• Title/Summary/Keyword: 대수 표현

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Parameters Estimation of Probability Distributions Using Meta-Heuristic Algorithms (Meta-Heuristic Algorithms를 이용한 확률분포의 매개변수 추정)

  • Yoon, Suk-Min;Lee, Tae-Sam;Kang, Myung-Gook;Jeong, Chang-Sam
    • Proceedings of the Korea Water Resources Association Conference
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    • 2012.05a
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    • pp.464-464
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    • 2012
  • 수문분야에 있어서 빈도해석의 목적은 특정 재현기간에 대한 발생 가능한 수문량의 규모를 파악하는데 있으며, 빈도해석의 정확도는 적합한 확률분포모형의 선택과 매개변수 추정방법에 의존하게 된다. 일반적으로 각 확률분포모형의 특성을 대표하는 매개변수를 추정하기 위해서는 모멘트 방법, 확률가중 모멘트 방법, 최대우도법 등을 이용하게 된다. 모멘트 방법에 의한 매개변수 추정은 해를 구하기 위한 과정이 단순한 반면, 비대칭형의 왜곡된 분포를 갖는 자료들에 대해서는 부정확한 결과를 나타내게 된다. 확률가중 모멘트 방법은 표본의 크기가 작거나 왜곡된 자료일 경우에도 비교적 안정적인 결과를 제공하는 반면, 확률 가중치가 정수로만 제한되는 단점을 갖고 있다. 그리고 대수 우도함수를 이용하여 매개변수를 추정하게 되는 최우도법은 가장 효율적인 매개변수 추정치를 얻을 수 있는 것으로 알려져 있으나, 비선형 연립방정식으로 표현되는 해를 구하기 위해서는 Newton-Raphson 방법을 사용하는 등 절차가 복잡하며, 때로는 수렴이 되지 않아 해룰 구하지 못하는 경우가 발생되게 된다. 이에 반해, 최근의 Genetic Algorithm, Ant Colony Optimization 및 Simulated Annealing과 같은 Meta-Heuristic Algorithm들은 복잡합 공학적 최적화 문제 있어서 효율적인 대안으로 주목받고 있으며, Hassanzadeh et al.(2011)에 의해 수문학적 빈도해석을 위한 매개변수 추정에 있어서도 그 적용성이 검증된바 있다. 본 연구의 목적은 연 최대강수 자료의 빈도해석에 적용되는 확률분포모형들의 매개변수 추정을 위해 Meta-Heuristic Algorithm을 적용하고자 함에 있다. 따라서 본 연구에서는 매개변수 추정을 위한 방법으로 Genetic Algorithm 및 Harmony Search를 적용하였고, 그 결과를 최우도법에 의한 결과와 비교하였다. GEV 분포를 이용하여 Simulation Test를 수행한 결과 Genetic Algorithm을 이용하여 추정된 매개변수들은 최우도법에 의한 결과들과 비교적 유사한 분포를 나타내었으나 과도한 계산시간이 요구되는 것으로 나타났다. 하지만 Harmony Search를 이용하여 추정된 매개변수들은 최우도법에 의한 결과들과 유사한 분포를 나타내었을 뿐만 아니라 계산시간 또한 매우 짧은 것으로 나타났다. 또한 국내 74개소의 강우관측소 자료와 Gamma, Log-normal, GEV 및 Gumbel 분포를 이용한 실증연구에 있어서도 Harmony Search를 이용한 매개변수 추정은 효율적인 매개 변수 추정치를 제공하는 것으로 나타났다.

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Word problem solving of simultaneous equations by 5th and 6th grade students (5.6학년 학생들의 이원일차연립방정식 형태의 문장제 해결 과정 분석)

  • Yun, Min-Ji;Pang, Jeong-Suk
    • Communications of Mathematical Education
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    • v.23 no.3
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    • pp.761-783
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    • 2009
  • Problem solving ability can be fostered by dealing with many different types of problems. We investigated how $5^{th}$ and $6^{th}$ graders who did not learn traditional algebraic methods might approach the word problems of simultaneous equations. This result reveals that the strategy of guess-and-check serves as a basis for elementary school students in solving simultaneous equations. A noticeable remark is that students used the guess-and-check strategy in various ways. Whereas some students changed a variable given in the problem step by step, others did in a sophisticated way focusing on the relation between two variables. Moreover, some students were able to write an equation which was not typical but meaningful and correct. This paper emphasizes the need of connections between pre-algebraic and algebraic solutions.

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A Study on Improvement of Gravity model Decay Function of Transporting Demand Forecasting Considering Space Syntax (Space Syntax를 이용한 교통수요예측의 중력모형 저항함수의 개선방안)

  • Jang, Jin-Young
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.20 no.3
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    • pp.617-631
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    • 2019
  • In the four-step demand model, a gravity mode is used most commonly at the trip distribution stage. The purpose of this study was to develop a new friction factor that can express the accessibility property as a single friction factor to compensate for the variable limits of the gravity model parameters (travel time, travel cost). To derive a new friction factor, a new friction factor was derived using the space syntax that can quantify the characteristics of the urban space structure, deriving the link-unit integration degree and then using the travel time and travel distance relationship. Calibration of the derived friction factor resulted in a similar level to that of the existing friction factor. As a result of verifying the various indicators, the explanatory power was found to be excellent in the short - and long - distance range. Therefore, it is possible to derive and apply the new friction factor using the integration index, which can complement the accessibility beyond the limit of the existing shortest distance, and it is believed to be more advantageous in future utilization.

Efficiency Improvement Using Two Balanced Subsets (두 개의 balanced subset을 이용한 효율성 개선)

  • Kim, HongTae
    • Convergence Security Journal
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    • v.18 no.1
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    • pp.13-18
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    • 2018
  • Efficiency is one of the most important factors in cryptographic systems. Cheon et al. proposed a new exponent form for speeding up the exponentiation operation in discrete logarithm based cryptosystems. It is called split exponent with the form $e_1+{\alpha}e_2$ for a fixed element ${\alpha}$ and two elements $e_1$, $e_2$ with low Hamming weight representations. They chose $e_1$, $e_2$ in two unbalanced subsets $S_1$, $S_2$ of $Z_p$, respectively. We achieve efficiency improvement making $S_1$, $S_2$ balanced subsets of $Z_p$. As a result, speedup for exponentiations on binary fields is 9.1% and speedup for scalar multiplications on Koblitz Curves is 12.1%.

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Case Study: Groundwater Recharge Hydrograph in Pyeongchang River (평창강 지하수 함양곡선 연구)

  • Kwak, Jaewon
    • Journal of Wetlands Research
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    • v.23 no.2
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    • pp.173-182
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    • 2021
  • It is important to extract and assess low-flow recession characteristics for water resources management in the upper reaches of a stream. It is difficult to express the groundwater flow recession characteristics for streamflow synthetically. The linear recession model has been widely used by baseflow recession analysis for reason of simplicity and convenience, but recent studies show that nonlinear recession models fit well, and the relationship between the reservoir storage of shallow unconfined aquifers and the groundwater discharge was to be identified as nonlinear in the literature based on the analysis of numerous streamflow recession curves. The objective of the study is to decode these nonlinear characteristics, including evaporation loss, storage, and recharge of groundwater using streamflow. By analyzing the observed time series of streamflow from the study area, which is the Pyeongchang River basin in Korea, the main components of the underlying groundwater balance, namely, discharge, evaporation loss, storage, and recharge, can be identified and quantified. As a result of the study, depletion of groundwater by evapotranspiration losses through the water uptake of tree roots was found to bias the recession curves and the estimated reservoir parameters. The seasonality of both rainfall and potential evaporation, analysis of the recession curves, stratified according to time of the year, allowed the quantification of evapotranspiration loss as a function of a calendar month and stored groundwater storage.

Evaluation of seismic fragility models for cut-and-cover railway tunnels (개착식 철도 터널 구조물의 기존 지진취약도 모델 적합성 평가)

  • Yang, Seunghoon;Kwak, Dongyoup
    • Journal of Korean Tunnelling and Underground Space Association
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    • v.24 no.1
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    • pp.1-13
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    • 2022
  • A weighted linear combination of seismic fragility models previously developed for cut-and-cover railway tunnels was presented and the appropriateness of the combined model was evaluated. The seismic fragility function is expressed in the form of a cumulative probability function of the lognormal distribution based on the peak ground acceleration. The model uncertainty can be reduced by combining models independently developed. Equal weight is applied to four models. The new seismic fragility function was developed for each damage level by determining the median and standard deviation, which are model metrics. Comparing fragility curves developed for other bored tunnels, cut-and-cover tunnels for high-speed railway system have a similar level of fragility. We postulated that this is due to the high seismic design standard for high-speed railway tunnel.

Seismic Risk Assessment of Extradosed Bridges with Lead Rubber Bearings (LRB 면진장치가 설치된 엑스트라도즈드교의 지진위험도 평가)

  • Kim, Doo Kie;Seo, Hyeong Yeol;Yi, Jin-Hak
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.26 no.1A
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    • pp.155-162
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    • 2006
  • This study presents the seismic risk assesment for an extradosed bridge with seismic isolators of lead rubber bearings(LRB). First, the seismic vulnerability of a structure and then the seismic hazard of the site are evaluated using earthquake data set and seismic hazard map in Korea, and then the seismic risk of the structure is assessed. The nonlinear seismic analyses are carried out to consider plastic hinges of bridge columns and nonlinear characteristics of soil foundation. The ductility demand is adopted to describe the nonlinear behavior of a column, and the moment-curvature curve of a column is assumed to be bilinear hysterestic. The fragility curves are represented as a log-normal distribution function for column damage, movement of superstructure, and cable yielding. And seismic hazard is estimated using the available seismic hazard maps. The results show that the effectiveness of the seismic isolators for the columns is more noticeable than those for cables and girders, in seismic isolated extradosed bridges under earthquakes.

A hybrid genetic algorithm for the optimal transporter management plan in a shipyard

  • Jun-Ho Park;Yung-Keun Kwon
    • Journal of the Korea Society of Computer and Information
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    • v.28 no.12
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    • pp.49-56
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    • 2023
  • In this study, we propose a genetic algorithm (GA) to optimize the allocation and operation order of transporters. The solution in the GA is represented by a set of lists each of which the operation order of the corresponding transporter. In addition, it was implemented in the form of a hybrid genetic algorithm combining effective local search operations for performance improvement. The local search reduces the number of operating transporters by moving blocks from a transporter with a low workload into that with a high workload. To evaluate the effectiveness of the proposed algorithm, it was compared with Multi-Start and a pure genetic algorithm through a simulation environment similar in scale to an actual shipyard. For the largest problem, compared to them, the number of transporters was reduced by 40% and 34%, and the total task time was reduced by 27% and 17%, respectively.

Transformation Conditions and Ampicillin-resistant Expression of E. coli Ts-mutant (온도감수성 대장균의 형질전환조건 및 Ampicillin 내성의 표현)

  • JIN Deuk Hee;HONG Yong Ki
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.20 no.1
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    • pp.57-62
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    • 1987
  • The transformational conditions of plasmids $pPL-\lambda$ and pAS 1 are as follows in E. coli, Ts-mutant M 5248 strain at $30^{\circ}C$. When the culture time was 2.5 hours of mid logarithemic phase, the cell concentration was $4.5\times10^7\;cells/ml$, the optical density was equal to 0.45 at 590 nm wave length, the transformational frequencies of plasmid$pPL-\lambda$ and pAS 1 had the highest values as $2\times10^{-6}\;and\;1.5\times10^{-6}\;and\;1.5\times10^{-6}$ and respectively. For $9\times10^6$ competent cells in $200{\mu}l$, the transformational frequency was as high as $4.4\times10^{-6}$ at 510 ng plasmid concentration. The competent cells treated with the mixture of calcium chloride and thymidine twice rates of transformation than those treated with calcium chloride. The ampicillin resistance of transformants was expressed in LB broth after 2 hours at $30^{\circ}C$.

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A Case Study on the Students' Covariational Reasoning in the Continuous Functional Situations (함수적 상황에 대한 초등학생들의 공변추론 사례연구)

  • Hur, Joonho;Park, Mangoo
    • Education of Primary School Mathematics
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    • v.21 no.1
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    • pp.55-73
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    • 2018
  • The purpose of this study is to investigate the effects of cognitive activity on cognitive activities that students imagine and cope with continuously changing quantitative changes in functional tasks represented by linguistic expressions, table of value, and geometric patterns, We identified covariational reasoning levels and investigated the characteristics of students' reasoning process according to the levels of covariational reasoning in the elementary quantitative problem situations. Participants were seven 4th grade elementary students using the questionnaires. The selected students were given study materials. We observed the students' activity sheets and conducted in-depth interviews. As a result of the study, the students' covariational reasoning level for two quantities that are continuously covaried was found to be five, and different reasoning process was shown in quantitative problem situations according to students' covariational reasoning levels. In particular, students with low covariational level had difficulty in grasping the two variables and solved the problem mainly by using the table of value, while the students with the level of chunky and smooth continuous covariation were different from those who considered the flow of time variables. Based on the results of the study, we suggested that various problems related with continuous covariation should be provided and the meanings of the tasks should be analyzed by the teachers.