• Title/Summary/Keyword: linear equations

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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.

Estimation and Comparison of Stem Volume for Larix kaempferi in South Korea using the Stem Volume Model (수간재적모델에 따른 일본잎갈나무의 수간재적 추정 및 비교)

  • Ko, Chi-Ung;Moon, Ga-Hyun;Yim, Jong-Su;Lee, Sun-Jeoung;Kim, Dong-Geon;Kang, Jin-Taek
    • Journal of Korean Society of Forest Science
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    • v.108 no.4
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    • pp.592-599
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    • 2019
  • This study aimed to develop an equation for estimating stem volume for Larix kaempferiin South Korea using independent variables, diameter at breast height (DBH), and height as being closely associated with stem volume. Analysis was conducted on the growth performance of 2,840 Larix kaempferi samples across South Korea after felling them and gleaning diameter data according to both stem height and stem analyses. In order to test the fitness of six different stem taper equations, empirical assessment was conducted for fitness index (FI), bias, mean, and absolute deviation (MAD), and coefficient variation (%CV). The two selectedmodels found to be optimal were the following: model one (V=a+bDBH2), established by employing DBH only; and model four (V=a+bDBH2H), established by utilizing DBH and height, respectively. The findings of non-linear regression indicated statistical significance (p < 0.05) in a and b, which were the coefficients for the intercepts and slopes of the models. The FI of the models ranged between 94% and 99%, and the bias was close to zero, while MAD ranged from 0.01 to 0.05, and %CV from 5.97 to 14.43, indicating a high level of fitness. Thus, using the suggested models, the basic information necessary for forest management was obtained, and an estimation of the stem volume was effected without delay soon after effecting DBH and height measurements.

The Wavelet Series Analysis for the Fourth-order Elliptic Differential Equation (4계 타원형 미분 방정식을 위한 웨이블릿 급수해석)

  • Jo, Jun-Hyung;Woo, Kwang-Sung;Sin, Young-Sik
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.24 no.4
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    • pp.355-364
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    • 2011
  • In this study, the details of WSA(wavelet series analysis) have been demonstrated to solve the 4th-order elliptic differential equation. It is clear to solve the 2nd-order elliptic differential equation with the basis function of Hat wavelet series that is used in the previous study existed in $H^1$-space. However, it is difficult to solve the 4th order differential equation with same basis function of Hat wavelet series because of insufficient differentiability and integrability. To overcome this problem, the linear equations in terms of moment and deflection have been formulated and solved sequentially that are similar to extension of Elastic Load Method and Moment Area Method in some senses. Also, the differences and common points between the proposed method and the meshless method are discussed in the procedure of WSA formulation. As we expect, it is easy to ascertain that the more terms of Hat wavelet series are used, the better numerical solutions are improved. Also the solutions obtained by WSA have been compared with the conventional FEM solutions in case of Euler beam problems with stress singularity.

Analytical Analysis of Segmented Arc Plasma Torch for Plasma Wind Tunnel Facility (플라즈마 풍동 시설용 분절형 아크 플라즈마 토치의 해석적 설계변수 해석)

  • Seo, Jun-Ho;Choi, Soo-Seok;Choi, Seong-Man;Hong, Bong-Gun
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2010.11a
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    • pp.768-774
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    • 2010
  • A parametric study is conducted for the segmented arc plasma torch with the input power and current of 0.4 MW and 300 A, respectively. For this purpose, we use the analytical relationship equations between plasma temperature, inner diameter (R) and length (L) of the torch constrictor at the given input power and current conditions based on the arc channel model. The results reveal that arc plasma temperatures show non-linear behavior or absence corresponding to the variations of L and R when their values become larger than 1.25 m and 7.5 mm, respectively. For L < 1.25 m and R < 7.5 mm, however, they can increase monotonically as L increase or R decrease when one of both parameters is fixed. From these parametric study results, optimum ranges of R and L are suggested as $5.5mm{\leq}R{\leq}7.0mm$ and $0.5m{\leq}L{\leq}1.0m$ for 0.4 MW class segmented arc plasma torch, under which stable arc plasma with the temperatures of ~15,000 K can be achived at the input currents of ~300 A.

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Studies on Thermophilic Flat-sour Bacteria in Soymilk: Isolation, Indentification and Determination of Heat Resistance (두유내의 고온성 Flat-sour 변질균의 분리.동정 및 열저항성에 관한 연구)

  • Chung, Je-Bong;Lee, Kyun-Hee;Sohn, Heon-Soo;Kim, Suk-Min
    • Korean Journal of Food Science and Technology
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    • v.20 no.2
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    • pp.218-224
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    • 1988
  • For the optimization of thermal processing conditions in soymilk process, 4 strains of thermoresistant flat-sour bacteria were isolated from soymilk. The isolates were aerobic spore-forming rods, and grew at $-65^{\circ}C$. Based on the morphological and physiological properties, all of the isolated strains were identified as Bacillus stearothermophilus. The heat resistance of spores of 3 isolates and Bacillus stearothermophillus ATCC 12980 as a reference was determined in soymilk(pH 7.0) and pH 7.0 buffer solution. For each of the spores studied, linear regression equations with standard error were presented for the thermal destruction at 110, 115, 121, and $125^{\circ}C$. It was not obvious that the components of soy milk increased the heat resistance of spores. Between the strains studied, variability was noted in the D values at the different temperature, and no one strain was consistently the most heat resistant at all the given temperatures. The average D value for the 4 strains was 77.27, 20.20, 2.76 and 1.39 min at 110, 115, 121 and $125^{\circ}C$, respectively, and the average z value was $8.36^{\circ}C$.

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Case Study on Meaningful use of Parameter - One Classroom of Third Grade in Middle School - (매개변수개념의 의미충실한 사용에 관한 사례연구 -중학교 3학년 한 교실을 대상으로-)

  • Jee, Young Myong;Yoo, Yun Joo
    • School Mathematics
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    • v.16 no.2
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    • pp.355-386
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    • 2014
  • Algebraic generalization of patterns is based on the capability of grasping a structure inherent in several objects with awareness that this structure applies to general cases and ability to use it to provide an algebraic expression. The purpose of this study is to investigate how students generalize patterns using an algebraic object such as parameters and what are difficulties in geometric-arithmetic pattern tasks related to algebraic generalization and to determine whether the students can use parameters meaningfully through pattern generalization tasks that this researcher designed. During performing tasks of pattern generalization we designed, students differentiated parameters from letter 'n' that is used to denote a variable. Also, the students understood the relations between numbers used in several linear equations and algebraically expressed the generalized relation using a letter that was functions as a parameter. Some difficulties have been identified such that the students could not distinguish parameters from variables and could not transfer from arithmetical procedure to algebra in this process. While trying to resolve these difficulties, generic examples helped the students to meaningfully use parameters in pattern generalization.

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A Three-Dimensional Galerkin-FEM Model with Density Variation (밀도 변화를 포함하는 3차원 연직함수 전개모형)

  • 이호진;정경태;소재귀;강관수;정종율
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.8 no.2
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    • pp.123-136
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    • 1996
  • A three-dimensional Galerkin-FEM model which can handle the temporal and spatial variation of density is presented. The hydrostatic approximation is used and density effects are included by means of conservation equation of heat and the equation of state. The finite difference grids are used in the horizontal plane and a set of linear-shape functions is used for the vertical expansion. The similarity transform is introduced to solve resultant matrix equations. The proposed model was first applied to the density-driven circulation in an idealized basin in the presence of the heat exchange between the air and the sea. The advection terms in the momentum equation were ignored, while the convection terms were retained in the heat equation. Coefficients of the vertical eddy viscosity and diffusivity were fixed to be constant. Calculation in a non-rotating idealized basin shows that the difference in heat capacity with depth gives rise to the horizontal gradient of temperature. Consequently, there is a steady new in the upper layer in the direction of increasing depth with compensatory counter flow .in the lower layer. With Coriolis force, geostrophic flow was predominant due to the balance between the pressure gradient and the Coriolis force. As a test in region of irregular topography, the model is applied to the Yellow Sea. Although the resultant flow was very complex, the character of the flow Showed to be geostrophic on the whole.

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Kinetic Behavior of Immobilized Tyrosinase on Carbon in a Simulated Packed-Bed Reactor (충전층에서 탄소에 고정시킨 Tyrosinase의 반응속도에 관한 연구)

  • Shin, Sun Kyoung;Kim, Kyeo-Keun
    • Analytical Science and Technology
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    • v.10 no.1
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    • pp.66-74
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    • 1997
  • Influence of the axial dispersion on immobilized enzyme catalytic bed was investigated in order to examine the kinetic behavior of the biocatalysis. The enzyme employed in this study was the tyrosinase(EC 1.14.18.1) immobilized on carbon support : this system requires two substrates of phenol and oxygen. This enzyme has potential application for phenol degradation in waste water. A simulated reactor was a packed-bed reactor of 2.54cm in diameter and 10cm long, loaded with the immobilized carbon particle with an average diameter of $550{\mu}m$. A phenol feed in the strength of 55.5mM(5220ppm) was used to observe the behavior of the immobilized enzyme column at three different dissolved oxygen levels of 0.08445mM(2.7ppm), 0.1689mM(5.4ppm) and 0.3378mM(9.5ppm) with the flow rates in the range of 60(1mL/s) to 180mL/min(3mL/s). Examination of the Biot number and Damkolher numbers of the immobilized system enables us to eliminate the contribution of external mass transfer to set of differential equations derived from the dispersion model. Solution of the equation was finally obtained numerically with the application of the Danckwert boundary conditions and the assumed zero-and first order rates on the non-linear two substrate enzyme kinetics. Higher conversion of phenol was observed at the low flow rates and at the higher oxygen concentration. Comparison of axial dispersion and plug flow model showed that no detectable difference was observed in the column outlet conversion between the axial and the plug flow models which was in complete agreement with the previous studies.

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Effects of Water Activity on the Non-Enzymatic Browning Reaction of Dry Milk (수분활성도(水分活性度)가 분유(粉乳)의 비효소적(非酵素的) 갈변(褐變)에 미치는 영향(影響))

  • Chang, Kyu-Seob;Chang, Yeong-Il;Chun, Ki-Chul;Lee, Seong-Gu
    • Applied Biological Chemistry
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    • v.28 no.4
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    • pp.261-270
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    • 1985
  • This study was carried out he effects of water activity on the nonenzymatic browning reactions of dry milk powders. Samples (Dry Whole Milk DWM, Nonfat Dry Milk NFDM) stored at $55^{\circ}C$ were analyzed for $O_2,\;CO_2$ and $H_2O$ by Gas chromatographic method. The brown color which developed from the Maillard reaction was also measured by a reflective spectrophotometer. And linear regression equations and the correlation coeffcients were determined for $O_2,\;CO_2$ and brown color vs. storage, and the results are as follows. The amount of brown and off-flavor development increase as the water activities increase about 0.44 Aw during storage. Both DWM and NFDM milk products show a plateau in water absorption between the 0.33 and 0.44 water activities. DWM produced more browning than NFDM which may be partially due to the carbonyl amine reaction. The $CaCl_2$ solution may exude a water activity lower than 0.44 and varies greatly with temperatures. Oxygen is depleted as brown color development.

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Determination of Unit Hydrograph for the Hydrological Modelling of Long-term Run-off in the Major River Systems in Korea (장기유출의 수문적 모형개발을 위한 주요 수계별 단위도 유도)

  • 엄병현;박근수
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.26 no.4
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    • pp.52-65
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    • 1984
  • In general precise estimation of hourly of daily distribution of the long-term run-off should be very important in a design of source of irrigation. However, there have not been a satisfying method for forecasting of stationar'y long-term run-off in Korea. Solving this problem, this study introduces unit-hydrograph method frequently used in short-term run-off analysis into the long-term run-off analysis, of which model basin was selected to be Sumgin-river catchment area. In the estimation of effective rainfall, conventional method neglects the Soil moisture condition of catchment area, but in this study, the initial discharge (qb) occurred just before rising phase of the hydrograph was selected as the index of a basin soil moisture condition and then introduced as 3rd variable in the analysis of the reationship between cumulative rainfall and cumulative loss of rainfall, which built a new type of separation method of effective rainfall. In next step, in order to normalize significant potential error included in hydrological data, especially in vast catchment area, Snyder's correlation method was applied. A key to solution in this study is multiple correlation method or multiple regressional analysis, which is primarily based on the method of least squres and which is solved by the form of systems of linear equations. And for verification of the change of characteristics of unit hydrograph according to the variation of a various kind of hydrological charateristics (for example, precipitation, tree cover, soil condition, etc),seasonal unit hydrograph models of dry season(autumn, winter), semi-dry season (spring), rainy season (summer) were made respectively. The results obtained in this study were summarized as follows; 1.During the test period of 1966-1971, effective rainfall was estimated for the total 114 run-off hydrograph. From this estimation results, relative error of estimation to the ovservation value was 6%, -which is mush smaller than 12% of the error of conventional method. 2.During the test period, daily distribution of long-term run-off discharge was estimated by the unit hydrograph model. From this estimation results, relative error of estimation by the application of standard unit hydrograph model was 12%. When estimating by each seasonal unit bydrograph model, the relative error was 14% during dry season 10% during semi-dry season and 7% during rainy season, which is much smaller than 37% of conventional method. Summing up the analysis results obtained above, it is convinced that qb-index method of this study for the estimation of effective rainfall be preciser than any other method developed before. Because even recently no method has been developed for the estimation of daily distribution of long-term run-off dicharge, therefore estimation value by unit hydrograph model was only compared with that due to kaziyama method which estimates monthly run-off discharge. However this method due to this study turns out to have high accuracy. If specially mentioned from the results of this study, there is no need to use each seasonal unit hydrograph model separately except the case of semi-dry season. The author hopes to analyze the latter case in future sudies.

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