but limited in flexibility, and have poor security and adaptability. At that time, many bio-inspired robots were created to overcome the traditional robotic challenges. Creatures gave us the inspiration to use a soft body to complete task, and then soft robotics were invented. This paper evaluated the future difficulties faced by this area, and listed the deficiencies that still need to be improved for soft robots that should be overcome in future projects as well. First of all, the first difficulty is that most soft robots rely on software drivers to complete tasks, and because of this, the driving functions of soft robots cannot be perfectly performed, and the action tasks are not diverse. Secondly, if the action moving is over flexible, it will be hard to control. The precision for missions cannot be satisfied. Thirdly, the choice of drivers’ type becomes another problem. For example, the memory alloy drive has the advantages of large driving force, controllable stiffness, good elasticity, etc., but it also has disadvantages such as easy aging and slow response speed. Although the pneumatic drive has a fast response rate, there is a risk that the fluid may leak, and the environment cannot be guaranteed to be airtight. Obviously, there is no ideal solution to work out actuation difficulties.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220112

    Modelling and Analysis of Quantum Security Architecture for B5G Fronthaul Network

    To satisfy the urgent requirements of security for fifth generation (5G) fronthaul network, quantum key distribution (QKD) technique is taken into consideration as a promising way. In this paper, we first propose an architecture for quantum security beyond fifth generation (B5G) fronthaul optical network, which merges facilities of QKD into the architecture of existing 5G fronthaul network, enabling quantum signals to be transmitted with classical signals within the same fiber. Secondly, theoretical model analysis of interference with quantum signals caused by four wave mixing noise is performed. Moreover, the theory of secure key rate calculation under noise interference is introduced. Lastly, the QKD performance in the proposed architecture is evaluated, which leads to the conclusion that even when the quantity of B5G fronthaul optical channels for classical signals reaches up to 12, the secure transmission distance of QKD is still beyond 20km, which satisfies the demand of B5G fronthaul optical network.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220118

    Realization of Wireless Remote Control Intelligent Street Lamp by Single Chip Microcomputer

    In order to better solve the huge power consumption of street lamps, it is not conducive to environmental protection and saving resources, and it is also to save manpower and financial resources. In this article, an infrared remote control LED light is designed, using the infrared control module and the single-chip control module, and also mainly used the characteristics of PWM combined with LED to save electricity. The designed LED light can be combined with the app on the mobile phone to realize the combination of software and hardware, and the control of the street light can be realized on the mobile phone. This article also propose to convert solar energy into electricity for street lighting, which is the direction of subsequent research and development.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220127

    Predict Gold Price Trend Based on ARIMA Model

    As a financial product, gold is one of the more important spot and futures trading products in the commodity market. Based on the time series model, the gold price can be fitted and predicted, in order to explore the law of gold price changes. It has positive implications for investors and government managers. This article selects the Prime Day price in 2018 as the research object. Combined with domestic and foreign research content on financial time series. First, through the time series diagram test and the unit root test, it is obtained that the gold daily price series is a cycle-free and non-stationary series. Therefore, the time series needs to be differentiated. Second, a new stationary sequence is obtained by making second-order differences. Third, after the time sequence diagram test, ADF test, and white noise test, the sequence is a non-white noise sequence. Comparing the AIC values of multiple time series models, the most ideal model for the series should be the ARIMA (2,2,2) model. The significance test of the model shows that the fitted model is significantly effective. And the significance test of the model parameters is also passed. Then make predictions with this model. Comparing the predicted value with the future real gold price, it is found that the predicted value is close to the real value. This is a good reference for the country to formulate relevant economic policies.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220132

    The Principle and State-of-Art Application of Quantum Hall Effect

    Contemporarily, quantum hall effect (QHE), as the quantum version of classic Hall effect, represented a turning point in the understanding of material physics, metrology, high energy physics, astrophysics. In the category of QHE, there are plenty of sub-types including fractional QHE (FQHE), anomalous QHE (QAHE), spin QHE (SPHE) etc. This paper will mainly focus on the latest progress and the state-of-art applications regarding to QHE. To be specific, a brief introduction of the principle of Hall effect and the differences among different types will be introduced. Afterwards, the applications will be discussed and demonstrated. Overall, these results would provide the audience a general view on QHE, and some recent applications regards it, which shed light on guiding further exploration for QHE.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220133

    Similarities of Influencers across Different Social Media Platforms by Using Four Centrality Measures

    Searching for influencers among a social network is important because marketers can then use this information to conduct word-of-mouth (WOM) advertisement, which is an important marketing technique. Literature Review provides detailed information about WOM advertisement. There are many ways to search influencers and often they are network centrality measurements. This paper aims to investigate whether each centrality measurement could produce similar results across different social media platforms (eg. Facebook, Twitter, Instagram). The social network data used in this research is from Huawei Company. This research uses four centrality measurements and three set similarity methods to analysis the data. As a result, this paper draws a conclusion about the binary question "Does it provide similar results or not?". Since various companies and applications may have different standards and definitions about being similar, please also check similarity data provided in this paper.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220134

    On the Copenhagen Interpretation and Its Alternative Theories

    Quantum mechanics has become the rising trend in modern physics and has completely changed people’s views of physics. This essay delves into the once-existing problems underlying quantum mechanics such as the conflict between substantiality and completeness in quantum mechanics and the relationship between causality and observation and analyzes the solutions to the controversies. The Copenhagen Interpretation is widely considered the most orthodox explanation of quantum mechanics; therefore, this paper focuses on the Copenhagen Interpretation and examines how it delicately manages to explain quantum mechanics. It also examines its alternative theories, such as Einstein’s local hidden variable theory, and disproves them with Bell’s inequality and other reasonings. The essay aims to clarify and systematize the historical development of quantum mechanics, showing the current progress of quantum mechanics.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220139

    Development of Number Theory and the Application in Cryptography

    The primary focus of number theory, one of the fields of fundamental mathematics, is on the characteristics of integers. The development of cryptography also benefited greatly from the contributions of number theory. The paper primarily examines the evolution of number theory and its use in cryptography using a method of literature review. The study discovers that number theory development in the East reached a prosperous phase in the 1930s. From the 15th and 16th centuries through the 19th century, number theory flourished in the first. Number theory is still being developed, as demonstrated by the discovery of the biggest known prime number by American mathematician Curtis Cooper. Numerology is also extensively employed in cryptography, including the RSA technique and digital signatures. Numerous algorithms used in cryptography mostly depend on a working understanding of number theory.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220143

    Neural Machine Translation in Translation and Program Repair

    Translation is a challenge for humans since it needs a good command of two or more languages. When it comes to computer programs, it is even more complex as it is difficult for computers to imitate human translators. With the emergence of deep learning algorithms, especially neural network architectures, neural machine translation (NMT) models gradually outperformed previous machine translation models and became the new mainstream in practical machine translation (MT) systems. Nowadays, NMT has been developing for several years and has been applied in many fields. This paper is focused on studies on four different application categories of NMT models: 1) Text NMT; 2) Automatic program repair (based on NMT); 3) Simultaneous translation. Our work provides a summary of the latest research on different applications of NMT and makes comments on their development in the future. This paper also mentioned the shortcomings of existing studies in this essay and pointed out some possible research directions.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220084

    Some Fundamental Results from Complex Analysis

    This paper is going to introduce the most basic theory of analytic functions of one complex variable. It begins at the discussion of meaning of complex number and the historical development from the formula of cubic equation to the square root of negative number. In the middle section, which is divided in to four small parts. First part states the expression of complex number z, algebraic properties, and the relationship of each single complex number with whole complex plane. Second part concerns about several elementary functions of complex number. Next part relates to the derivative of complex number, such as the partial derivative and Cauchy-Riemann Equation to verdict that whether a function is analytic in the domain. Last part is the integral of complex functions, which concludes some important theorems with the proof, and examples. After the section of introduction of complex number, it comes to the final section which is talking about an identity involving complex number and the prove of it.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220085

    A Fundamental Tour of Complex-valued World

    Throughout the learning, the topic of complex variables has always been a very special area in mathematics. As progressed through the complex variable courses, our group started to raise our interest in this area and wish to learn further. Hence, this essay will focus on several perspectives on the topic of complex variables. This will include the historical development, application, general theorem and solving real problems.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220086

    Elegant Theory of Complex Analysis

    A complex number is an element in a number system containing both real numbers and the imaginary unit 𝑖, satisfying 𝑖^2 = −1. Since their discovery, complex numbers have been a powerful means of mathematical calculation. Complex analysis is a part of mathematical analysis that investigates complex numbers and their analyticity, holomorphicity, etc. Many renowned mathematical giants once had their own research in complex analysis, such as Cauchy, Gauss, Euler, etc. On the grounds that it deals with functions of complex numbers, complex analysis is a helpful area in the whole mathematics field. There are plenty of applications of complex analysis in both the mathematical field and the physics field. In this paper, the history of complex numbers and complex analysis is presented. Also, some contents of complex variables are shown, including the basic properties of complex numbers, the derivative and integral of functions of complex numbers, and several critical theorems in the area of complex analysis.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220087

    Complex Analysis and its Several Applications

    Complex analysis is important for science because it extends analytical methods from real variables to complex variables and complex numbers. Also, complex number has two independent components, one variable will not change when the other is changing, that are particularly useful when two variables must be dealt with simultaneously. In this essay, we are going to talk about the history chronologically such as who first introduced the idea of complex number, who first discovered the rule of complex number, and why complex analysis is important. Also, the essay includes some basics about the complex variable and complex analysis. For example, the definition of complex number, Cauchy-Riemann Equations, and Cauchy Goursat theorem can help us to get further known of the complex analysis and solve some basic analytic problems.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220089

    A Fascinating Expedition of Complex Analysis

    The invention of complex numbers was essential in the rapid development of mathematics. Although most people consider complex numbers to be nonsensical notations, they are critical in technical disciplines. Human beings entered a wonderful realm when mathematicians began to investigate complex numbers. Our universe is amazing, full of beautiful discoveries, and even miraculous, according to complex analysis. We begin by giving a brief review of complex analysis' history, including when and how it originated. The root of a quadratic equation was used to find complex numbers. We look at some of the ways complex numbers are used in engineering domains like acoustic wave propagation. A thorough examination of certain key theorems of complex analysis is also included.

  • Open Access | Article 2023-02-20 Doi: 10.54254/2753-8818/2/20220090

    Some Fundamentals of Complex Analysis

    In this paper, we first introduced the significance of complex variables as a field in the first section. Then, for the main body section, we explored the history and development of complex numbers. In addition, we demonstrated the key concepts and theorems that are crucial in the fundamentals of this field. We dive in depth to the such fundamental knowledge, which is the preliminaries of complex numbers. We analyzed the preliminaries via three smaller sections: complex numbers and the complex plane, functions on the complex plane, and integration along curves. Finally, we applied these knowledges into deriving a proof for the product of different sine expressions, which results in a generalized formula. Ultimately, the last section will be the conclusion of the paper.

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