• Title/Summary/Keyword: mathematical model development

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Exploring Changes in Multi-ethnic Students' Mathematics Achievement Motivation : A Longitudinal Study using Expectancy-Value Theory (다문화가정 학생의 수학학업성취 동기 변화 연구: 기대가치 이론에 따른 종단연구)

  • Cho, Eunhye;Hwang, Sunghwan
    • The Mathematical Education
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    • v.58 no.1
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    • pp.101-120
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    • 2019
  • The goal of this study was to apply an expectancy-value model(Wigfield & Eccles, 2000) to explain changes in six multi-ethnic students' achievement motivation in mathematics during sixth (2012) to eighth (2014) grades. In order to achieve this goal, we used narrative research methods. Although individual students' achievement motivation and mathematics related life experiences differed, there are some common factors influencing their motivation development, especially (a) roles played by parents and teachers; (b) assessment of peers' competencies; (c) past learning experiences related to mathematics curriculum; (d) perception of the relationship between mathematics competency and other subjects; (e) home backgrounds; and (f) perceived task values. In this study, we achieved some insight into why some multi-ethnic students are willing to study hard to get good scores while others are uninterested in mathematics, and why some multi-ethnic students are likely to pursue new mathematical tasks and persist despite challenges, while others easily give up studying mathematics in the face of adversity. We argue that in order to increase and sustain multi-ethnic students' achievement motivation, educators and parents should recognize that motivation is contextually formulated in the intersection of current people, time, and space, not a personal entity formed in an individual's mind. The findings of this study shed light on the development of achievement motivation and can inform efforts to develop multi-ethnic students' positive motivation, which might influence their mathematics achievement and success in school.

Development of Predictive Growth Model of Imitation Crab Sticks Putrefactive Bacteria Using Mathematical Quantitative Assessment Model (수학적 정량평가모델을 이용한 게맛살 부패균의 성장 예측모델의 개발)

  • Moon, Sung-Yang;Paek, Jang-Mi;Shin, Il-Shik
    • Korean Journal of Food Science and Technology
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    • v.37 no.6
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    • pp.1012-1017
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    • 2005
  • Predictive growth model of putrefactive bacteria of surimi-based imitation crab in the modified surimi-based imitation crab (MIC) broth was investigated. The growth curves of putrefactive bacteria were obtained by measuring cell number in MIC broth under different conditions (Initial cell number, $1.0{\times}10^2,\;1.0{\times}10^3$ and $1.0{\times}10^4$ colony forming unit (CFU)/mL; temperature, $15^{\circ}C,\;20^{\circ}C\;and\;25^{\circ}C$) and applied them to Gompertz model. The microbial growth indicators, maximum specific growth rate constant (k), lag time (LT) and generation time (GT), were calculated from Gompertz model. Maximum specific growth rate (k) of putrefactive bacteria was become fast with rising temperature and fastest at $25^{\circ}C$. LT and GT were become short with rising temperature and shortest at $25^{\circ}C$. There were not significant differences in k, LT and GT by initial cell number (p>0.05). Polynomial model, $k=-0.2160+0.0241T-0.0199A_0$, and square root model, $\sqrt{k}=0.02669$ (T-3.5689), were developed to express the combination effects of temperature and initial cell number, The relative coefficient of experimental k and predicted k of polynomial model was 0.87 from response surface model. The relative coefficient of experimental k and predicted k of square root model was 0.88. From above results, we found that the growth of putrefactive bacteria was mainly affected by temperature and the square root model was more credible than the polynomial model for the prediction of the growth of putrefactive bacteria.

Development of Predictive Growth Model of Vibrio parahaemolyticus Using Mathematical Quantitative Model (수학적 정량평가모델을 이용한 Vibrio parahaemolyticus의 성장 예측모델의 개발)

  • Moon, Sung-Yang;Chang, Tae-Eun;Woo, Gun-Jo;Shin, Il-Shik
    • Korean Journal of Food Science and Technology
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    • v.36 no.2
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    • pp.349-354
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    • 2004
  • Predictive growth model of Vibrio parahaemolyticus in modified surimi-based imitation crab broth was investigated. Growth curves of V. parahaemolyticus were obtained by measuring cell concentration in culture broth under different conditions ($Initial\;cell\;level,\;1{\times}10^{2},\;1{\times}10^{3},\;and\;1{\times}10^{4}\;colony\;forming\;unit\;(CFU)/mL$; temperature, 15, 25 37, and $40^{\circ}C$; pH 6, 7, and 8) and applying them to Gompertz model. Microbial growth indicators, maximum specific growth rate (k), lag time (LT), and generation time (GT), were calculated from Gompertz model. Maximum specific growth rate (k) of V. parahaemolyticus increased with increasing temperature, reaching maximum rate at $37^{\circ}C$. LT and GT were also the shortest at $37^{\circ}C$. pH and initial cell number did not influence k, LT, and GT values significantly (p>0.05). Polynomial model, $k=a{\cdot}\exp(-0.5{\cdot}((T-T_{max}/b)^{2}+((pH-pH_{max)/c^{2}))$, and square root model, ${\sqrt{k}\;0.06(T-9.55)[1-\exp(0.07(T-49.98))]$, were developed to express combination effects of temperature and pH under each initial cell number using Gauss-Newton Algorism of Sigma plot 7.0 (SPSS Inc.). Relative coefficients between experimental k and k Predicted by polynomial model were 0.966, 0.979, and 0.965, respectively, at initial cell numbers of $1{\times}10^{2},\;1{\times}10^{3},\;and\;1{\times}10^{4}CFU/mL$, while that between experimental k and k Predicted by square root model was 0.977. Results revealed growth of V. parahaemolyticus was mainly affected by temperature, and square root model showing effect of temperature was more credible than polynomial model for prediction of V. parahaemolyticus growth.

A Study on the Development of a Simulation Model for Predicting Soil Moisture Content and Scheduling Irrigation (토양수분함량 예측 및 계획관개 모의 모형 개발에 관한 연구(I))

  • 김철회;고재군
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.19 no.1
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    • pp.4279-4295
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    • 1977
  • Two types of model were established in order to product the soil moisture content by which information on irrigation could be obtained. Model-I was to represent the soil moisture depletion and was established based on the concept of water balance in a given soil profile. Model-II was a mathematical model derived from the analysis of soil moisture variation curves which were drawn from the observed data. In establishing the Model-I, the method and procedure to estimate parameters for the determination of the variables such as evapotranspirations, effective rainfalls, and drainage amounts were discussed. Empirical equations representing soil moisture variation curves were derived from the observed data as the Model-II. The procedure for forecasting timing and amounts of irrigation under the given soil moisture content was discussed. The established models were checked by comparing the observed data with those predicted by the model. Obtained results are summarized as follows: 1. As a water balance model of a given soil profile, the soil moisture depletion D, could be represented as the equation(2). 2. Among the various empirical formulae for potential evapotranspiration (Etp), Penman's formula was best fit to the data observed with the evaporation pans and tanks in Suweon area. High degree of positive correlation between Penman's predicted data and observed data with a large evaporation pan was confirmed. and the regression enquation was Y=0.7436X+17.2918, where Y represents evaporation rate from large evaporation pan, in mm/10days, and X represents potential evapotranspiration rate estimated by use of Penman's formula. 3. Evapotranspiration, Et, could be estimated from the potential evapotranspiration, Etp, by introducing the consumptive use coefficient, Kc, which was repre sensed by the following relationship: Kc=Kco$.$Ka+Ks‥‥‥(Eq. 6) where Kco : crop coefficient Ka : coefficient depending on the soil moisture content Ks : correction coefficient a. Crop coefficient. Kco. Crop coefficients of barley, bean, and wheat for each growth stage were found to be dependent on the crop. b. Coefficient depending on the soil moisture content, Ka. The values of Ka for clay loam, sandy loam, and loamy sand revealed a similar tendency to those of Pierce type. c. Correction coefficent, Ks. Following relationships were established to estimate Ks values: Ks=Kc-Kco$.$Ka, where Ks=0 if Kc,=Kco$.$K0$\geq$1.0, otherwise Ks=1-Kco$.$Ka 4. Effective rainfall, Re, was estimated by using following relationships : Re=D, if R-D$\geq$0, otherwise, Re=R 5. The difference between rainfall, R, and the soil moisture depletion D, was taken as drainage amount, Wd. {{{{D= SUM from { {i }=1} to n (Et-Re-I+Wd)}}}} if Wd=0, otherwise, {{{{D= SUM from { {i }=tf} to n (Et-Re-I+Wd)}}}} where tf=2∼3 days. 6. The curves and their corresponding empirical equations for the variation of soil moisture depending on the soil types, soil depths are shown on Fig. 8 (a,b.c,d). The general mathematical model on soil moisture variation depending on seasons, weather, and soil types were as follow: {{{{SMC= SUM ( { C}_{i }Exp( { - lambda }_{i } { t}_{i } )+ { Re}_{i } - { Excess}_{i } )}}}} where SMC : soil moisture content C : constant depending on an initial soil moisture content $\lambda$ : constant depending on season t : time Re : effective rainfall Excess : drainage and excess soil moisture other than drainage. The values of $\lambda$ are shown on Table 1. 7. The timing and amount of irrigation could be predicted by the equation (9-a) and (9-b,c), respectively. 8. Under the given conditions, the model for scheduling irrigation was completed. Fig. 9 show computer flow charts of the model. a. To estimate a potential evapotranspiration, Penman's equation was used if a complete observed meteorological data were available, and Jensen-Haise's equation was used if a forecasted meteorological data were available, However none of the observed or forecasted data were available, the equation (15) was used. b. As an input time data, a crop carlender was used, which was made based on the time when the growth stage of the crop shows it's maximum effective leaf coverage. 9. For the purpose of validation of the models, observed data of soil moiture content under various conditions from May, 1975 to July, 1975 were compared to the data predicted by Model-I and Model-II. Model-I shows the relative error of 4.6 to 14.3 percent which is an acceptable range of error in view of engineering purpose. Model-II shows 3 to 16.7 percent of relative error which is a little larger than the one from the Model-I. 10. Comparing two models, the followings are concluded: Model-I established on the theoretical background can predict with a satisfiable reliability far practical use provided that forecasted meteorological data are available. On the other hand, Model-II was superior to Model-I in it's simplicity, but it needs long period and wide scope of observed data to predict acceptable soil moisture content. Further studies are needed on the Model-II to make it acceptable in practical use.

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Development of L-Threonine Producing Recombinant Escherichia coli using Metabolic Control Analysis (대사 조절 분석 기법을 이용한 L-Threonine 생산 재조합 대장균 개발)

  • Choi, Jong-Il;Park, Young-Hoon;Yang, Young-Lyeol
    • KSBB Journal
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    • v.22 no.1
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    • pp.62-65
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    • 2007
  • New strain development strategy using kinetic models and metabolic control analysis was investigated. In this study, previously reported mathematical models describing the enzyme kinetics of intracellular threonine synthesis were modified for mutant threonine producer Escherichia coli TF5015. Using the modified models, metabolic control analysis was carried out to identify the rate limiting step by evaluating the flux control coefficient on the overall threonine synthesis flux exerted by individual enzymatic reactions. The result suggested the production of threonine could be enhanced most efficiently by increasing aspartate semialdehyde dehydrogenase (asd) activity of this strain. Amplification of asd gene in recombinant strain TF5015 (pCL-$P_{aroF}$-asd) increased the threonine production up to 23%, which is much higher than 14% obtained by amplifying aspartate kinse (thrA), other gene in threonine biosynthesis pathway.

Modeling and Optimizing Brightness Development in Peroxide Bleaching of Thermomechanical Pulp

  • Wang, Li-Jun;Park, Kyoung-Hwa;Yoon, Byung-Ho
    • Journal of Korea Technical Association of The Pulp and Paper Industry
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    • v.31 no.5
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    • pp.86-94
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    • 1999
  • Alkaline peroxide bleaching of chemi-mechanical pulp is a very complicated system where various process factors affect the bleacing performance and pulp properties. Traditional onefactor-at a time method is ineffective and costly infinding the optimal bleaching conditions. In this study, statistical experimental design and multiple regression method wre used to investigated the interactions among various bleaching factors and to find out the possbile maximal brightness development during one stage alkaline peroxide bleacing of TMP. The TMP was made from 10% Korean red pine and 90% Korean spruce and had an initial brightness of 54.5% ISO. the TMP was pretreated with EDTA(0.5% on O.D. pulp, 3% pulp consistency, 30$^{\circ}C$ for 60 minutes) and bleached in a 2 L Mark V Quantum Reactor at 750 rmp, 7.5% of bleaching consistency and with 0.05% magnesium sulfate addition. The ranges of chemical factors studied , based on oven-ried pulp, were 1-5% for hydrogen peroxide, 1-4% for sodium hydroxide and 1-4% for sodium silicate. The rages of reaction temperature and time were 50-90$^{\circ}C$ and 40-180minutes respectively. Interactions of hydrogen peroxide with alkali , time with temperature ature, alkali with time and silicate with temperature were found to be significant which means that hydrogen peroxide bleaching will be favored at stable concentration of perhydroxyl ion, relatively short time and low temperature, and high level of silicate. Mathematical model which has good predictability for target brightness in one stage peroxide bleaching can also be established easily. Base ion the model, maximal brightness of 70% ISO was found to at 50$^{\circ}C$ and 50 minutes by chemical additions of 5% for hydrogen peroxide, 3.2-3.4% for sodium hydroxide and 4% for silicate based on O.D. pulp. However, this result might not be suitable for situation where furnishes are different from ours, or different pretreatment is used, or bleaching carried out at different pulp consistency. In these cases it will be good to re-investigate the process by a similar methodology as was used in this study.

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Modeling and Simulation of Aircraft Motion for Performance Assessment of Airborne AESA Radar Considering Wind and Vibration (바람과 진동을 고려한 항공기 탑재 AESA 레이다 성능 평가용 운동 모델링 및 시뮬레이션)

  • Lee, Donguk;Im, Jaehan;Lee, Haemin;Jung, Youngkwang;Jeong, Jaehyeon;Shin, Jong-Hwan;Lee, Sungwon;Park, June Hyune;Ahn, Jaemyung
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.48 no.11
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    • pp.903-910
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    • 2020
  • This paper introduces a simulator to assess the impacts of the wind and the airframe vibration on the performance of the Active Electronically Scanned Array (AESA) radar mounted in an aircraft. The AESA radar is mounted on the nose cone of an aircraft, and vibration occurs due to the drag force. This vibration affects the behavior of the AESA radar and can cause phase errors in signal. The simulator adopts the geometric model for nose cone, the mathematical models on the rigid-body dynamics of the aircraft, the average/turbulent winds, and the mode/ambient vibrations to compute the position and the attitude of the radar accurately. Numerical studies reflecting a set of test scenarios were conducted to demonstrate the effectiveness of the developed simulator.

Vibration Control of Working Booms on Articulated Bridge Inspection Robots (교량검사 굴절로봇 작업붐의 진동제어)

  • Hwang, In-Ho;Lee, Hu-Seok;Lee, Jong-Seh
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.21 no.5
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    • pp.421-427
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    • 2008
  • A robot crane truck is developed by the Bridge Inspection Robot Development Interface(BRIDI) for an automated and/or teleoperated bridge inspection. This crane truck looks similar to the conventional bucket crane, but is much smaller in size and light-weight. At the end of the telescoping boom which is 12m long, a robot platform is mounted which allows the operator to scan the bridge structure under the deck trough the camera. Boom vibration induced by wind and deck movement can cause serious problems in this scanning system. This paper presents a control system to mitigate such vibration of the robot boom. In the proposed control system, an actuator is installed at the end of the working boom. This control system is studied using a mathematical model analysis with LQ control algorithm and a scaled model test in the laboratory. The study indicates that the proposed system is efficient for the vibration control of the robot booms, thereby demonstrating its immediate applicability in the field.

A Study on How to Extend The Inspection Period for The One-Shot System (One-Shot System에 대한 점검주기 연장 방안 연구)

  • Kim, Jong-jin;Song, Jeong-hun;Han, Jung-won;Lee, Chang-kyu
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.22 no.2
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    • pp.113-118
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    • 2021
  • The guided weapon system should ensure economical operation and user safety. In particular, in the case of guided weapon systems developed in the form of a guaranteed bomb, the standards for maintaining reliability considering the long-term storage environment are presented during the development stage, and an optimized inspection cycle is required to maintain this. This study calculated the reliability through a trend test, fitness test, and distribution analysis using a mathematical model based on the maintenance status and shooting results during the inspection period for OO missiles currently in operation for a long time in the military. Through this, it was applied to the inspection period model (Martinez) set during the development stage to determine if the improved inspection period can be utilized. Finally, by synthesizing the data from these studies, a policy management plan was developed according to the extension of the inspection period. The One-Shot system was operated at the inspection period set when it was developed. The study analyzed the actual failure and maintenance data to reset the efficient inspection period.

A Development of Groundwater Level Fluctuations Due To Precipitations and Infiltrations (강우에 의한 지하수위 변동 예측모델의 개발 및 적용)

  • Park, Eun-Gyu
    • Journal of Soil and Groundwater Environment
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    • v.12 no.4
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    • pp.54-59
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    • 2007
  • In this study, a semi-analytical model to address groundwater level fluctuations in response to precipitations and its infiltration is developed through mathematical modeling based on water balance equation. The developed model is applied to a prediction of groundwater level fluctuations in Hongcheon area. The developed model is calibrated through a nonlinear parameter estimator by using daily precipitation rates and groundwater fluctuations data of a same year 2003. The calibrated input parameters are directly applied to the prediction of groundwater fluctuations of year 2004 and the simulated curve successfully mimics the observed. The developed model is also applied to practical problems such as a prediction of a effect of reduced recharge due to surface coverage change and a induced water level reduction. Through this study, we found that recharge to precipitation ratio is not a constant and may be a function of a precipitation pattern.