• 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.

• Journal of Korea Water Resources Association
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• v.55 no.6
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• pp.405-419
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• 2022

Flood frequency analysis commonly used to design the hydraulic structures to minimize flood damage includes uncertainty. Therefore, the most appropriate design flood within a uncertainty should be selected in the final stage of a hydraulic structure, but related studies were rarely carried out. The total expected cost function introduced into the flood frequency analysis is a new approach for determining the optimal design flood. This procedure has been used as UNCODE (UNcertainty COmpliant DEsign), but the application has not yet been introduced in South Korea. This study introduced the mathematical procedure of UNCODE and calculated the optimal design flood using the annual maximum inflow of hydroelectric dams located in the Bukhan River system and results were compared with that of the existing flood frequency. The parameter uncertainty was considered in the total expected cost function using the Gumbel and the GEV distribution, and the Metropolis-Hastings algorithm was used to sample the parameters. In this study, cost function and damage function were assumed to be a first-order linear function. It was found that the medians of the optimal design flood for 4 Hydroelectric dams, 2 probability distributions, and 2 return periods were calculated to be somewhat larger than the design flood by the existing flood frequency analysis. In the future, it is needed to develop the practical approximated procedure to UNCODE.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.33 no.1
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• pp.9-16
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• 2020

The objective of this study is to propose closed-form solutions to the free vibration response of single-degree-of-freedom (SDOF) systems, as part of fundamental research on dynamic systems with Coulomb friction. The motion of a dynamic system with Coulomb friction is described by a nonlinear differential equation, and, due to the variation in the sign of friction force term with the direction of motion, it is difficult to obtain the closed-form solution. To solve this problem, the nonlinear differential equation is directly computed by numerical integration, or an approximated solution is indirectly obtained using a linear differential equation wherein the damping effect due to Coulomb friction is replaced by an equivalent viscous damping term. However, these conventional methods do not provide a closed-form solution from a mathematical point of view. In this regard, closed-form solutions to the free vibration response of SDOF systems with Coulomb friction are derived herein by considering that the sign of the friction force term is reversed in each half-cycle of motion and by expanding it to the entire time history using the power series function. In addition, for a given initial condition, both the number of free vibration half-cycles and the response at the instant when free vibration motion stops are predicted under the condition that the motion of free vibration is stopped when the amplitude of the friction force is higher than that of the restoring force due to stiffness.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.35 no.1
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• pp.25-34
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• 1999

The Steering and Sailing Rules of International Regulation for Preventing Collisions at Sea now in use direct actions to avoid collision when two power-driven vessels are meeting on reciprocal or nearly reciprocal courses so as to involve risk of collision. But these rules do not refer to the minimum relative distances and safety relative distances between two vessels when they should take such actions.In this paper the ship's collision avoiding actions being analyzed from a viewpoint of ship motions, the mathematical formulas to calculate such relative distances necessary for taking actions to avoid collision were worked out. The values of maneuvering indices being figured out through experiments of 20 actual ships of small, medium, large and mammoth size and applied to calculating formulas, the minimum relative distances and safety relative distances were calculated. The main results were as follows. 1. It was confirmed that the criterion elements for collision avoiding actions in head-on situation of two vessels shall be the minimum relative distances and safety relative distances between them. 2. On the assumption that two vessels same in size and condition were approaching each other in head-on situation, the minimum relative distance of small vessel(GT : 160~650tons) was found to be about 4.7 times her own length, and those of medium (GT:2,300~4,500tons),large(GT:15,000~62,000tons) and mommoth (GT:91,000~194,000tons) vessels were found to be about 5.2 times, about 5.2 times and about 6.1 times their own lengths respectively. 3. On the assumption that two vessels same in size and condition were approaching each other in head-on situation, the safe relative distance of small vessel (GT : 160~650tons) was found to be about 6.8 times her own length, and those of medium (GT : 2,300~4,500tons), large (GT: 15,000~62,000tons) and mammoth (GT : 91,000~194,000tons) vessels were found to be about 9.0 times, about 6.3 times, and about 8.0 times their own lengths respectively. 4. It is considered to be helpful for the safety of ship handling that the sufficient safe relative distances for every vessels shall be more than about 12~14 times which are 2 times minimum relative distance, their own length on above assumption.

• Economic and Environmental Geology
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• v.36 no.3
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• pp.243-255
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• 2003

The mathematical models for GIS-based spatial data integration have been developed for geological applications such as mineral potential mapping or landslide susceptibility analysis. Among various models, the effectiveness of fuzzy logic based integration of multiple sets of geological data is investigated and discussed. Unlike a traditional target-driven fuzzy integration approach, we propose a data-driven approach that is derived from statistical relationships between the integration target and related spatial geological data. The proposed approach consists of four analytical steps; data representation, fuzzy combination, defuzzification and validation. For data representation, the fuzzy membership functions based on the likelihood ratio functions are proposed. To integrate them, the fuzzy inference network is designed that can combine a variety of different fuzzy operators. Defuzzification is carried out to effectively visualize the relative possibility levels from the integrated results. Finally, a validation approach based on the spatial partitioning of integration targets is proposed to quantitatively compare various fuzzy integration maps and obtain a meaningful interpretation with respect to future events. The effectiveness and some suggestions of the schemes proposed here are illustrated by describing a case study for landslide susceptibility analysis. The case study demonstrates that the proposed schemes can effectively identify areas that are susceptible to landslides and ${\gamma}$ operator shows the better prediction power than the results using max and min operators from the validation procedure.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.6
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• pp.78-86
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• 2014

In this paper, a novel intensity-based fiber optic vibration sensor using a mass-spring structure, which consists of four serpentine flexure springs and a rectangular aperture within a proof mass, is proposed and its feasibility test is given by the simulation and experiment. An optical collimator is used to broaden the beam which is modulated by the displacement of the rectangular aperture within the proof mass. The proposed fiber optic vibration sensor has been analyzed and designed in terms of the optical and mechanical parts. A mechanical structure has been designed using theoretical analysis, mathematical modeling, and 3D FEM (Finite Element Method) simulation. The relative aperture displacement according to the base vibration is given using FEM simulation, while the output beam power according to the relative displacement is measured by experiment. The simulated sensor sensitivity of $15.731{\mu}W/G$ and detection range of ${\pm}6.087G$ are given. By using reference signal, the output signal with 0.75% relative error shows a good stability. The proposed vibration sensor structure has the advantages of a simple structure, low cost, and multi-point sensing characteristic. It also has the potential to be made by MEMS (Micro-Electro-Mechanical System) technology.

• Journal of Korea Water Resources Association
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• v.46 no.7
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• pp.745-754
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• 2013

The systematic analysis and evaluation of required energy in the processes of drinking water production and supply have attracted considerable interest considering the need to overcome electricity shortage and control greenhouse gas emissions. On the basis of a review of existing research results, a practical method is developed in this study for evaluating energy in water supply networks. The proposed method can be applied to real water supply systems. A model based on the proposed method is developed by combining the hydraulic analysis results that are obtained using the EPANET2 software with a mathematical energy model on the MATLAB platform. It is suggested that performance indicators can evaluate the inherent efficiency of water supply facilities as well as their operational efficiency depending on the pipeline layout, pipe condition, and leakage level. The developed model is validated by applying it to virtual and real water supply systems. It is expected that the management of electric power demand on the peak time of water supply and the planning of an energy-efficient water supply system can be effectively achieved by the optimal management of energy by the proposed method in this study.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.2
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• pp.422-429
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• 2007

Location awareness is one of the key functionalities to build an U-city. Recently, many of works of the location-aware systems are emerging to commercially apply to on-going large-scale apartment complex based on U-city. As dwellers or cars being attached with active tags are moving in the U-city complex, the active tags periodically broadcast their own identifiers and receivers fixed along the street or in building use those information to calculate location of them. There are several issues to be considered for such an environment. The first is that the number of active tags operating in the same region are large as much as tens of thousands, and the second is that the active tags should be alive without change of batteries more than a year, hence low power consumption is very important. In this paper we propose i) a new architecture for location-aware system considering such issues, ii) technical issues to implement it using active tags, and iii) a mathematical analytic model to investigate overall performance and verify it by comparing with actual experimental results. Through the analysis we can show the theoretical boundary of the lowest packet loss rate and the maximum number of tags with acceptable performance for the systems based on active tags. The results can be applied to practical design of location-based systems of U-City projects.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.113-135
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• 2017

The purpose of the research was to develop an analysis framework for Korean mathematics textbooks from a critical mathematics education perspective. For this, we conducted a comprehensive literature review regarding critical theory, critical education, and critical mathematics education. Based on the literature review, we derived a preliminary framework for textbook analysis. To validate the preliminary framework delphi survey was carried out twice with 21 expert panelists in the field of mathematics education and multicultural education. The first delphi survey was conducted with open-ended questions to investigate diverse opinions regarding educational goals, contents, and teaching methods of critical mathematics education. The second delphi survey was conducted with Likert-type scale and it was analyzed using Mean, Contents Validity Ratio, Degree of Consensus. As the result of the whole research procedures, the final analysis framework was developed consisting of four categories: classical knowledge, community knowledge, communicative knowledge, and political knowledge. A development of the analysis framework from a critical mathematics education perspective could give a significant impact on the mathematics curriculum or mathematic teacher education in the Korea and a meaningful initial step for the effort of practicing critical mathematics education. It is expected that this study could not only incite consideration for the better mathematics education but also expand the prospect of research and practice in mathematics education. This study would provide a new paradigm of future mathematics education with which to teach and guide students to become members of world civil society with mathematical power and critical competency.

• Journal of the Korean Society of Marine Environment & Safety
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• v.22 no.1
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• pp.129-137
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• 2016

In the present study we verified performance of feed-forward control algorithm using short term prediction of ship motion information by taking advantage of developed numerical simulation model of FPSO motion. Up until now, various studies have been conducted about thrust control and allocation for dynamic positioning systems maintaining positions of ships or marine structures in diverse sea environmental conditions. In the existing studies, however, the dynamic positioning systems consist of only feedback control gains using a motion of vessel derived from environmental loads such as current, wind and wave. This study addresses dynamic positioning systems which have feedforward control gain derived from forecasted value of a motion of vessel occurred by current, wind and wave force. In this study, the future motion of vessel is forecasted via Brown's Exponential Smoothing after calculating the vessel motion via a selected mathematical model, and the control force for maintaining the position and heading angle of a vessel is decided by the feedback controller and the feedforward controller using PID theory and forecasted vessel motion respectively. For the allocation of thrusts, the Lagrange Multiplier Method is exploited. By constructing a simulation code for a dynamic positioning system of FPSO, the performance of feedforward control system which has feedback controller and feedforward controller was assessed. According to the result of this study, in case of using feedforward control system, it shows smaller maximum thrust power than using conventional feedback control system.