• Title/Summary/Keyword: Difference equation

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Analysis and Forecast of Non-Stationary Monthly Steam Flow (비정상 월유량 시계열의 해석과 예측)

  • 이재형;선우중호
    • Water for future
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    • v.11 no.2
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    • pp.54-61
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    • 1978
  • An attemption of synthesizing and forecasting of monthly river flow has been made by employing a linear stochastic difference equation model. As one of the linear stochestic difference equation model, an ARIMA Type is tested to find the suitability of the model to the monthly river flows. On the assumption of the stationary covariacne of differenced monthly river flows the model is identrfield and is evaluated so that the residuale have the minimum variance. Finally a test is performed to finld the residerals beings White noise. Monthly river flows at six stations in Han River Basin are applied for case studies. It was found that the difference operator is a good measure of forecasting the monthly river flow.

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Estimating Diameter and Height Growth for Pinus densiflora S. et Z. Using Non-linear Algebraic Difference Equations (비선형(非線型) 대수차분(代數差分) 방정식(方程式)을 이용(利用)한 소나무 직경(直徑) 및 수고(樹高) 생장(生長) 추정(推定))

  • Lee, Sang-Hyun
    • Journal of Korean Society of Forest Science
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    • v.90 no.2
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    • pp.210-216
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    • 2001
  • Pinus densiflora S. et Z. has widely been distributed, and is one of the important main foret resources in Korea. Diameter and height growth patterns were estimated using non-linear algebraic difference equation, which requires two-measurement times $T_1$ and $T_2$. To maximize data use, all possible measurement interval data were derived using Lag and Put statements in the SAS. In results, of the algebraic difference equations applied, the Schumacher and the Gompertz polymorphic equations for diameter and height, respectively showed the higher precision of the fitting. In order to allow more precise estimation of growth than those of the basic Schumacher and the Gompertz, further refinement that combine biological realism as input into the equation would be necessary.

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Accuracy of Predictive Equations for Resting Metabolic Rate in Korean College Students (남녀 대학생에 있어서 휴식대사량 예측공식의 정확도 평가)

  • Lee, Ga-Hee;Kim, Myung-Hee;Kim, Eun-Kyung
    • Korean Journal of Community Nutrition
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    • v.14 no.4
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    • pp.462-473
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    • 2009
  • The purpose of this study is to analyze the accuracy of predictive equations for resting metabolic rate (RMR) in Korean college students. Subjects were 60 healthy Korean college students (30 males, 30 females) aged 18-25 years. RMR was measured by indirect calorimetry. Predicted RMRs were calculated using the Harris-Benedict, Schofield (W)/(WH), FAO/ WHO/UNU(W)/(WH), Owen, Mifflin, Cunningham, Liu, IMNA and Henry (W)/(WH) equations. The accuracy of the equations was evaluated on basis of accurate prediction (the percentage of subjects whose RMR was predicted within 90% to 110% of the RMR measured), mean difference, RMSPE, mean % difference, limits of agreement of Bland- Altman method between predicted and measured RMR. Measured RMR of male and female students were $1833.4{\pm}307.4kcal/day$ and $1454.3{\pm}208.0kcal/day$, respectively. All predictive equations underestimated measured RMR. Of the predictive equations tested, the Harris-Benedict equation (mean difference: -80.4 kcal/day, RMSPE: 236 kcal/day, mean % difference: -3.1%) was the most accurate and precise, but accurate prediction of the equation was only 42%. Thus, this study suggests that the ethnicity-specific predictive equation from Korean people should be developed to improve the accuracy of predicted RMR for Koreans. (Korean J Community Nutrition 14(4) : 462${\sim}$473, 2009)

2D Crank-Nicolson FDTD Method Based on Isotropic-Dispersion Finite Difference Equation for Lossy Media (손실 매질에 대한 Isotropic-Dispersion 유한 차분식의 2D Crank-Nicolson FDTD 기법)

  • Kim, Hyun;Koh, Il-Suek;Yook, Jong-Gwan
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.21 no.7
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    • pp.805-814
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    • 2010
  • The Crank-Nicolson isotropic-dispersion finite difference time domain(CN ID-FDTD) scheme is proposed based on isotropic-dispersion finite difference(ID-FD) $equation^{[1],[2]}$. The dispersion relation of CN ID-FDTD is derived for lossy media by solving the eigenvalue problem of iteration matrix in spatial spectral domain, in addition, the weighting factors and scaling factors of the CN ID-FDTD scheme are presented for low dispersion error. The CN ID-FDTD scheme makes the dispersion error drastically reduced and shows accurate numerical results compared to the conventional Crank-Nicolson FDTD method.

The Study of Character of Electron Drift Velocity in CF4 Molecular Gas by the Boltzmann Equation (볼츠만 방정식에 의한 CF4 분자가스의 전자이동속도 특성에 관한 연구)

  • Song, Byoung-Doo;Ha, Sung-Chul
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.17 no.11
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    • pp.1252-1257
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    • 2004
  • This paper describes the information for quantitative simulation of weakly ionized plasma. In previous paper, we calculated the electron transport coefficients by using two-term approximation of Boltzmann equation. But there is difference between the result of the two-term approximation of the Boltzmann equation and experiments in pure CF$_4$ molecular gas and in CF$_4$+Ar gas mixture. Therefore, In this paper, we calculated the electron drift velocity (W) in pure CF$_4$ molecular gas and CF$_4$+Ar gas mixture (1 %, 5 %, 10 %) for range of E/N values from 0.17~300 Td at the temperature was 300 K and pressure was 1 Torr by multi-term approximation of the Boltzmann equation by Robson and Ness. The results of two-term and multi-term approximation of the Boltzmann equation have been compared with each other for a range of E/N.

The study of electron drift velocity in $CF_4+Ar$ molecular gas mixture by 2-term and multi-term approximation of the Boltzmann equation (다항근사 및 2항근사 볼츠만 방정식을 이용한 $CF_4+Ar$ 혼합기체의 전자이동속도 연구)

  • Song, Byoung-Doo;Ha, Sung-Chul;Jeon, Byoung-Hoon
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2004.07b
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    • pp.1179-1182
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    • 2004
  • This paper describes the information for quantitative simulation of weakly ionized plasma. In previous paper, we calculated the electron transport coefficients in $CF_4+Ar$ gas mixture by using two-term approximation of Boltzmann equation. but there is difference between the result of the two-term and the multi-term approximation of the Boltzmann equation in $CF_4$ gas. Therefore, in this paper, we calculated the electron drift velocity (W) in $CF_4+Ar$ gas mixture for range of E/N values from $0.01\sim500[Td}$ at the temperature was 300[K] and pressure was 1[Torr] by multi-term approximation of the Boltzmann equation by Robson and Ness. The results of two-term and multi-term approximation of the Boltzmann equation has been compared with each other for a range of E/N.

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Assessing the Unit Load Reduction Equation of Drainage Outlet Raising Management in Paddy Fields (논 물꼬관리 기법 적용에 따른 원단위 삭감부하량 산정식 평가)

  • Kim, Dong-Hyeon;Oh, Heung-Keun;Jang, Taeil;Ham, Jong-Hwa
    • Journal of The Korean Society of Agricultural Engineers
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    • v.65 no.2
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    • pp.35-45
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    • 2023
  • The DOR (Drainage outlet raising) in the paddy field has been suggested as one of the most important best management practices for the TMDL (Total maximum daily load) management in the technical guidelines by the NIER (National institute of environmental research). However, this method is underestimated and is not well adopted by local governments for the TMDL. The purpose of this study is to evaluate the unit load reduction equation according to the application of DOR in order to expand this equation. The original equation in the guideline was derived using the HSPF (Hydrological Simulation Program-Fortran) model for 1 year in Changnyeong. We analyzed the reduction effect of the original equation application by collecting additional long-term monitoring data from the Buan, Icheon, Iksan, and Jeonju. When comparing the reduction loads between the original equation and monitoring results, the evaluation results of the original equation were 11% of the monitoring analysis results, which was underestimated. This means that the original equation needs to be improved. For assessing the equation, the HSPF Paddy-RCH model was established according to the NI ER guideline and evaluated for applicability. The performance results of the model showed a reasonable range by the statistical criteria. Modified equations 1 and 2 were proposed based on the monitoring and modeling results. Modified equation 1 was the method of modifying the original equation's main factors, and modified equation 2 was the method of applying the non-point pollution reduction efficiency according to the rainfall class using the long-term modeling results. At the level of 58.6~64.6% of monitoring data, the difference between them could be further reduced compared to the original equation. The suggested approach will be more reasonable and practicable for decision-makers and will contribute to the TMDL management plans.

Inhomogeneous Helmholtz equation for Water Waves on Variable Depth (비균질 Helmholtz 방정식을 이용한 변동 수심에서의 파랑변형)

  • Kim, Hyo-Seob;Jang, Chang-Hwan
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.13 no.3
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    • pp.174-180
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    • 2010
  • The inhomogeneous Helmholtz equation is introduced for variable water depth and potential function and separation of variables are introduced for the derivation. Only harmonic wave motions are considered. The governing equation composed of the potential function for irrotational flow is directly applied to the still water level, and the inhomogeneous Helmholtz equation for variable water depth is obtained. By introducing the wave amplitude and wave phase gradient the governing equation with complex potential function is transformed into two equations of real variables. The transformed equations are the first and second-order ordinary differential equations, respectively, and can be solved in a forward marching manner when proper boundary values are supplied, i.e. the wave amplitude, the wave amplitude gradient, and the wave phase gradient at a side boundary. Simple spatially-centered finite difference numerical schemes are adopted to solve the present set of equations. The equation set is applied to two test cases, Booij’ inclined plane slope profile, and Bragg’ wavy bed profile. The present equations set is satisfactorily verified against other theories including the full linear equation, Massel's modified mild-slope equation, and Berkhoff's mild-slope equation etc.

Comparison of total energy expenditure between the farming season and off farming season and accuracy assessment of estimated energy requirement prediction equation of Korean farmers

  • Kim, Eun-Kyung;Yeon, Seo-Eun;Lee, Sun-Hee;Choe, Jeong-Sook
    • Nutrition Research and Practice
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    • v.9 no.1
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    • pp.71-78
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    • 2015
  • BACKGROUND/OBJECTIVES: The purposes of this study were to compare total energy expenditure (including PAL and RMR) of Korean farmers between the farming season and off farming season and to assess the accuracy of estimated energy requirement (EER) prediction equation reported in KDRIs. SUBJECTS/METHODS: Subjects were 72 Korean farmers (males 23, females 49) aged 30-64 years. Total energy expenditure was calculated by multiplying measured RMR by PAL. EER was calculated by using the prediction equation suggested in KDRIs 2010. RESULTS: The physical activity level (PAL) was significantly higher (P < 0.05) in the farming season (male $1.77{\pm}0.22$, female $1.69{\pm}0.24$) than the off farming season (male $1.53{\pm}0.32$, female $1.52{\pm}0.19$). But resting metabolic rate was significantly higher (P < 0.05) in the off farming season (male $1,890{\pm}233kcal/day$, female $1,446{\pm}140kcal/day$) compared to the farming season (male $1,727{\pm}163kcal/day$, female $1,356{\pm}164kcal/day$). TEE ($2,304{\pm}497kcal/day$) of females was significantly higher in the farming season than that ($2,183{\pm}389kcal/day$) of the off farming season, but in males, there was no significant difference between two seasons in TEE. On the other hand, EER of male and female ($2,825{\pm}354kcal/day$ and $2,115{\pm}293kcal/day$) of the farming season was significantly higher (P < 0.05) than those ($2,562{\pm}339kcal/day$ and $1,994{\pm}224kcal/day$) of the off farming season. CONCLUSIONS: This study indicates that there is a significant difference in PAL and TEE of farmers between farming and off farming seasons. And EER prediction equation proposed by KDRI 2010 underestimated TEE, thus EER prediction equation for farmers should be reviewed.

Performance Analysis of Mapping Functions and Mean Temperature Equations for GNSS Precipitable Water Vapor in the Korean Peninsula

  • Park, Han-Earl;Yoo, Sung-Moon;Yoon, Ha Su;Chung, Jong-Kyun;Cho, Jungho
    • Journal of Positioning, Navigation, and Timing
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    • v.5 no.2
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    • pp.75-85
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    • 2016
  • The performance of up-to-date mapping functions and various mean temperature equations were analyzed to derive optimal mapping function and mean temperature equation when GNSS precipitable water vapor (PWV) was investigated in the Korean Peninsula. Bernese GNSS Software 5.2, which can perform high precision GNSS data processing, was used for accurate analysis, and zenith total delay (ZTD) required to calculate PWV was estimated via the Precise Point Positioning (PPP) method. GNSS, radiosonde, and meteorological data from 2009 to 2014 were acquired from Sokcho Observatory and used. ZTDs estimated by applying the global mapping function (GMF) and Vienna mapping function 1 (VMF1) were compared with each other in order to evaluate the performance of the mapping functions. To assess the performance of mean temperature equations, GNSS PWV was calculated by using six mean temperature equations and a difference with radiosonde PWV was investigated. Conclusively, accuracy of data processing was improved more when using VMF1 than using GMF. A mean temperature equation proposed by Wu (2003) had the smallest difference with that in the radiosonde in the analysis including all seasons. In summer, a mean temperature equation proposed by Song & Grejner-Brzezinska (2009) had the closest results with that of radiosonde. In winter, a mean temperature equation proposed by Song (2009) showed the closest results with that of radiosonde.