• Title/Summary/Keyword: Quadratic Equation

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Effects of Protein Levels on Growth and Nitrogen Balance in Growing Jindo Dog (단백질 수준이 진도자견의 성장과 질소평형에 미치는 영향)

  • Kang, T.I.;Maeng, W.J.;Kim, M.H.;Lee, Sang-Rak
    • Journal of Animal Science and Technology
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    • v.49 no.5
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    • pp.633-638
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    • 2007
  • This study was conducted to determine the protein requirement level in growing Jindo dog through nitrogen balance experiment. Twelve female dogs aged 18~20 weeks old were allotted one of 3 dietary treatments containing 21, 23 and 25% of crude protein. Average daily gain of dogs fed experimental diets containing 21, 23 and 25% of crude protein were 65.42, 79.58 and 99.17g/d, respectively, and there was a significant difference between 21 and 25% of crude protein treatments(p<0.05). Retained nitrogen were calculated 0.74, 0.96 and 1.31g/kgBW.75/d for dogs fed diets containing 21, 23 and 25% of crude protein, respectively, and were significantly higher(p<0.05) in dogs fed 25% of crude protein diet then those of other dogs. A quadratic regression equation was calculated between nitrogen intake(x) and nitrogen retention(y); y=-2.519x2+12.79x-14.79, and it was found a significantly(p<0.05) higher regression coefficient of 0.782. From the above equation, it was estimated maintenance requirement of crude protein for growing Jindo dog is 11.25g/kg BW.75/d.

Temperature Response and Prediction Model of Leaf Appearance Rate in Rice (벼의 생육온도에 따른 출엽양상과 출엽속도 추정모델)

  • 이충근;이변우;윤영환;신진철
    • KOREAN JOURNAL OF CROP SCIENCE
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    • v.46 no.3
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    • pp.202-208
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    • 2001
  • Under the constant daylength of 13 hours and growth temperatures of 15$^{\circ}C$ to 27$^{\circ}C$, the final number of loaves (FNL) on the main culm was constant as 15 regardless of temperature in rice variety 'Kwanganbyeo'. Leaf appearance rate (LAR) increased with rising temperature and decreased with phenological development. Threshold temperature (T$_{o}$) was not constant across growth stages, but increased with phenological development. Effective accumulated temperature (EAT), which is calculated by the summation of values subtracting T0 from daily mean temperature, is closely related with number of leaves appeared (LA). LA was fitted to bilinear, quadratic, power and logistic function of EAT. Among the functions, logistic function had the best fitness of which coefficient of determination was $R^2$=0.995. Therefore, LAR prediction model was established by differentiating this function in terms of time: (equation omitted). where dL/dt is LAR, T$_1$ is daily mean temperature, L is the number of leaves appeared, and a, b, and c are constants that were estimated as 41.8, 1098.38, and -0.9273, respectively. When predictions of LA were made by LAR prediction model using data independent of model establishment, the observed and predicted LA showed good agreement of $R^2$$\geq$0.99.

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Optimal Dimension of PE Film Bag According to Fruit Size in MAP Storage of 'Fuyu' Persimmon Fruit ('부유' 단감 MAP 저장에서 과실 크기에 따른 PE 필름 봉지의 적정 규격)

  • Lee, Yong-Jae
    • Korean Journal of Food Science and Technology
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    • v.36 no.5
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    • pp.733-739
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    • 2004
  • Model for optimally dimensioned PE film bag was developed according to fruit size to maintain best quality of 'Fuyu' persimmon in modified atmosphere packaging (MAP) storage based on relationship between quality and oxygen and carbon dioxide in PE film bag. Harvested persimmons were graded into five sizes, and average weights were LL:261, L:217, M:188, S:168, and SS:154 g. Five fruit units of each grade were optimized in five PE film bag sizes of $150{\times}376,\;140{\times}357,\;130{\times}344,\;130{\times}333,\;and\;120{\times}3l8\;mm$. To minimize quality deterioration such as softening and discoloration, optimal oxygen and carbon dioxide concentrations in PE film bag were 0.5-1.0 and 6.0-8.0%, respectively, and optimal thickness of PE film bag according to fruit size were LL:45, L:50, M:55, S:60, and $SS:65\;{\mu}m$. For all fruit sizes, model for PE film bag area $(mm^2)$ was good quadratic simple equation by fruit weight (g): $Y=-4055.707+627.993X_1-0.701{X_1}^2$. Model far optimal oxygen and carbon dioxide (Y) concentration in PE film bag was suited to linear multiple equation by fruit weight $(X_1,\;g)$ and PE film thickness $(X_2,\;{\mu}m)$. Equations for oxygen and carbon dioxide concentrations (%) were $Y=5.798-0.0109X_l-0.0491X_2\;and\;Y=-2.427+0.01927X_l +0.09646X_2$, respectively.

Development of FURA Code and Application for Load Follow Operation (FURA 코드 개발과 부하 추종 운전에 대한 적용)

  • Park, Young-Seob;Lee, Byong-Whi
    • Nuclear Engineering and Technology
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    • v.20 no.2
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    • pp.88-104
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    • 1988
  • The FUel Rod Analysis(FURA) code is developed using two-dimensional finite element methods for axisymmetric and plane stress analysis of fuel rod. It predicts the thermal and mechanical behavior of fuel rod during normal and load follow operations. To evaluate the exact temperature distribution and the inner gas pressure, the radial deformation of pellet and clad, the fission gas release are considered over the full-length of fuel rod. The thermal element equation is derived using Galerkin's techniques. The displacement element equation is derived using the principle of virtual works. The mechanical analysis can accommodate various components of strain: elastic, plastic, creep and thermal strain as well as strain due to swelling, relocation and densification. The 4-node quadratic isoparametric elements are adopted, and the geometric model is confined to a half-pellet-height region with the assumption that pellet-pellet interaction is symmetrical. The pellet cracking and crack healing, pellet-cladding interaction are modelled. The Newton-Raphson iteration with an implicit algorithm is applied to perform the analysis of non-linear material behavior accurately and stably. The pellet and cladding model has been compared with both analytical solutions and experimental results. The observed and predicted results are in good agreement. The general behavior of fuel rod is calculated by axisymmetric system and the cladding behavior against radial crack is used by plane stress system. The sensitivity of strain aging of PWR fuel cladding tube due to load following is evaluated in terms of linear power, load cycle frequency and amplitude.

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Estimation of Chlorophyll-a Concentrations in the Nakdong River Using High-Resolution Satellite Image (고해상도 위성영상을 이용한 낙동강 유역의 클로로필-a 농도 추정)

  • Choe, Eun-Young;Lee, Jae-Woon;Lee, Jae-Kwan
    • Korean Journal of Remote Sensing
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    • v.27 no.5
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    • pp.613-623
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    • 2011
  • This study assessed the feasibility to apply Two-band and Three-band reflectance models for chlorophyll-a estimation in turbid productive waters whose scale is smaller and narrower than ocean using a high spatial resolution image. Those band ratio models were successfully applied to analyzing chlorophyll-a concentrations of ocean or coastal water using Moderate Imaging Spectroradiometer(MODIS), Sea-viewing Wide Field-fo-view Sensor(SeaWiFS), Medium Resolution Imaging Spectrometer(MERIS), etc. Two-band and Three-band models based on band ratio such as Red and NIR band were generally used for the Chl-a in turbid waters. Two-band modes using Red and NIR bands of RapidEye image showed no significant results with $R^2$ 0.38. To enhance a band ratio between absorption and reflection peak, We used red-edge band(710 nm) of RapidEye image for Twoband and Three-band models. Red-RE Two-band and Red-RE-NIR Three-band reflectance model (with cubic equation) for the RapidEye image provided significance performances with $R^2$ 0.66 and 0.73, respectively. Their performance showed the 'Approximate Prediction' with RPD, 1.39 and 1.29 and RMSE, 24.8, 22.4, respectively. Another three-band model with quadratic equation showed similar performances to Red-RE two-band model. The findings in this study demonstrated that Two-band and Three-band reflectance models using a red-edge band can approximately estimate chlorophyll-a concentrations in a turbid river water using high-resolution satellite image. In the distribution map of estimated Chl-a concentrations, three-band model with cubic equation showed lower values than twoband model. In the further works, quantification and correction of spectral interferences caused by suspended sediments and colored dissolved organic matters will improve the accuracy of chlorophyll-a estimation in turbid waters.

Characterization of Symptom and Determination of Tissue Critical Concentration for Diagnostic Criteria in 'Maehyang' Strawberry (Fragaria $\times$ ananassa Duch.) as Influenced by Calcium Concentrations in the Fertigation Solution ('매향' 딸기의 칼슘 영양진단을 위한 결핍증상 및 식물체 내 한계농도)

  • Choi, Jong-Myung;Jeong, Suck-Kee;Yoon, Moo-Kyung
    • Journal of Bio-Environment Control
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    • v.17 no.3
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    • pp.231-237
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    • 2008
  • Objective of this research was to investigate the effect of calcium concentrations in the fertilizer solution on growth and development of Ca deficiency in 'Maehyang' strawberry (Fragaria $\times$ ananassa Duch.). The margins of the youngest leaves were scorched and they developed a cupped shape as they were expanded in Ca deficient plants. The vein area of the youngest leaves became brown when the deficiency became severe. The quadratic responses were observed in dry weight production to elevated Ca concentrations in fertilizer solutions with the highest growth in 4.5 mM treatment. The regression equation was y=2.4026+1.0209x-$0.098x^2$ $(R^2=0.3546^{***})$. However, tissue Ca contents increased lineally as the Ca concentrations in fertilizer solutions were elevated (y=1.2108+0.1333x, $R^2=0.9189^{***}$). In changes of the fresh weight and Ca concentrations in petiole sap, fresh weight production showed quadratic responses to elevated Ca concentrations in fertilizer solution, but Ca concentration increased lineally. The equations in changes of fresh weight and Ca concentrations were y=9.273+4.882x-$0.4245x^2$ $(R^2=0.4935^{***})$ and y=52.311+3.2917x $(R^2=0.6918^{***})$, respectively. When the concentration of calcium at which plant growth was retarded by 10% is regarded as critical concentration level, the calcium contents based on dry weight of above ground plant tissue and in petiole sap should be in the range between 1.6 to 2.25% and 63 to $79mg{\cdot}kg^{-1}$, respectively.

A METHOD OF CAPABILITY EVALUATION FOR KOREAN PADDY SOILS -Part 2. The rice yield prediction by soil fertility constituents and other characters (한국(韓國) 답토양(畓土壤)의 생산력(生産力) 평가방법에 관한 연구 -2 보(報)·비옥도(肥沃度) 구성인자(構成因子) 및 기타(其他) 특성(特性)에 의(依)한 쌀수확량(收穫量)의 추정(推定))

  • Hong, Ki-Chang;Maeng, Do-Won;Kazutake, Kyuma;Hisao, Furukawa;Suh, Yoon-Soo
    • Korean Journal of Soil Science and Fertilizer
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    • v.12 no.1
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    • pp.15-23
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    • 1979
  • In the first paper of the series the five soil fertility factors were evaluated by means of principal component analysis and varimax method. They are interpreted as representing, 1) skeletal available phosporus status, 2) organnic matter status, 3) salt status 4) base status, and 5) free oxide status. In order to resynthesize such fragmented information for the overall soil fertility evaluation, the method of multiple regression analysis was adopted, using the five factor scores and yield data for Korean paddy soils as independent and dependent variables respectively. As test of linear models with different combinations of independent variables the results of t-test of regression coefficient were revealed that the organic matter status (FII) has no relevance to the yield of paddy and that the free oxides and salt supply has by it self only an insignificant contribution to the yield. The multiple correlation coefficient (R) revealed its multiple regression analysis was as low as 0.43. Introduction of quadratic terms to the linear model bettered the result. Thus multiple correlation coefficient (R) was increased as 0.59. Therefore, a coefficient of determination 0.35 was obtained by a quadratic model with interaction terms among the five fertility constituents. Generally we think that the fertility factor has more contribution to raise the rice yield in paddy and that the failure of yield prediction by fertility factor scores was caused by one of follows; 1) the roughness of the yield inspection, and 2) missextraction of fertility constituents. The second step in this study, assuming that the residuals by multiple regression analysis were due to factors other than soil fertility, we can now proceed to predicting the yield from the field characters with the classified fertility groups by means of Hayashi's theory of quantification No. 1. Such variables as fertility groups (FTYG), water availability (WATER), soil drainage (DRNG), climatic zone (CLIZ), surface soil's stickiness (STCKT), surface soil's dry consistence (DCNST), and surface soil's texture (FTEXT) are taken up as the explanatory variables. The quantification appears reasonable; the well to extremely well in soil drainage, very sticky of surface soil, inefficiency in water availability, coarse texture, and very hard to extremely hard dry consistence in soil are detrimental to the rice yield. The R was as high as 0.90 for the set of variables. But the given explanatory variables in this study were not quite effective in explaining rice yield. The method developed seems to be promising only if properly collected data are available. Conditions that should be satisfied in the yield inspection obtained from common cultivator for the purpose of deriving a prediction equation were put forward.

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Estimating the Yield of Marketable Potato of Mulch Culture using Climatic Elements (시기별 기상값 활용 피복재배 감자 상서수량 예측)

  • Lee, An-Soo;Choi, Seong-Jin;Jeon, Shin-Jae;Maeng, Jin-Hee;Kim, Jong-Hwan;Kim, In-Jong
    • KOREAN JOURNAL OF CROP SCIENCE
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    • v.61 no.1
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    • pp.70-77
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    • 2016
  • The object of this study was to evaluate the effects of climatic elements on potato yield and create a model for estimating the potato yield. We used 35 yield data of Sumi variety produced in mulching cultivation from 17 regions over 11 years. According to the results, some climatic elements showed significant level of correlation coefficient with marketable yield of potato. Totally 22 items of climatic elements appeared to be significant. Especially precipitation for 20 days after planting (Prec_1 & 2), relative humidity during 11~20 days after planting (RH_2), precipitation for 20 days before harvest (Prec_9 & 10), sunshine hours during 50~41 days before harvest (SH_6) and 20 days before harvest (SH_9 & 10), and days of rain during 10 days before harvest (DR_10) were highly significant in quadratic regression analysis. 22 items of predicted yield ($Y_i=aX_i{^2}+bX_i+c$) were induced from the 22 items of climatic elements (step 1). The correlations between the predicted yields and marketable yield were stepwised using SPSS, statistical program, and we selected a model (step 2), in which 4 items of independent variables ($Y_i$) were used. Subsequently the $Y_i$ were replaced with the equation in step 1, $aX_i{^2}+bX_i+c$. Finally we derived the model to predict the marketable yield of potato as below. $$Y=-336{\times}DR_-10^2+854{\times}DR_-10-0.422{\times}Prec_-9^2+43.3{\times}Prec_-9\\-0.0414{\times}RH_-2^2+46.2{\times}RH_-2-0.0102{\times}Prec_-2^2-7.00{\times}Prec_-2-10039$$.

Application of nonlocal elasticity theory for buckling analysis of nano-scale plates (나노 스케일 판의 좌굴해석을 위한 비국소 탄성 이론의 적용)

  • Lee, Won-Hong;Han, Sung-Cheon;Park, Weon-Tae
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.13 no.11
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    • pp.5542-5550
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    • 2012
  • Third-order shear deformation theory is reformulated using the nonlocal elasticity of Eringen. The equation of equilibrium of the nonlocal elasticity are derived. This theory has ability to capture the both small scale effects and quadratic variation of shear strain through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions of buckling of nano-scale plates are presented using this theory to illustrate the effect of nonlocal theory on buckling load of the nano-scale plates. The relations between nonlocal third-order and local theories are discussed by numerical results. Further, effects of (i) length (ii) nonlocal parameter, (iii) aspect ratio and (iv) mode number on nondimensional buckling load are studied. In order to validate the present solutions, the reference solutions are used and discussed. The present results of nano-scale plates using the nonlocal theory can provide a useful benchmark to check the accuracy of related numerical solutions.

A Study on the cognition for generality of solution in Algebra - Focusing on Quadratic equation - (대수 해법 일반성 인식에 관한 연구: 이차방정식 문항을 중심으로)

  • Kang, Jeong Gi
    • Communications of Mathematical Education
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    • v.28 no.1
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    • pp.155-178
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    • 2014
  • This study starts from the problem that although the solution premise the generality in algebra, a lot of students don't understand the generality of algebraic solution. We investigated this problem to understand cognitive characteristic of students. Moreover, we tried to find the elements which helping students understand the generality of algebraic solution. The purpose is to get the didactical implications. To do this, we had investigated the cognition of twenty middle school students for generality of solution. As result, 70 % of them didn't cognize the generality of solution. We had a personal interview with four students who showed a lack of sense of generality of algebraic solution. Putting into three action which we designed to help the change of their recognition, we observed and analyzed students cognizance change. Three action is the check of accordance for individual results, the check of solution accordance for different variables and the check of arbitrary variables. Based on the analysis, we discussed on the cognitive characteristic of students and the effect of three action. We finally discussed on the didactical implications to help students understand the generality of algebraic solution.