Uiler-Lagrange 식을 사용한 확장형 완경사방정식 유도

이창훈(Lee Changhoon),김규한(Kim Kyu-Han) 대한토목학회 2009 대한토목학회논문집 B Vol.29 No.5B

본 연구에서 Euler-Lagrange 식을 사용하여 속도포텐셜로 표현되는 확장형 완경사방정식을 유도하였다. 먼저, Euler-Lagrange 식을 사용하여 흐름함수로 표현된 확장형 완경사방정식을 유도한 Kim과 Bai(2004)의 유도과정을 따라가면서 속도표텐셜로 표현된 확장형 완경사방정식과의 관계를 찾았다. 속도포텐셜로 표현된 Euler-Lagrange 식을 찾아낸 다음 고차의 수심변화 항을 유도하였다. 본 연구에서 유도된 확장형 완경사방정식은 기존의 식인 Massel(1993)의 식과 Chamberlain과 Porter(1995)의 식과 정확히 일치하였다. 본 연구의 연구 성과는 확장형 완경사방정식의 유도 방법을 새로 제시하여 해안공학의 영역을 넓히는데 의의가 있다. In this study, we derive the extended mild-slope equation in terms of the velocity potential using the Euler-Lagrange equation. First, we follow Kim and Bai (2004) who derive the complementary mild-slope equation in terms of the stream function using the Euler-Lagrange equation and we compare their equation to the existing extended mild-slope equations of the velocity potential. Second, we derive the extended mild-slope equation in terms of the velocity potential using the Euler-Lagrange equation. In the developed equation, the higher-order bottom variation terms are newly developed and found to be the same as those of Massel (1993) and Chamberlain and Porter (1995). The present study makes wide the area of coastal engineering by developing the extended mild-slope equation with a way which has never been used before.

Condensed Cramer rule for computing a kind of restricted matrix equation

Chao Gu,Zhaoliang Xu 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.5

The problem of finding Cramer rule for solutions of some restricted linear equation Ax = b has been widely discussed. Recently Wang and Qiao consider the following more general problem AXB = D, R(X) ⊂ T, N(X) ⊃ S. They present the solution of above general restricted matrix equation by using generalized inverses and give an explicit expression for the elements of the solution matrix for the matrix equation. In this paper we re-consider the restricted matrix equation and give an equivalent matrix equation to it. Through the equivalent matrix equation, we derive condensed Cramer rule for above restricted matrix equation. As an application, condensed determinantal expressions for A(2)T,S A and AA(2) T,S are established. Based on above results, we present a method for computing the solution of a kind of restricted matrix equation. The problem of finding Cramer rule for solutions of some restricted linear equation Ax = b has been widely discussed. Recently Wang and Qiao consider the following more general problem AXB = D, R(X) ⊂ T, N(X) ⊃ S. They present the solution of above general restricted matrix equation by using generalized inverses and give an explicit expression for the elements of the solution matrix for the matrix equation. In this paper we re-consider the restricted matrix equation and give an equivalent matrix equation to it. Through the equivalent matrix equation, we derive condensed Cramer rule for above restricted matrix equation. As an application, condensed determinantal expressions for A(2)T,S A and AA(2) T,S are established. Based on above results, we present a method for computing the solution of a kind of restricted matrix equation.

폐기능 예측식에 따른 폐환기능 장해도 변화

이정오 ( Joung Oh Lee ),최병순 ( Byung Soon Choi ) 대한결핵 및 호흡기학회 2010 Tuberculosis and Respiratory Diseases Vol.69 No.2

Background: The aim was to estimate the differences between pulmonary disability grades according to the spirometry reference equations (the Korean equation and the Morris equation). Methods: Spirometry was performed on 16,916 male and 1,353 female special examination for pneumoconiosis, in the period of 2007~2009. Changes in predictive values for forced expiratory volume in one second (FEV1), forced vital capacity (FVC) and FEV1/FVC and in disability grade were evaluated using both equations. Results: Mean FVCs for men and women were 4,218.7 mL and 2,801.5 mL in predictive values after the application of the Korean equation, and 3,763.9 mL and 2,395.6 mL after the Morris equation, respectively. Compared with the Morris equation, the Korean equation showed 10.8% and 14.5% of excesses for men and women (p<0.001). Mean FEV1s for men and women were 3,102.5 mL and 2,107.1 mL in the Korean equation, and 2,667.8 mL and 1,699.6 mL in the Morris equation, respectively. Compared with the Morris equation, the Korean equation showed 14.0% and 19.3% of excesses for men and women (p<0.001). Men and women who showed the changes of disability grades using the Korean equation in place of the Morris equation were 23.9% (4,052/16,916) and 22.9% (311/1,353) on FVC, and 23.1% (3,913/16,916) and 10.7% (145/1,353) on FEV1. Conclusion: Applying different reference equations for spirometry has resulted in changes for disability grades in special examination for pneumoconiosis.

Estimated Glomerular Filtration Rates Show Minor but Significant Differences Between the Single and Subgroup Creatinine-Based Chronic Kidney Disease Epidemiology Collaboration Equations

박설희,정태동 대한진단검사의학회 2019 Annals of Laboratory Medicine Vol.39 No.2

The creatinine-based Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation can be calculated according to race, sex, and creatinine concentration (subgroup equation) or in the form expressed by one equation (single equation). Minor differences in the constants used in the CKD-EPI equations (subgroup vs single equations) could result in a significant difference in the estimated glomerular filtration rate (eGFR). We evaluated the impact of this difference in 79,709 Korean patients. The eGFR was calculated as an integer using the single and subgroup CKD-EPI equations. The differences in eGFR and GFR categories between the equations were analyzed. eGFR was higher in the subgroup equation than the single equation by 1 mL/min/1.73 m2 for 12,476 (27.4%) Korean females. The GFR category based on the subgroup equation was reclassified using the single equation for 352 (0.77%) females. Based on the results, the constant of the single equation was optimized. There was no difference in eGFR values between equations using a multiplier of 1.0213 instead of 1.018 for the “white or other” females constant in the single CKD-EPI equation. Clinicians should carefully apply the CKD-EPI equation because eGFR values may differ by 1 mL/min/1.73 m2 depending on the manner of calculation. To minimize these differences, the constants of the single equation should be revised.

관측방정식을 활용한 다각망도선법 조정에 관한 연구

이은수(Lee, Eun Soo) 한국지적학회 2014 한국지적학회지 Vol.30 No.2

본 연구는 관측방정식을 이용하여 다각망도선법의 계산을 수행하고 그 결과를 조건방정식에 의한 다각망도선법 결과와 비교한 것이다. H형 다각망에 대해 조건방정식과 관측방정식을 이용하여 교점에 대한 방위각과 종횡선 좌표를 각각 도출하여 비교한 결과, 두 방법 모두 동일한 결과를 얻었다. 다만, 조건방정식 방법에서 조건식의 구성을 다르게 할 경우 약 1cm의 차이를 보였다. 조건방정식 방법에 비해 관측방정식 방법은 계산에 사용되는 도선의 수가 훨씬 적고, 방정식의 형태 또한 단순하여 방정식을 쉽게 구성할 수 있으므로 관측방정식을 이용하여 결과를 도출하는 것이 보다 경제적이라 사료된다. This study performed the graphical traversing method for traverse network using an observation equation and compared the results with the outcome of the graphical traversing method for traverse network under condition equation. In the H-type traverse network, azimuth and grid coordinates on the point of intersection were derived and compared using condition equation and observation equation respectively. Then, the same results were obtained. When condition was differently configured in the condition equation, however, about 1cm of difference was found. Compared to condition equation, observation equation is far fewer in terms of the number of traverse lines used for calculation. Because observation equation has simpler equation type, in addition, equation can be easily configured. Therefore, it appears that observation equation is more efficient economically than condition equation in deriving the results.

Martin’s Equation as the Most Suitable Method for Estimation of Low-Density Lipoprotein Cholesterol Levels in Korean Adults

강미정,김종우,이선영,김규남,윤준형,기홍석 대한가정의학회 2017 Korean Journal of Family Medicine Vol.38 No.5

Background: Friedewald equation is the most widely used method for estimating low-density lipoprotein choles-terol (LDL-C) level. However, due to potential over- or underestimation, many studies have used a modified equa-tion. This study aimed to compare estimates by 4 different equations to directly measured LDL-C concentrations in order to propose the most appropriate method for LDL-C estimation in the Korean population.Methods: We studied data of 4,350 subjects that included total cholesterol, high-density lipoprotein cholesterol (HDL-C), triglyceride (TG), and LDL-C concentrations that had been measured at one university hospital in Seoul. We investigated 4 equations: LDL-C by Friedewald’s original equation (LDL-CF) and its 3 modifications. Pearson correlation analysis was performed to compare these estimates to the direct measurement.Results: Pearson correlation analysis revealed a good correlation among all 4 estimated LDL-C values and the di-rectly measured LDL-C value. The Pearson coefficients were 0.951 for LDL-CF, 0.917 for LDL-C by Hatta equation (LDL-CH), 0.968 for LDL-C by Puavilai equation (LDL-CP), and 0.983 for LDL-C by Martin equation (LDL-CM). Mar-tin equation (LDL-CM) resulted in the best approximation (mean difference from the direct measurement, 5.5 mg/dL; mean percentage difference from the direct measurement, 5.1%) and the best agreement with the direct mea-surement (86.1%). LDL-CP resulted in the second-best approximation (mean difference, 7.0 mg/dL; mean percent-age difference, 6.2%; concordance, 82.5%). LDL-CM was found to be less influenced by TG and HDL-C levels than by LDL-CF.Conclusion: Estimates by Martin equation had the best agreement with direct LDL-C concentrations and both Martin and Puavilai equations were superior to Friedewald equation for estimating LDL-C concentrations in Kore-an adults.

A proposal of Simplified Eigenvalue Equation for an Analysis of Dielectric Slab Waveguide

Young-Kyu Choi 대한전기학회 2006 Journal of Electrical Engineering & Technology Vol.1 No.3

In dielectric waveguide analysis and synthesis, we often encounter an awkward task of solving the eigenvalue equation to find the value of propagation constant. Since the dispersion equation is an irrational equation, we cannot solve it directly. Taking advantage of approximated calculation, we attempt here to solve this irrational dispersion equation. A new type of eigenvalue equation, in which guide index is expressed as a function of frequency, bas been developed. In practical optical waveguide designing and in calculating the propagation mode, this equation will be used more conveniently than the previous one. To expedite the design of the waveguide, we then solve the eigenvalue equation of a slab waveguide, which is sufficiently accurate for practical purpose.

표면 폭발하중 파라메타의 수정 산정식

전두진,김기태,한상을 한국공간구조학회 2017 한국공간구조학회지 Vol.17 No.3

The Kingery-Bulmash equation is the most common equation to calculate blast load. However, the Kingery-Bulmash equation is complicated. In this paper, a modified equation for surface blast load is proposed. The equation is based on Kingery-Bulmash equation. The proposed equation requires a brief calculation process, and the number of coefficients is reduced under 5. As a result, each parameter obtained by using the modified equation has less than 1% of error range comparing with the result by using Kingery-Bulmash equation. The modified equation may replace the original equation with brief process to calculate.

Improvement of the two-fluid momentum equation using a modified Reynolds stress model for horizontal turbulent bubbly flows

Lee, Seung-Jun,Lee, Jae Hwa,Kim, Byoung Jae Elsevier 2017 Chemical engineering science Vol.173 No.-

<P><B>Abstract</B></P> <P>Two-fluid equations are widely used for practical applications involving multi-phase flows in chemical reactor, nuclear reactor, desalination systems, boilers, and internal combustion engines. The popular two-fluid equation for a gas-liquid two-phase flow is based on the assumption of interpenetrating continua. According to the experimental data of fully-developed turbulent bubbly flows in a horizontal pipe, the bubble phase velocity is close to or slightly smaller than the liquid phase velocity. The velocity profile is nearly symmetric along the vertical centerline of the horizontal pipe, or tends to be slightly skewed toward the bottom region of the pipe. However, numerical simulations using the momentum equation based on interpenetrating continua showed that, in contrast, the bubble phase was faster than the liquid phase. In addition, the velocity profile was predicted to be skewed toward the upper region of the pipe. These simulation results are not consistent with experimental observations. In the meantime, there are particle averaged momentum equations in which the continuous and disperse phase equations are developed from the equations of motions of fluid and particle, respectively. We considered two different particle averaged momentum equations. The form of one particle averaged momentum equation is similar to that of the momentum equation based on interpenetrating continua, except for the laminar viscosity term. Thus, for a turbulent bubbly flow, this particle averaged equation showed similar results as observed in the momentum equation based on interpenetrating continua. The other particle averaged equation differs from the momentum equation based on interpenetrating continua in both laminar and turbulent viscosity terms. This particle averaged equation showed good agreement with experimental observations.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Numerical simulations are performed for horizontal turbulent bubbly flows. </LI> <LI> Three different ways to formulate the momentum diffusion terms are tested. </LI> <LI> Proper forms of the momentum diffusion terms are suggested. </LI> </UL> </P>

우리나라 기준증발산량 추정을 위한 Hargreaves 공식의 계수 보정

황선아,한경화,장용선,조희래,옥정훈,김동진,김기선,정강호 한국농림기상학회 2019 한국농림기상학회지 Vol.21 No.4

The evapotranspiration is estimated based on weather factors such as temperature, wind speed and humidity, and the Hargreaves equation is a simple equation for calculating evapotranspiration using temperature data. However, the Hargreaves equation tends to be underestimated in areas with wind speeds above 3 m s-1 and overestimated in areas with high relative humidity. The study was conducted to determine Hargreaves equation coefficient in 82 regions in Korea by comparing evapotranspiration determined by modified Hargreaves equation and the Penman-Monteith equation for the time period of 2008~2018. The modified Hargreaves coefficients for 50 inland areas were estimated to be 0.00173~0.00232(average 0.00196), which is similar to or lower than the default value 0.0023. On the other hand, there are 32 coastal areas, and the modified coefficients ranged from 0.00185 to 0.00303(average 0.00234). The east coastal area was estimated to be similar to or higher than the default value, while the west and south coastal areas showed large deviations by area. As results of estimating the evapotranspiration by the modified Hargreaves coefficient, root mean square error(RMSE) is reduced from 0.634~1.394(average 0.857) to 0.466~1.328(average 0.701), and Nash-Sutcliffe Coefficient(NSC) increased from -0.159~0.837(average 0.647) to –0.053~0.910(average 0.755) compared with original Hargreaves equation. Therefore, we confirmed that the Hargreaves equation can be overestimated or underestimated compared to the Penman-Monteith equation, and expected that it will be able to calculate the high accuracy evapotranspiration using the modified Hargreaves equation. This study will contribute to water resources planning, irrigation schedule, and environmental management. 기준증발산량은 기온, 풍속, 습도 등 기상요소를 바탕으로 추정하는 방법을 이용하고 있으며, Hargreaves 공식은 기온자료를 이용하여 기준증발산량을 산정할 수 있는 간단한 경험식이라 할 수 있다. 그러나 Hargreaves 공식은 풍속이 3 m s-1 이상인 지역에서는 과소평가 되고, 상대습도가 높은 지역은 과대평가 되는 경향이 있다. 본 연구에서는 Hargreaves 공식을 우리나라에 적용하기 위해 보다 정확한 기준증발산량 추정이 가능하도록 계수 산정 연구를 수행하였다. 우리나라 종관기상관측지점(ASOS, Automated Synoptic Observing System)의 최근 11 년(2008-2018) 동안의 기상자료를 이용하여 Panman-Monteith 공식으로 기준증발산량을 추정하였고, 이 값을 기준으로 하여 각 지점별로 Hargreaves 공식의 계수를 보정하였다. 우리나라 82 개 지점에 대하여 지역별로 보정된 계수는 내륙지역이 50 개 지점이며, 0.00173∼0.00232(평균 0.00196)로 기본값인 0.0023 과 비슷하거나 낮게 산정되었다. 반면, 해안지역은 32 개 지점이며 지역별로 보정된 계수의 범위는 0.00185∼0.00303(평균 0.00234)으로 동해안지역은 기본값과 비슷하거나 높게 산정된 반면, 서해안과 남해안지역은 지역별로 편차가 크게 나타났다. Hargreaves 공식의 계수를 보정하여 기준증발산량을 추정한 결과 RMSE(Root Mean Square Error)는 계수 보정 전 0.634∼1.394(평균 0.857)에서 계수 보정 후 0.466∼1.328(평균 0.701)로 낮아지고, NSC(Nash-Sutcliffe Coefficient)는 계수 보정 전 -0.159∼0.837(평균 0.647)에서 계수 보정 후 -0.053∼0.910(평균 0.755)로 높아짐에 따라 기준증발산량의 추정효율이 크게 향상되는 것으로 나타났다. 연구 결과, Hargreaves 공식을 그대로 이용할 경우 Penman-Monteith 공식에 비해 과대 또는 과소 산정될 수 있음을 확인하였으며, 계수를 보정하여 이용할 경우 정확도가 높은 기준증발산량을 추정할 수 있을 것으로 판단된다.