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Characterization of Weed Occurrence in Major Horticultural Crops - III. Phenological Aspects of Major Weeds (원예경작지(園藝耕作地)에서의 잡초발생(雜草發生) 특성에 관(關)한 연구(硏究) - III. 주요잡초종(主要雜草種)의 발생계절성(發生季節性))

  • Woo, I.S.;Pyon, J.Y.;Guh, J.O.
    • Korean Journal of Weed Science
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    • v.9 no.2
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    • pp.130-140
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    • 1989
  • 1) Dormancy brocken weed seeds were planted in soil at 15 days interval from June to December in 1986 and 1987 and test of normality and normal distribution curve were made to determine seasonal distribution characteristics of weed emergence in fields. Monthly emergence distribution pattern of each species can be concluded as following normal distribution equations. E. crusgalli $y={\frac{1}{2.52{\sqrt{2{\pi}}}}}e^{-{\frac{(x-10.057)^2}{12.7}}}$ E. indica $y={\frac{1}{2.17{\sqrt{2{\pi}}}}}e^{-{\frac{(x-9.16)^2}{9.45}}}$ A. lividus $y={\frac{1}{7.74{\sqrt{2{\pi}}}}}e^{-{\frac{(x-10.06)^2}{15.46}}}$ S. nigrum $y={\frac{1}{2.7{\sqrt{2{\pi}}}}}e^{-{\frac{(x-9.695)^2}{14.58}}}$ C. busrsa-pastoris $y={\frac{1}{2.83{\sqrt{2{\pi}}}}}e^{-{\frac{(x-9.02)^2}{16.02}}}$ D. sanguinalis $y={\frac{1}{2.8{\sqrt{2{\pi}}}}}e^{-{\frac{(x-8.58)^2}{15.67}}}$ S. viridis $y={\frac{1}{2.72{\sqrt{2{\pi}}}}}e^{-{\frac{(x-9.36)^2}{14.8}}}$ C. album $y={\frac{1}{2.596{\sqrt{2{\pi}}}}}e^{-{\frac{(x-8.07)^2}{13.48}}}$ P. oleraeda $y={\frac{1}{2.45{\sqrt{2{\pi}}}}}e^{-{\frac{(x-10.83)^2}{12.01}}}$ 2) Emergence peak period of weed species tested were from the end of May to early August and yearly variation of emergence was observed in E. crus-galli, S. viridis, S, nigrum, and P. oleracea and this fact may more related to rainfall pattern rather than temperature.

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A Study on Seasonal Pollutant Distribution Characteristics of Contaminated Tributaries in Nakdong River Basin (낙동강 중점관리지류·지천의 계절적 오염발생특성 분석)

  • Na, Seungmin;Kwon, Heongak;Shin, Sang Min;Son, YoungGyu;Shin, Dongseok;Im, Tae Hyo
    • Journal of Wetlands Research
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    • v.18 no.3
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    • pp.301-312
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    • 2016
  • This study has performed comparative analysis on characteristics of contaminated 35 tributaries on seasonal variation/point discharge load/pollutant distribution of water quality factors(8) in order to understand the effect of the watershed in Nakdong River Basin. As a results, the water quality of $BOD_5$(Biochemical Oxygen Demand), Chl-a(Chlorophyll a) and Fecal E. Coli shows II grade at tributaries of more than 50% without COD(Chemical Oxygen Demand), TP(Total Phosphate), TOC(Total Oxygen Carbon) and TN(Total Nitrogen) factors. The specific discharge(Q) were occupied about 54.4% (19 sites) as $0.05m^3/sec/km^2$ value. Among these results, the contaminant level of Dalseocheon, Hyeonjicheon, Seokkyocheon 1, Uriyeongcheon and Dasancheon was also high, which has to consider a discharged pollutant load(kg/day). The 35 major tributaries of Nakdong River were included in 7 mid-watershed, such as Nakdong Waegwan, Geumho River, Nakdong Goryung, Nakdong Changnyung, Nam River, Nakdong Milyang, Nakdong River Hagueon. Especially, the discharged pollutant load of Nam River and Geumho River also was high according to the amount of discharge such as Kachang dam, Gongsan dam and Nam river dam. Seasonal difference of the water quality factors such as $BOD_5$, TN, SS and Q was observed largely, on the other hand the TP and Chl-a was not. This is guessed due to the precipitation effect of site, biological and physicochemical degradation properties of pollutant and etc. The co-relationship between the seasonal difference and water quality factors was observed using a Pearson correlation coefficients. Besides, the Multiple Regression analysis using a Stepwise Regression method was conducted to understand the effect between seasonal difference and water quality factors/regression equations. As a result, the Multiple Regression analysis was adapted in the spring, summer and autumn without the winter, which was observed high at spring, summer and autumn in the order COD/TP, Chl-a/TOC, TOC/COD/$BOD_5$ water quality factors, respectively.

The PRISM-based Rainfall Mapping at an Enhanced Grid Cell Resolution in Complex Terrain (복잡지형 고해상도 격자망에서의 PRISM 기반 강수추정법)

  • Chung, U-Ran;Yun, Kyung-Dahm;Cho, Kyung-Sook;Yi, Jae-Hyun;Yun, Jin-I.
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.11 no.2
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    • pp.72-78
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    • 2009
  • The demand for rainfall data in gridded digital formats has increased in recent years due to the close linkage between hydrological models and decision support systems using the geographic information system. One of the most widely used tools for digital rainfall mapping is the PRISM (parameter-elevation regressions on independent slopes model) which uses point data (rain gauge stations), a digital elevation model (DEM), and other spatial datasets to generate repeatable estimates of monthly and annual precipitation. In the PRISM, rain gauge stations are assigned with weights that account for other climatically important factors besides elevation, and aspects and the topographic exposure are simulated by dividing the terrain into topographic facets. The size of facet or grid cell resolution is determined by the density of rain gauge stations and a $5{\times}5km$ grid cell is considered as the lowest limit under the situation in Korea. The PRISM algorithms using a 270m DEM for South Korea were implemented in a script language environment (Python) and relevant weights for each 270m grid cell were derived from the monthly data from 432 official rain gauge stations. Weighted monthly precipitation data from at least 5 nearby stations for each grid cell were regressed to the elevation and the selected linear regression equations with the 270m DEM were used to generate a digital precipitation map of South Korea at 270m resolution. Among 1.25 million grid cells, precipitation estimates at 166 cells, where the measurements were made by the Korea Water Corporation rain gauge network, were extracted and the monthly estimation errors were evaluated. An average of 10% reduction in the root mean square error (RMSE) was found for any months with more than 100mm monthly precipitation compared to the RMSE associated with the original 5km PRISM estimates. This modified PRISM may be used for rainfall mapping in rainy season (May to September) at much higher spatial resolution than the original PRISM without losing the data accuracy.

The Application of Computer Program for Determination of Fluid Properties and P-T Condition from Microthermometric Data on Fluid Inclusions (유체포유물의 생성시 온도-압력 조건과 유체포유물의 물리화학적 특성연구에 있어서의 컴퓨터 프로그램이용)

  • Oh, Chang-Whan;Choi, Sang-Hoon
    • Economic and Environmental Geology
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    • v.26 no.1
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    • pp.21-27
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    • 1993
  • Fluid inclusion has been widely used to study the origin and physiochemical conditions of ore deposits. However, it is difficult to get the accurate physiochemical data from fluid inclusion study due to the error of microthermometric data and the complexity of calculation of density and isochore of fluid inclusion. The computer programs HALWAT, $CO_2$, and CHNACL written by Nicholls and Crowford (1985) partly contributed to improve the accuracy of physiochemical data by using complicated equations. These programs are applied to determine the densities and isochores of fluid inclusions for the Cretaceous Keumhak mine using Choi and So's data (1992) and for the Jurassic Samhwanghak mine using Yun's data (1990). The estimated PoT for Keumhak mine from calculated isochores of coexisting fluid inclusions are $230^{\circ}{\sim}290^{\circ}C$ and 500~800 bar which matche well to the poT estimated by Choi and So ($280^{\circ}{\sim}360^{\circ}C$ and 500~800 bar, 1992). However, the poT for Samwhanghak mine estimated in this study by combining the calculated isochores and sulfur isotope geothermometer data by Yun (1990) are about 4~7 kb at $329{\pm}50^{\circ}{\sim}344{\pm}55^{\circ}C$ which are quite different form the P-T estimates by Yun ($255^{\circ}{\sim}294^{\circ}C$ and 1.2~1.9kb, 1990). This discrepancy caused by misinterpretation of homogenization temperature (Th) of fluid inclusion and by application of inappropriate isochores. The application of homogenization temperature and/or inappropriately selected isochore to determine the trapping PoT condition of ore-deposits should be avoided, particularly for ore-deposits formed at pressures higher than 1~2 kb.

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Analysis of Correlation with Cross Sectional Area of Flow and Flow Rate Variation of Discharge Measurement Point in the Upper Stream of Seomjin River (섬진강상류 유량측정지점의 유수단면적과 유량변화에 따른 상관관계 분석)

  • Song, KwangDuck;Kim, KapSoon;Lee, DongJin;Ham, SangIn;Kim, DaeYoung;Oh, TaeYoun;Lee, JaeChoon;Lim, ByungJin
    • Korean Journal of Ecology and Environment
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    • v.46 no.1
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    • pp.94-102
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    • 2013
  • This study was carried out to determine the variation of the water level and crosssection area for investigating changes of stream foreland, and to determine the correlation between the average flow velocity and cross-section area so as to understand the hydrological characteristics of the stream. The slope of the cross-sectional area was changed in water levels of 0.6~1.0 m and 1.8~2.0 m. The first change occurred in the low-water level season, and the second change occurred in the high-water level seasons. It is assumed that the changes occurred due to the geological transfigure. The correlation between the cross-sectional area and the average flow velocity was 0.22~0.86 in the exponential equation and 0.20~0.87 in the linear equation. The low water level had a higher correlation than the high water level, and free weirs in the upper stream showed a very low correlation. Therefore, this study provides novel information for the management of water quality in the riverside, using correlation equations of the water level and flow velocity with the cross section area.

Impact of Sulfur Dioxide Impurity on Process Design of $CO_2$ Offshore Geological Storage: Evaluation of Physical Property Models and Optimization of Binary Parameter (이산화황 불순물이 이산화탄소 해양 지중저장 공정설계에 미치는 영향 평가: 상태량 모델의 비교 분석 및 이성분 매개변수 최적화)

  • Huh, Cheol;Kang, Seong-Gil;Cho, Mang-Ik
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.13 no.3
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    • pp.187-197
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    • 2010
  • Carbon dioxide Capture and Storage(CCS) is regarded as one of the most promising options to response climate change. CCS is a three-stage process consisting of the capture of carbon dioxide($CO_2$), the transport of $CO_2$ to a storage location, and the long term isolation of $CO_2$ from the atmosphere for the purpose of carbon emission mitigation. Up to now, process design for this $CO_2$ marine geological storage has been carried out mainly on pure $CO_2$. Unfortunately the $CO_2$ mixture captured from the power plants and steel making plants contains many impurities such as $N_2$, $O_2$, Ar, $H_2O$, $SO_2$, $H_2S$. A small amount of impurities can change the thermodynamic properties and then significantly affect the compression, purification, transport and injection processes. In order to design a reliable $CO_2$ marine geological storage system, it is necessary to analyze the impact of these impurities on the whole CCS process at initial design stage. The purpose of the present paper is to compare and analyse the relevant physical property models including BWRS, PR, PRBM, RKS and SRK equations of state, and NRTL-RK model which are crucial numerical process simulation tools. To evaluate the predictive accuracy of the equation of the state for $CO_2-SO_2$ mixture, we compared numerical calculation results with reference experimental data. In addition, optimum binary parameter to consider the interaction of $CO_2$ and $SO_2$ molecules was suggested based on the mean absolute percent error. In conclusion, we suggest the most reliable physical property model with optimized binary parameter in designing the $CO_2-SO_2$ mixture marine geological storage process.

Effect of Nitrogen Impurity on Process Design of $CO_2$ Marine Geological Storage: Evaluation of Equation of State and Optimization of Binary Parameter (질소 불순물이 이산화탄소 해양 지중저장 공정설계에 미치는 영향 평가: 상태방정식의 비교 분석 및 이성분 매개변수 최적화)

  • Huh, Cheol;Kang, Seong-Gil
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.12 no.3
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    • pp.217-226
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    • 2009
  • Marine geological storage of $CO_2$ is regarded as one of the most promising options to response climate change. Marine geological storage of $CO_2$ is to capture $CO_2$ from major point sources, to transport to the storage sites and to store $CO_2$ into the marine geological structure such as deep sea saline aquifer. Up to now, process design for this $CO_2$ marine geological storage has been carried out mainly on pure $CO_2$. Unfortunately the captured $CO_2$ mixture contains many impurities such as $N_2$, $O_2$, Ar, $H_2O$, $SO_x$, $H_2S$. A small amount of impurities can change the thermodynamic properties and then significantly affect the compression, purification and transport processes. In order to design a reliable $CO_2$ marine geological storage system, it is necessary to perform numerical process simulation using thermodynamic equation of state. The purpose of the present paper is to compare and analyse the relevant equations of state including PR, PRBM, RKS and SRK equation of state for $CO_2-N_2$ mixture. To evaluate the predictive accuracy of the equation of the state, we compared numerical calculation results with reference experimental data. In addition, optimum binary parameter to consider the interaction of $CO_2$ and $N_2$ molecules was suggested based on the mean absolute percent error. In conclusion, we suggest the most reliable equation of state and relevant binary parameter in designing the $CO_2-N_2$ mixture marine geological storage process.

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Study on the Travel and Tractive Characteristics of the Two-Wheel Tractor on the General Slope Land(III)-Tractive Performance of Power Tiller- (동력경운기의 경사지견인 및 주행특성에 관한 연구 (III)-동력경운의 경사지 견인성능-)

  • 송현갑;정창주
    • Journal of Biosystems Engineering
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    • v.3 no.2
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    • pp.35-61
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    • 1978
  • To find out the power tiller's travel and tractive characteristics on the general slope land, the tractive p:nver transmitting system was divided into the internal an,~ external power transmission systems. The performance of power tiller's engine which is the initial unit of internal transmission system was tested. In addition, the mathematical model for the tractive force of driving wheel which is the initial unit of external transmission system, was derived by energy and force balance. An analytical solution of performed for tractive forces was determined by use of the model through the digital computer programme. To justify the reliability of the theoretical value, the draft force was measured by the strain gauge system on the general slope land and compared with theoretical values. The results of the analytical and experimental performance of power tiller on the field may be summarized as follows; (1) The mathematical equation of rolIing resistance was derived as $$Rh=\frac {W_z-AC \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\] sin\theta_1}} {tan\phi \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]+\frac{tan\theta_1}{1}$$ and angle of rolling resistance as $$\theta _1 - tan^1\[ \frac {2T(AcrS_0 - T)+\sqrt (T-AcrS_0)^2(2T)^2-4(T^2-W_2^2r^2)\times (T-AcrS_0)^2 W_z^2r^2S_0^2tan^2\phi} {2(T^2-W_z^2r^2)S_0tan\phi}\] $$and the equation of frft force was derived as$$P=(AC+Rtan\phi)\[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]cos\phi_1 \ulcorner \frac {W_z \ulcorner{AC\[ [1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]sin\phi_1 {tan\phi[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\]+ \frac {tan\phi_1} { 1} \ulcorner W_1sin\alpha $$The slip coefficient K in these equations was fitted to approximately 1. 5 on the level lands and 2 on the slope land. (2) The coefficient of rolling resistance Rn was increased with increasing slip percent 5 and did not influenced by the angle of slope land. The angle of rolling resistance Ol was increasing sinkage Z of driving wheel. The value of Ol was found to be within the limits of Ol =2\ulcorner "'16\ulcorner. (3) The vertical weight transfered to power tiller on general slope land can be estim ated by use of th~ derived equation: $$R_pz= \frac {\sum_{i=1}^{4}{W_i}} {l_T} { (l_T-l) cos\alpha cos\beta \ulcorner \bar(h) sin \alpha - W_1 cos\alpha cos\beta$$The vertical transfer weight $R_pz$ was decreased with increasing the angle of slope land. The ratio of weight difference of right and left driving wheel on slop eland,$\lambda= \frac { {W_L_Z} - {W_R_Z}} {W_Z} $, was increased from ,$\lambda$=0 to$\lambda$=0.4 with increasing the angle of side slope land ($\beta = 0^\circ~20^\circ) (4) In case of no draft resistance, the difference between the travelling velocities on the level and the slope land was very small to give 0.5m/sec, in which the travelling velocity on the general slope land was decreased in curvilinear trend as the draft load increased. The decreasing rate of travelling velocity by the increase of side slope angle was less than that by the increase of hill slope angle a, (5) Rate of side slip by the side slope angle was defined as $ S_r=\frac {S_s}{l_s} \times$ 100( %), and the rate of side slip of the low travelling velocity was larger than that of the high travelling velocity. (6) Draft forces of power tiller did not affect by the angular velocity of driving wheel, and maximum draft coefficient occurred at slip percent of S=60% and the maximum draft power efficiency occurred at slip percent of S=30%. The maximum draft coefficient occurred at slip percent of S=60% on the side slope land, and the draft coefficent was nearly constant regardless of the side slope angle on the hill slope land. The maximum draft coefficient occurred at slip perecent of S=65% and it was decreased with increasing hill slope angle $\alpha$. The maximum draft power efficiency occurred at S=30 % on the general slope land. Therefore, it would be reasonable to have the draft operation at slip percent of S=30% on the general slope land. (7) The portions of the power supplied by the engine of the power tiller which were used as the source of draft power were 46.7% on the concrete road, 26.7% on the level land, and 13~20%; on the general slope land ($\alpha = O~ 15^\circ ,\beta = 0 ~ 10^\circ$) , respectively. Therefore, it may be desirable to develope the new mechanism of the external pO'wer transmitting system for the general slope land to improved its performance.l slope land to improved its performance.

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Study on the Travel and Tractive Characteristics of the Two-Wheel Tractor on the General Slope Land(Ⅲ)-Tractive Performance of Power Tiller- (동력경운기의 경사지견인 및 주행특성에 관한 연구 (Ⅲ)-동력경운의 경사지 견인성능-)

  • Song, Hyun Kap;Chung, Chang Joo
    • Journal of Biosystems Engineering
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    • v.3 no.2
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    • pp.34-34
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    • 1978
  • To find out the power tiller's travel and tractive characteristics on the general slope land, the tractive p:nver transmitting system was divided into the internal an,~ external power transmission systems. The performance of power tiller's engine which is the initial unit of internal transmission system was tested. In addition, the mathematical model for the tractive force of driving wheel which is the initial unit of external transmission system, was derived by energy and force balance. An analytical solution of performed for tractive forces was determined by use of the model through the digital computer programme. To justify the reliability of the theoretical value, the draft force was measured by the strain gauge system on the general slope land and compared with theoretical values. The results of the analytical and experimental performance of power tiller on the field may be summarized as follows; (1) The mathematical equation of rolIing resistance was derived as $$Rh=\frac {W_z-AC \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\] sin\theta_1}} {tan\phi \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]+\frac{tan\theta_1}{1}$$ and angle of rolling resistance as $$\theta _1 - tan^1\[ \frac {2T(AcrS_0 - T)+\sqrt (T-AcrS_0)^2(2T)^2-4(T^2-W_2^2r^2)\times (T-AcrS_0)^2 W_z^2r^2S_0^2tan^2\phi} {2(T^2-W_z^2r^2)S_0tan\phi}\] $$and the equation of frft force was derived as$$P=(AC+Rtan\phi)\[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]cos\phi_1 ? \frac {W_z ?{AC\[ [1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]sin\phi_1 {tan\phi[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\]+ \frac {tan\phi_1} { 1} ? W_1sin\alpha $$The slip coefficient K in these equations was fitted to approximately 1. 5 on the level lands and 2 on the slope land. (2) The coefficient of rolling resistance Rn was increased with increasing slip percent 5 and did not influenced by the angle of slope land. The angle of rolling resistance Ol was increasing sinkage Z of driving wheel. The value of Ol was found to be within the limits of Ol =2? "'16?. (3) The vertical weight transfered to power tiller on general slope land can be estim ated by use of th~ derived equation: $$R_pz= \frac {\sum_{i=1}^{4}{W_i}} {l_T} { (l_T-l) cos\alpha cos\beta ? \bar(h) sin \alpha - W_1 cos\alpha cos\beta$$The vertical transfer weight $R_pz$ was decreased with increasing the angle of slope land. The ratio of weight difference of right and left driving wheel on slop eland,$\lambda= \frac { {W_L_Z} - {W_R_Z}} {W_Z} $, was increased from ,$\lambda$=0 to$\lambda$=0.4 with increasing the angle of side slope land ($\beta = 0^\circ~20^\circ) (4) In case of no draft resistance, the difference between the travelling velocities on the level and the slope land was very small to give 0.5m/sec, in which the travelling velocity on the general slope land was decreased in curvilinear trend as the draft load increased. The decreasing rate of travelling velocity by the increase of side slope angle was less than that by the increase of hill slope angle a, (5) Rate of side slip by the side slope angle was defined as $ S_r=\frac {S_s}{l_s} \times$ 100( %), and the rate of side slip of the low travelling velocity was larger than that of the high travelling velocity. (6) Draft forces of power tiller did not affect by the angular velocity of driving wheel, and maximum draft coefficient occurred at slip percent of S=60% and the maximum draft power efficiency occurred at slip percent of S=30%. The maximum draft coefficient occurred at slip percent of S=60% on the side slope land, and the draft coefficent was nearly constant regardless of the side slope angle on the hill slope land. The maximum draft coefficient occurred at slip perecent of S=65% and it was decreased with increasing hill slope angle $\alpha$. The maximum draft power efficiency occurred at S=30 % on the general slope land. Therefore, it would be reasonable to have the draft operation at slip percent of S=30% on the general slope land. (7) The portions of the power supplied by the engine of the power tiller which were used as the source of draft power were 46.7% on the concrete road, 26.7% on the level land, and 13~20%; on the general slope land ($\alpha = O~ 15^\circ ,\beta = 0 ~ 10^\circ$) , respectively. Therefore, it may be desirable to develope the new mechanism of the external pO'wer transmitting system for the general slope land to improved its performance.

A Study of the Representation in the Elementary Mathematical Problem-Solving Process (초등 수학 문제해결 과정에 사용되는 표현 방법에 대한 연구)

  • Kim, Yu-Jung;Paik, Seok-Yoon
    • Journal of Elementary Mathematics Education in Korea
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    • v.9 no.2
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    • pp.85-110
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    • 2005
  • The purpose of this study is to examine the characteristics of visual representation used in problem solving process and examine the representation types the students used to successfully solve the problem and focus on systematizing the visual representation method using the condition students suggest in the problems. To achieve the goal of this study, following questions have been raised. (1) what characteristic does the representation the elementary school students used in the process of solving a math problem possess? (2) what types of representation did students use in order to successfully solve elementary math problem? 240 4th graders attending J Elementary School located in Seoul participated in this study. Qualitative methodology was used for data analysis, and the analysis suggested representation method the students use in problem solving process and then suggested the representation that can successfully solve five different problems. The results of the study as follow. First, the students are not familiar with representing with various methods in the problem solving process. Students tend to solve the problem using equations rather than drawing a diagram when they can not find a word that gives a hint to draw a diagram. The method students used to restate the problem was mostly rewriting the problem, and they could not utilize a table that is essential in solving the problem. Thus, various errors were found. Students did not simplify the complicated problem to find the pattern to solve the problem. Second, the image and strategy created as the problem was read and the affected greatly in solving the problem. The first image created as the problem was read made students to draw different diagram and make them choose different strategies. The study showed the importance of first image by most of the students who do not pass the trial and error step and use the strategy they chose first. Third, the students who successfully solved the problems do not solely depend on the equation but put them in the form which information are decoded. They do not write difficult equation that they can not solve, but put them into a simplified equation that know to solve the problem. On fraction problems, they draw a diagram to solve the problem without calculation, Fourth, the students who. successfully solved the problem drew clear diagram that can be understood with intuition. By representing visually, unnecessary information were omitted and used simple image were drawn using symbol or lines, and to clarify the relationship between the information, numeric explanation was added. In addition, they restricted use of complicated motion line and dividing line, proper noun in the word problems were not changed into abbreviation or symbols to clearly restate the problem. Adding additional information was useful source in solving the problem.

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