• Title/Summary/Keyword: linear error equation

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Trapezoidal Cyclic Voltammetry as a Baseline for Determining Reverse Peak Current from Cyclic Voltammograms

  • Carla B. Emiliano;Chrystian de O. Bellin;Mauro C. Lopes
    • Journal of Electrochemical Science and Technology
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    • v.15 no.3
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    • pp.405-413
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    • 2024
  • Several techniques for determining the reverse peak current from a cyclic voltammogram (CV) for a reversible system are described in the literature: CV itself as a baseline with long switching potential (Eλ) that serves as a baseline for other CVs, Nicholson equation that uses CV parameters to calculation reverse peak current and linear extrapolation of the current obtained at the switching potential. All methods either present experimental difficulties or large errors in the peak current determination. The paper demonstrates, both theoretically and experimentally, that trapezoidal cyclic voltammetry (TCV) can be used as a baseline to determine anodic peak current (iap) with high accuracy and with a switching potential shorter than that used by CV, as long as Eλ is at least 130 mV away from the cathodic peak. Beyond this value of switching potential the electroactive specie is completely depleted from the electrode surface. Using TCV with Eλ = 0.34 V and a switching time (tλ) of 240 s as a baseline, the determination of the reverse peak current presents a deviation from the expected value of less than 1% for most of the CVs studied (except cases when Eλ is close to the direct potential peak). This result presents better accuracy than the Nicholson equation and the linear extrapolation of the current measured at the switching potential, in addition to presenting a smaller error than that obtained in the acquisition of the experimental current. Furthermore, determining the reverse peak current by extrapolating the linear fit of iap vs. ${\sqrt[1/]{t_{\lambda}}}$ to infinite time gave a reasonable approximation to the expected value. Experiments with aqueous potassium hexacyanoferrate (II) and ferrocene in acetonitrile confirmed the theoretical predictions.

The Development of Leaves in Amaranthus retroflexus and Chenopodium album Represented by the Plastochron(I. The Derivation of the Plastochron Index) (Plastochron 에 의한 Amaranthus retroflexus 와 Chenopodium album 의 잎의 성장 해석 1. Plastochron Index 의 유도)

  • Park, Bong-Kyu;Joung-Hee Kim
    • The Korean Journal of Ecology
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    • v.8 no.1
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    • pp.1-5
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    • 1985
  • The plastochron index (PI) provides possibility on studies of the effects of various environmental factors on morphological and physiological development of plants. The PI of Erickson and Michemlini(1957) could be used merely when leaf n is longer an leaf n+1 is smaller than the references length at any time. If both the lengths of leaf n and n+1 are smaller or longer than the reference length, it could not estimated. In this study, the PI of Erickson and Michelini was complemented and the linear patterns according to leaf arrangement was represented, PI is n-(lnLR-lnLn)/(lnLn-lnLn+1). And when both the lengths of leaf n and n+1 are longer than the length of reference, PI is n+1+(ln Ln+1-lnLR)/(lnLn-lnLn+1). The linear model of PI is changed by the various environmental factors and the linear patterns are different according to leaf arrangement. According to leaf arrangement, the equation of the general regression lines is Yin-(i-j)=a-(n-1)(q1+...+qi-1)-(q1+...+qj-1)+rt+$\varepsilon$. Where Y:the logarithmic of the leaf length in question, i:leaf number hang on the one node, n:the number counting from base, q:spacing on the Y-axis, j:0, 1, 2, ..., r:slope, t:time, $\varepsilon$:error.

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Buckling analysis of noncontinuous linear and quadratic axially graded Euler beam subjected to axial span-load in the presence of shear layer

  • Heydari, Abbas
    • Advances in Computational Design
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    • v.5 no.4
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    • pp.397-416
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    • 2020
  • Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

High Precision Solenoid Type Nuclear Reactor Control Rod Position Indicator (고정밀도 솔레노이드 방식의 원자로 제어봉 위치지시기)

  • Baek, Min-Ho;Hong, Hoon-Bin;Park, Hee-June
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.65 no.11
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    • pp.1848-1853
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    • 2016
  • Control Rod Position Indicator in nuclear reactor vessel has developed for small reactor in Korea. Because of severe environment in reactor vessel, target of this study is to develop the suitable position indicator. In this study, solenoid type position indicator made of Mineral Insulated Cable(MI Cable) was introduced to adapt in severe environment. And inductance of the solenoid was used to indicate the rod position for high precision. But problem of this concept is that a linear slope of inductance is changed by temperature effect. To resolve this problem, two sensing coils were introduced for temperature compensation. A role of the sensing coil is to make reference linear equation about certain temperature. To confirm this concept, also, inductance of solenoid and sensing coils were measured at room and high temperature (${\sim}300^{\circ}C$). The results of measurement show that the position error of sensing coil between room and high temperature was about 2%. But it was identified that this error was resulted from insufficient test environment (temperature error between solenoid and sensing coils was about 2% at high temperature condition). Therefore, solenoid type position indicator shows that it is very suitable in reactor vessel as a high precision rod position indicator.

Calibration Update for the Measuring Total Nitrogen Content in Rice Plant Tissue Using the Near Infrared Spectroscopy

  • Kwon, Young-Rip;Song, Young-Eun;Choi, Dong-Chil;Ryu, Jeong
    • KOREAN JOURNAL OF CROP SCIENCE
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    • v.54 no.1
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    • pp.29-35
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    • 2009
  • The aim of the present study was to update the calibration that is used for the measurement of the total nitrogen content in the rice plant samples by using the visible and near infrared spectrum. Before the equation merge, correlation coefficient of calibration equation for nitrogen content on each rice parts was 0.945 (Leaf), 0.928 (Stem), and 0.864 (Whole plant), respectively. In the calibration models created by each part in the rice plant under the various regression method, the calibration model for the leaf was recorded with relatively high accuracy. Among of those, the calibration equation developed by Partial least squares (PLS) method was more accurate than the Multiple linear regression (MLR) method. The calibration equation was sensitive based on variety and location variations. However, we have merged and enlarged various of the samples that made not only to measure the nitrogen content more accurately, but also later sampling populations became more diversified. After merging, $R^2$ value becomes more accurate and significantly to 0.950 (L.), 0.974 (S.), 0.940 (W.). Also, after removal of outlier, R2 values increased into 0.998, 0.995, and 0.997. In view of the results so far achieved, Standard error of prediction (SEP) and SEP (C) were reduced in the stem and whole plant. Biases were reduced in the leaf, stem as well as whole plant. Slopes were high in the stem. Standard deviation reduced in the stem but $R^2$ was high in the stem and whole plant. Result was indicated that calibration equation make update, and updating robust calibration equation from merge function and multi-variate calibration.

Evaluation of the equation for predicting dry matter intake of lactating dairy cows in the Korean feeding standards for dairy cattle

  • Lee, Mingyung;Lee, Junsung;Jeon, Seoyoung;Park, Seong-Min;Ki, Kwang-Seok;Seo, Seongwon
    • Animal Bioscience
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    • v.34 no.10
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    • pp.1623-1631
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    • 2021
  • Objective: This study aimed to validate and evaluate the dry matter (DM) intake prediction model of the Korean feeding standards for dairy cattle (KFSD). Methods: The KFSD DM intake (DMI) model was developed using a database containing the data from the Journal of Dairy Science from 2006 to 2011 (1,065 observations 287 studies). The development (458 observations from 103 studies) and evaluation databases (168 observations from 74 studies) were constructed from the database. The body weight (kg; BW), metabolic BW (BW0.75, MBW), 4% fat-corrected milk (FCM), forage as a percentage of dietary DM, and the dietary content of nutrients (% DM) were chosen as possible explanatory variables. A random coefficient model with the study as a random variable and a linear model without the random effect was used to select model variables and estimate parameters, respectively, during the model development. The best-fit equation was compared to published equations, and sensitivity analysis of the prediction equation was conducted. The KFSD model was also evaluated using in vivo feeding trial data. Results: The KFSD DMI equation is 4.103 (±2.994)+0.112 (±0.022)×MBW+0.284 (±0.020)×FCM-0.119 (±0.028)×neutral detergent fiber (NDF), explaining 47% of the variation in the evaluation dataset with no mean nor slope bias (p>0.05). The root mean square prediction error was 2.70 kg/d, best among the tested equations. The sensitivity analysis showed that the model is the most sensitive to FCM, followed by MBW and NDF. With the in vivo data, the KFSD equation showed slightly higher precision (R2 = 0.39) than the NRC equation (R2 = 0.37), with a mean bias of 1.19 kg and no slope bias (p>0.05). Conclusion: The KFSD DMI model is suitable for predicting the DMI of lactating dairy cows in practical situations in Korea.

Measurement of lipid content of compost fermentation using near-infrared spectroscopy

  • Daisuke Masui;Suehara, Ken-ichiro;Yasuhisa Nakano;Takuo Yano
    • Near Infrared Analysis
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    • v.2 no.1
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    • pp.37-42
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    • 2001
  • Near infrared spectroscopy (NIRS) was applied to determination of the lipid content of the compost during the compost fermentation of tofu (soybean0curd) refuse. The absorption of lipid observed at 5 wavelengths, 1208, 1712, 1772, 2312 and 2352 nm on the second derivative spectra. To formulated a calibration equation, a multiple linear regression analysis was carried out between the near-infrared spectral data and on the lipid content in the calibration sample set (sample number, n=60) obtained using Soxhlet extraction method. The value of the multiple correlation coefficient (R) was 0.975 when using the wavelengths of 1208 and 1712 nm were used in the calibration equation. To validate the calibration equation obtained, the lipid content in the validation sample set (n=35) not used for formulating the calibration equation was calculated using the calibration equation, and compared with the value obtained using the Soxhlet extraction method. Good agreement was observed between the results of the Soxhlet extraction method and those values of the NIRS method. The simple correlation coefficient (r) and standard error of prediction (SEP) were 0.964 and 0.815 %, respectively. suitability of the lipid content as an indicator of the compost fermentation of tofu refuse was also studied. The decrease of the lipid content in the compost corresponded to the decrease of the total dry weight of the compost in the composter. The lipid content was a significant indicator of the compost fermentation. The NIRS method was applied to measure the time course of the lipid content in the compost fermentation and good results were obtained. The study indicates that NIRS is a useful method for process management of the compost fermentation of tofu refuse.

THE BEST TEETH COMBINATION TO PREDICT MESIODISTAL DIAMETERS OF THE UNERUPTED CANINE AND PREMOLARS OF KOREANS (한국인에서 미맹출 견치와 소구치의 근원심 폭경 예측을 위한 최적의 치아조합)

  • Kim, So-Hwa;Kim, Seong-Oh;Choi, Hyung-Jun;Choi, Byung-Jai;Lee, Jae-Ho
    • Journal of the korean academy of Pediatric Dentistry
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    • v.34 no.3
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    • pp.430-437
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    • 2007
  • The probability table of Moyers and prediction equation of Tanaka and Johnston that have been the most frequently used, cannot produce accurate prediction when used in Korean because they are based on the Caucasian popularity of the Northern European race. The method of Moyers or Tanaka and Johnston predicts sizes of the unerupted canine and premolars on the basis of the sizes of mandibular incisors. However, some of the recent papers raise a question as to whether the mandibular incisors are the best combination to predict the sizes of the unerupted canine and premolars. The purpose of this study is to determine which sum or combination of sums of permanent tooth widths present the best prediction for the unerupted canine and premolars in a Korean sample, to calculate a specific linear regression equation for this population, and to evaluate the clinical significance. A new linear regression equation was calculated based on the data of 178 Korean young adults(70 women, 108 men, mean age 21.63 years) with complete permanent dentitions. Fifty three more children(28 girls, 25 boys, mean age 14.22 years) were used as a validation sample for the application of the multiple linear regression equation. The conclusions were as follows: 1. The combination of the sums of permanent upper central incisors, lower lateral incisors and upper first molars was the best predictor for the unerupted canine and premolars in this sample($r=0.65{\sim}0.80$). 2. The multiple linear regression equation was calculated including sex and arch as additional predictor variables. male, upper: $Y\;=\;0.332{\times}X_0\;+\;6.195$ male, lower: $Y\;=\;0.332{\times}X_0\;+\;5.269$ female, upper: $Y\;=\;0.332{\times}X_0\;+\;5.929$ female, lower: $Y\;=\;0.332{\times}X_0\;+\;5.003$. The determination coefficient of the equation was 64% and a standard error of the estimate was 0.71mm. 3. In about 97% of the validation sample, the estimation of the tooth width sums of unerupted canine and premolars using the new multiple linear regression equation was smaller than 1mm compaired with the actual values.

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Estimation of hourly daytime air temperature on slope in complex terrain corrected by hourly solar radiation (복잡지형 경사면의 일사 영향을 반영한 매시 낮 기온 추정 방법)

  • Yun, Eun-jeong;Kim, Soo-ock
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.20 no.4
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    • pp.376-385
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    • 2018
  • To estimate the hourly temperature distribution due to solar radiation during the day, on slope in complex terrain, an empirical formula was developed including the hourly deviation in the observed temperature following solar radiation deviation, at weather stations on the east-facing and west-facing slopes. The solar radiation effect was simulated using the empirical formula to estimate hourly temperature at 11 weather observation sites in mountainous agricultural areas, and the result was verified for the period from January 2015 to December 2017. When the estimated temperature was compared with the control, only considering temperature lapse rate, it was found that the tendency to underestimate the temperature from 9 am to 3 pm was reduced with the use of an empirical formula in the form of linear expression; consequently, the estimation error was reduced as well. However, for the time from 5 pm to 6 pm, the estimation error was smaller when a hyperbolic equation drawn from the deviation in solar radiation on the slope, which was calculated based on geometric conditions, was used instead of observed values. The reliability of estimating the daytime temperature at 3 pm was compared with existing estimation model proposed in other studies; the estimation error could be mitigated up to an ME (mean error) of $-0.28^{\circ}C$ and RMSE (root mean square error) of $1.29^{\circ}C$ compared to the estimation error in previous models (ME $-1.20^{\circ}C$, RMSE $2.01^{\circ}C$).

Duty Ratio-Displacement Model in PWM Control of Voice Coil Actuator (보이스 코일 액츄에이터의 PWM 제어에서 듀티비-변위 모델 연구)

  • Hwang, Jin-Dong;Kwak, Yong-Kil;Kim, Ju-Hyun;Kim, Sun-Ho;Ahn, Jung-Hwan
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.6 no.2
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    • pp.59-66
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    • 2007
  • Voice coil actuator is used linear motion system that requires precision positioning control. In order to control precision positioning of voice coil actuator, relation model between duty ratio and moving displacement of voice coil actuator is needed. This paper present a duty ratio - displacement model in PWM control of voice coil actuator. Transfer function of voice coil actuator is obtained by combining voice coil motor's equation of motion with the equation of circuit and characteristic of voice coil motor. Consider to initial condition of velocity and current, transfer function is transformed mathematical model. The induced model can predict output displacement, velocity and current according to duty ratio and amplitude. The model is verified by experimental tests such as velocity and displacement response of voice coil motor. Simulated results have tracking errors of less than 10 percent of experimental results.

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