• Title/Summary/Keyword: Mathematical Analysis

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A Study of Antiquity YulRyeo (고대(古代) 율려(律呂)에 관한 연구)

  • Choi, Won-Ho;Kim, Ki-Seung
    • Industry Promotion Research
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    • v.7 no.1
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    • pp.59-74
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    • 2022
  • There are three main ways to interpret Zhouyi(周易). The first is to interpret it as a number, the second is to interpret it as an image symbolized by the Gwae(卦), and the third is to interpret it as the moral reason contained in it. Although YulRyeo(律呂) is not as widely known as Zhouyi, its use in ancient times was the same as that of the main character. First, the mathematical analysis method using the three-pronged method for tuning musical instruments, second, the symbolic interpretation using the musical meaning symbolized by YulRyeo, and third, the applied interpretation method that expands to the moral reason contained in YulRyeo. The purpose of this thesis is to organize the dictionary meaning of YulRyeo and various meanings of ancient YulRyeo. In addition, by studying ancient literature on the meaning of YulRyeo's magic spell mechanics(術數易學) and Naepeum and Five Elements(納音五行), which is the origin of Gobeop Myongriology, I classify and interpret them in detail. and to find ways to apply it to Myongriology. It is hoped that this study will give a more in-depth understanding of YulRyeo and will be of little help to related studies such as the mechanics of magic and Myongriology studies in the future.

The Geometrical Imagination of the MCU 'Phase 3' Movie (MCU '페이즈3'영화에 나타난 기하학적 상상력)

  • Kim, Young-Seon;Kim, Tae-Soo
    • The Journal of the Korea Contents Association
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    • v.22 no.10
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    • pp.132-142
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    • 2022
  • The purpose of this study is to interpret the MCU's universal worldview from the perspective of geometry and to storytell narrative elements with mathematical imagination. For storytelling, data from the Phase 3 series aired from 2016 to 2019 was used. The Phase 3 series stimulates the imagination of the public with the sense of reality shown in the narrative and images based on geometrical theory and various predictions about future technology. Imagination is the driving force for diverse and original thinking about the unexperienced, and the ability to find order in chaos and create new perceptions of matter. The power of imagination is very necessary not only in artistic activities, but also in the scientific field where logic and rationality are important. Bachelard's imagination aims for art, the primitive realm of human beings, and contains sincerity and passion for the wonders of nature and all things. By exploring the MCU's worldview and superhero narrative through geometrical logic and imagination-driven imagery, you can understand the cosmic messages and laws in the film. From a convergence point of view of art and science, various and original techniques based on mathematics and scientific imagination used in MCU video production will help to improve the quality of video analysis.

Assessment of a fresh submarine groundwater discharge in eastern Jeju Island using analytic seawater intrusion models (해수침투 해석해 기반 제주 동부 담해저 지하수 유출의 정량적 산정)

  • Kim, Il-Hwan;Chang, Sun Woo
    • Journal of Korea Water Resources Association
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    • v.55 no.12
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    • pp.1011-1020
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    • 2022
  • Previous studies for the assessment of submarine groundwater discharge (SGD) were perfomed for areas where a large amount of SGD was observed. Newly developed assessment methods were proposed that was based on an analytic solution using sharp interface model. The proposed mathematical equations used the existing observed groundwater level and hydrogeological data of Jeju Island as input data. The quantitatively assessed FSGD values were compared to the basin-scale recharge estimation values in Seong-San area in eastern Jeju. As a result of the study, it was estimated that the amount of FSGD in the Seongsan area ranges from about 2.65 to 9.15% of the amount of areal-recharge. Through the analysis of the FSGD combined with the analytic model, it is to be provided as a scientific tool to establish a more reasonable coastal water resource management plan.

The Analysis of Proportional Reasoning Tasks in Elementary School Mathematics Textbooks (초등학교 수학 교과서에 제시된 비례추론 과제의 분석)

  • Song, Dong Hyun;Park, Young Hee
    • Education of Primary School Mathematics
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    • v.25 no.1
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    • pp.57-79
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    • 2022
  • Current mathematics It is necessary to ensure that ratio and proportion concept is not distorted or broken while being treated as if they were easy to teach and learn in school. Therefore, the purpose of this study is to analyze the activities presented in the textbook. Based on prior work, this study reinterpreted the proportional reasoning task from the proportional perspective of Beckmann and Izsak(2015) to the multiplicative structure of Vergnaud(1996) in four ways. This compared how they interpreted the multiplicative structure and relationships between two measurement spaces of ratio and rate units and proportional expression and proportional distribution units presented in the revised textbooks of 2007, 2009, and 2015 curriculum. First, the study found that the proportional reasoning task presented in the ratio and rate section varied by increasing both the ratio structure type and the proportional reasoning activity during the 2009 curriculum, but simplified the content by decreasing both the percentage structure type and the proportional reasoning activity. In addition, during the 2015 curriculum, the content was simplified by decreasing both the type of multiplicative structure of ratio and rate and the type of proportional reasoning, but both the type of multiplicative structure of percentage and the content varied. Second, the study found that, the proportional reasoning task presented in the proportional expression and proportional distribute sections was similar to the previous one, as both the type of multiplicative structure and the type of proportional reasoning strategy increased during the 2009 curriculum. In addition, during the 2015 curriculum, both the type of multiplicative structure and the activity of proportional reasoning increased, but the proportional distribution were similar to the previous one as there was no significant change in the type of multiplicative structure and proportional reasoning. Therefore, teachers need to make efforts to analyze the multiplicative structure and proportional reasoning strategies of the activities presented in the textbook and reconstruct them according to the concepts to teach them so that students can experience proportional reasoning in various situations.

Characteristics of Measurement Errors due to Reflective Sheet Targets - Surveying for Sejong VLBI IVP Estimation (반사 타겟의 관측 오차 특성 분석 - 세종 VLBI IVP 결합 측량)

  • Hong, Chang-Ki;Bae, Tae-Suk
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.40 no.4
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    • pp.325-332
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    • 2022
  • Determination of VLBI IVP (Very Long Baseline Interferometry Invariant Point) position with high accuracy is required to compute local tie vectors between the space geodetic techniques. In general, reflective targets are attached on VLBI antenna and slant distances, horizontal and vertical angles are measured from the pillars. Then, adjustment computation is performed by using the mathematical model which connects measurements and unknown parameters. This indicates that the accuracy of the estimated solutions is affected by the accuracy of the measurements. One of issues in local tie surveying, however, is that the reflective targets are not in favorable condition, that is, the reflective sheet target cannot be perfectly aligned to the instrument perpendicularly. Deviation from the line of sight of an instrument may cause different type of measurement errors. This inherent limitation may lead to incorrect stochastic modeling for the measurements in adjustment computation procedures. In this study, error characteristics by measurement types and pillars are analyzed, respectively. The analysis on the studentized residuals is performed after adjustment computation. The normality of the residuals is tested and then equal variance test between the measurement types are performed. The results show that there are differences in variance according to the measurement types. Differences in variance between distances and angle measurements are observed when F-test is performed for the measurements from each pillar. Therefore, more detailed stochastic modeling is required for optimal solutions, especially in local tie survey.

A System Dynamic for Investigating to Use of Building Information Modeling (BIM) for Hanok Construction (시스템 다이내믹스 기반 한옥건축의 BIM 접목 활성화 방안 연구)

  • Seo, Seung-Ha;Bang, Yei-Dam;Hyen, Ju-Hwan;Yu, Chaeyeon;Lee, Donghoon;Kim, Sungjin
    • Korean Journal of Construction Engineering and Management
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    • v.24 no.5
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    • pp.3-11
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    • 2023
  • Building information modeling (BIM) can help to visualize and manage the building-related information at the object-based level, and it is possible to help link the tasks in the network of Hanok construction. While many studies have significant interest in using BIM for modern construction, there is only few studies to observe the use of BIM for traditional construction, commonly called Hanok construction in South Korea. Hence, the main goal of this study is to develop a system dynamic model for investigating how the BIM can be widely used for Hanok construction. To this end, this study identified the factors influencing the BIM uses for the Hanok construction, developed a causal loop diagram (CLD) to investigate the interrelationships among the factors, and provided a final model based on the mathematical definitions. Based on the scenario analysis, it is demonstrated that the support to building Hanok and education cost for BIM positively influence activating and using the BIM for the Hanok construction. Based on the dynamics of the factors identified in this study, it is important to consider expanding support for Hanok construction and education cost for BIM to successfully integrate and utilize BIM in the construction industry.

Analysis of Crushing/Classification Process for Recovery of Black Mass from Li-ion Battery and Mathematical Modeling of Mixed Materials (폐배터리 블랙 매스(black mass) 회수를 위한 파쇄/분급 공정 분석 및 2종 혼합물의 수학적 분쇄 모델링)

  • Kwanho Kim;Hoon Lee
    • Resources Recycling
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    • v.31 no.6
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    • pp.81-91
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    • 2022
  • The use of lithium-ion batteries increases significantly with the rapid spread of electronic devices and electric vehicle and thereby an increase in the amount of waste batteries is expected in the near future. Therefore, studies are continuously being conducted to recover various resources of cathode active material (Ni, Co, Mn, Li) from waste battery. In order to recover the cathode active material, black mass is generally recovered from waste battery. The general process of recovering black mass is a waste battery collection - discharge - dismantling - crushing - classification process. This study focus on the crushing/classification process among the processes. Specifically, the particle size distribution of various samples at each crushing/classification step were evaluated, and the particle shape of each particle fraction was analyzed with a microscope and SEM (Scanning Electron Microscopy)-EDS(Energy Dispersive Spectrometer). As a result, among the black mass particle, fine particle less than 74 ㎛ was the mixture of cathode and anode active material which are properly liberated from the current metals. However, coarse particle larger than 100 ㎛ was present in a form in which the current metal and active material were combined. In addition, this study developed a PBM(Population Balance Model) system that can simulate two-species mixture sample with two different crushing properties. Using developed model, the breakage parameters of two species was derived and predictive performance of breakage distribution was verified.

Perception of Science Core Competencies of High School Students who Participated in the 'Skills' based Inquiry Class of the 2015 Revised Science Curriculum (2015 개정 과학과 교육과정의 '기능' 기반 탐구 수업에 참여한 고등학생의 과학과 핵심역량에 대한 인식)

  • Sangyou Park;Wonho Choi
    • Journal of The Korean Association For Science Education
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    • v.43 no.2
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    • pp.87-98
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    • 2023
  • In this study, we investigated the change in science core competency perception of high school students and the reason for change when science inquiry classes were conducted using eight 'skills' of the 2015 revised science curriculum. Fifteen first-year high school students in Jeollanam-do participated in the science inquiry class of this study, and the class was conducted for 20 hours (5 hours a day for four days). The inquiry activities used in the class consisted of four activity stages (research problems, research methods, research results, and conclusions) and each stage was constructed to include at least one 'skill (Problem Recognition, Model Development and Use, Inquiry Design and Performance, Data Collection, Analysis and Interpretation, Mathematical Thinking and Computer Application, Conclusion and Evaluation, Evidence-based Discussion and Demonstration, and Communication)'. As a result of the study, students' perception of the five science core competencies increased statistically significantly at the significance level of 0.01 through inquiry classes and more than 93% of students recognized that their science core competencies improved through the classes. However, since the class of this study was conducted for a small number of students, it is difficult to generalize the effect of the class, and so it is necessary to conduct a quantitative study for many students.

Customized maxillary incisor position relative to dentoskeletal and soft tissue patterns in Chinese women: A retrospective study

  • Zhou, Xueman;Zheng, Yingcheng;Zhang, Zhenzhen;Zhang, Zihan;Wu, Lina;Liu, Jiaqi;Yang, Wenke;Wang, Jun
    • The korean journal of orthodontics
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    • v.52 no.2
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    • pp.150-160
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    • 2022
  • Objective: To provide reliable prediction models based on dentoskeletal and soft tissue variables for customizing maxillary incisor positions and to optimize digitalized orthodontic treatment planning. Methods: This study included 244 Chinese women (age, 18-40 years old) with esthetic profiles after orthodontic treatment with fixed appliances (133 in group I: 1° ≤ The angle between the nasion [N]-A point [A] plane and the N-B point [B] plane [ANB] ≤ 4°; 111 in group II: 4° < ANB ≤ 7°). Dental, skeletal, and soft tissue measurements were performed on lateral cephalograms of the participants. Correlation and multiple linear regression analyses were used to determine the influence of dentoskeletal and soft tissue variables on maxillary incisor position. Results: The ideal anteroposterior position of the maxillary incisor varied between sagittal skeletal patterns. The position of the maxillary incisor correlated with the sagittal discrepancy between the maxilla and the mandible (ANB), protrusion of the midface, nasal tip projection, development of the chin, and inclination of both the maxillary and mandibular incisors. Distance from the maxillary central incisor to nasion-pogonion plane predicted using multiple linear regression analysis was accurate and could be a practical measurement in orthodontic treatment planning. Conclusions: Instead of using an average value or norm, orthodontists should customize a patient's ideal maxillary incisor position using dentoskeletal and soft tissue evaluations.

Propagation Analysis of Dam Break Wave using Approximate Riemann solver (Riemann 해법을 이용한 댐 붕괴파의 전파 해석)

  • Kim, Byung Hyun;Han, Kun Yeon;Ahn, Ki Hong
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.5B
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    • pp.429-439
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    • 2009
  • When Catastrophic extreme flood occurs due to dam break, the response time for flood warning is much shorter than for natural floods. Numerical models can be powerful tools to predict behaviors in flood wave propagation and to provide the information about the flooded area, wave front arrival time and water depth and so on. But flood wave propagation due to dam break can be a process of difficult mathematical characterization since the flood wave includes discontinuous flow and dry bed propagation. Nevertheless, a lot of numerical models using finite volume method have been recently developed to simulate flood inundation due to dam break. As Finite volume methods are based on the integral form of the conservation equations, finite volume model can easily capture discontinuous flows and shock wave. In this study the numerical model using Riemann approximate solvers and finite volume method applied to the conservative form for two-dimensional shallow water equation was developed. The MUSCL scheme with surface gradient method for reconstruction of conservation variables in continuity and momentum equations is used in the predictor-corrector procedure and the scheme is second order accurate both in space and time. The developed finite volume model is applied to 2D partial dam break flows and dam break flows with triangular bump and validated by comparing numerical solution with laboratory measurements data and other researcher's data.