• Title/Summary/Keyword: exponential function

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Mechanical and Operational Factors Affecting the Efficiency of Rice Polishing Machines (정미기의 능률에 미치는 기계적 요인및 작동조건에 관한 연구)

  • 노상하;최재갑
    • Journal of Biosystems Engineering
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    • v.1 no.1
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    • pp.17-48
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    • 1976
  • In analyzing the operational characteristics of a rice whitening machine, the internal radial pressure of the machine was measured using strain gage equipment. Changes in cylinder and feed screw configurations, screen type, cylinder speed and counter-pressure levels were examined to determine their impact on the quality and quantity of milled rice and the performance of the machine. The results are summarized as follows: 1. The internal radial pressure in the whitening chamber varied with the surface condition of the grain being processed. During the first or second pass through the machine, pressure was relatively low, reached a maximum after two to three passes with combinations I and II, three to six with combination III and then began to fall. 2. The pitch of the feed screw and the size of the feed gate opening which determine the rate of entry of grain into the whitening chamber, appeared to be the most important factor aff-::cting the degree of radial pressure, quality and quantity of milled rice and the efficiency of the machine. Using a feed screw with a wide pitch (4.8cm), radial pressure was relatively high and head rice recovery ratio \vere quite low. In this case capacity and machine effic\ulcorneriency were much higher than obtained when using a feed screw with a narrow pitch (2.3cm). Very significant responses in radial pressure, head rice recovery rates and machine capacity were observed with changes in cylinder speed and counter-pressure levels when using the wide pitch feed screw. 3. The characteristics of the screen which surrounds the whitening chamber had an important effect on whitening efficiency. The existence of small protuberances on the original screen resulted in significant increases in both machine capacity and efficiency but without a significant decrease in head rice recovery or development of excessive radial pressure. Further work is required to determine the effects of screen surface conditions and the shape of the cylinderical steel roller on the rate of bran removal, machine efficiency and recovery rates. The size of the slotted perforations 0:1 the screen affects total milled rice recovery. The opening size on the original screen was fabricated to accommodate the round shape of Japonica rice varieties but was not suitable for the more slender Indica type. Milling Indica varieties with this screen resulted in a reduction in total milled rice recovery. 4. An increase in cylinder speed from 380 to 820 rpm produced a positive effect on head rice recovery for all machine combinations at every level of counter-pressure used in the tests. Head rice recovery was considerably lower at 380rpm using a wide screw pitch when compared to the results obtained at speeds from 600 to 820 r.p.m. The effects of cylinder speed On radial pressure, capacity and machine efficiency showed contrasting results, depending on the width of the feed screw pitch. With a narrow feed screw pitch (2.3cm), a direct proportional relationship was observed bet\ulcornerween cylinder speed and both radial pressure and machine efficiency. In contrast, using a 4.8 centimeter pitch feed roller produced a series of inverse relationships between the above variables. Based on the results of this study it is recommended when milling Indica type long grain rice varieties that the cylinder speed of the original machine be increased from 500-600 rmp up to a minimum of 800 rpm to obtain a greater abrasive effect between the grain and the screen. The pitch of the feed screw should be also reduced to decr\ulcornerease the level of internal radial pressure and to obtain higher machine efficiency and increased quality of milled rice with increased cylinder speeds. Further study on the interaction between cylinder speed and feed screw pitch is recommended. 5. An increase in the counter pressure level produced a negative effect On the head rice recovery with an increase in radial pressure, capacity, and machine efficiency over all combinations and at every level of cylinder speed. 6. Head rice recovery rates were conditioned primarily by the pressure inside the whitening chamber. According to the empirical cha racteristics curve developed in this study, the relationships of head rice recovery ($Y_h$) and machine capacity ($Y_c$/TEX>) to internal radial pressure ($X_p$) followed an inverse quadratic function and a linear function respectively: $$Y_h^\Delta=\frac{1}{{1.4383-0.2951X_p^\ast+0.1425X_p^{\ast\ast}}^2} , (R^2=0.98)$$ $$Y_c^\Delta=-305.83+374.37X_p^{\ast\ast}, (R^2=0.88)$$ The correlation between capacity and power consumption per unit of brown rice expressed in the following exponential function: $$Y_c^\Delta=1.63Y_c^{-0.7786^\{\ast\ast}, (R^2=0.94)$$ These relationships indicate that when radial pressure increases above a certain range (1. 6 to 2.0 kg/$cm^2$ based On the results of the experiment) head ricerecovery decrea\ulcornerses in a quadratic relation with a inear increase in capacity but without any decrease in power consump tion per unit of brown rice. On the other hand, if radial pressure is below the range shown above, power consumption increases dramatically with a lin\ulcornerear decrease in capacity but without significant increases in head rice recovery. During the operation of a given whitening machine, the optimum radial pressure range or the correct capacity range should be selected by controlling the feed rate and/or counter-pressure keeping in mind the condition of the grain, particulary the hardness. It was observed that the total number of passes is related to radial pessure level, feed rate and counter-pressure level. The higher theradial pressure the fewer num\ulcornerber of pass required but with decreased head rice recovery. In particular, when using high feed rates, the total number of passes should be increased to more than three by reducing the counter-pressure level to avoid decreaseases in head rice recovery (less than 65 percent head rice recovery on the basis of brown rice) at every cylinder speed. 7. A rapid rise in grain temperature seemed to have a close relationship with the pressure generated inside the whitening chamber and, subsequently with head rice reco\ulcornervery rates. The higher the rate of increase, the lower were the resulting head rice recoveries.

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A Two-Stage Learning Method of CNN and K-means RGB Cluster for Sentiment Classification of Images (이미지 감성분류를 위한 CNN과 K-means RGB Cluster 이-단계 학습 방안)

  • Kim, Jeongtae;Park, Eunbi;Han, Kiwoong;Lee, Junghyun;Lee, Hong Joo
    • Journal of Intelligence and Information Systems
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    • v.27 no.3
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    • pp.139-156
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    • 2021
  • The biggest reason for using a deep learning model in image classification is that it is possible to consider the relationship between each region by extracting each region's features from the overall information of the image. However, the CNN model may not be suitable for emotional image data without the image's regional features. To solve the difficulty of classifying emotion images, many researchers each year propose a CNN-based architecture suitable for emotion images. Studies on the relationship between color and human emotion were also conducted, and results were derived that different emotions are induced according to color. In studies using deep learning, there have been studies that apply color information to image subtraction classification. The case where the image's color information is additionally used than the case where the classification model is trained with only the image improves the accuracy of classifying image emotions. This study proposes two ways to increase the accuracy by incorporating the result value after the model classifies an image's emotion. Both methods improve accuracy by modifying the result value based on statistics using the color of the picture. When performing the test by finding the two-color combinations most distributed for all training data, the two-color combinations most distributed for each test data image were found. The result values were corrected according to the color combination distribution. This method weights the result value obtained after the model classifies an image's emotion by creating an expression based on the log function and the exponential function. Emotion6, classified into six emotions, and Artphoto classified into eight categories were used for the image data. Densenet169, Mnasnet, Resnet101, Resnet152, and Vgg19 architectures were used for the CNN model, and the performance evaluation was compared before and after applying the two-stage learning to the CNN model. Inspired by color psychology, which deals with the relationship between colors and emotions, when creating a model that classifies an image's sentiment, we studied how to improve accuracy by modifying the result values based on color. Sixteen colors were used: red, orange, yellow, green, blue, indigo, purple, turquoise, pink, magenta, brown, gray, silver, gold, white, and black. It has meaning. Using Scikit-learn's Clustering, the seven colors that are primarily distributed in the image are checked. Then, the RGB coordinate values of the colors from the image are compared with the RGB coordinate values of the 16 colors presented in the above data. That is, it was converted to the closest color. Suppose three or more color combinations are selected. In that case, too many color combinations occur, resulting in a problem in which the distribution is scattered, so a situation fewer influences the result value. Therefore, to solve this problem, two-color combinations were found and weighted to the model. Before training, the most distributed color combinations were found for all training data images. The distribution of color combinations for each class was stored in a Python dictionary format to be used during testing. During the test, the two-color combinations that are most distributed for each test data image are found. After that, we checked how the color combinations were distributed in the training data and corrected the result. We devised several equations to weight the result value from the model based on the extracted color as described above. The data set was randomly divided by 80:20, and the model was verified using 20% of the data as a test set. After splitting the remaining 80% of the data into five divisions to perform 5-fold cross-validation, the model was trained five times using different verification datasets. Finally, the performance was checked using the test dataset that was previously separated. Adam was used as the activation function, and the learning rate was set to 0.01. The training was performed as much as 20 epochs, and if the validation loss value did not decrease during five epochs of learning, the experiment was stopped. Early tapping was set to load the model with the best validation loss value. The classification accuracy was better when the extracted information using color properties was used together than the case using only the CNN architecture.

Mathematical Models to Predict Staphylococcus aureus Growth on Processed Cheeses

  • Kim, Kyungmi;Lee, Heeyoung;Moon, Jinsan;Kim, Youngjo;Heo, Eunjeong;Park, Hyunjung;Yoon, Yohan
    • Journal of Food Hygiene and Safety
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    • v.28 no.3
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    • pp.217-221
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    • 2013
  • This study developed predictive models for the kinetic behavior of Staphylococcus aureus on processed cheeses. Mozzarella slice cheese and cheddar slice cheese were inoculated with 0.1 ml of a S. aureus strain mixture (ATCC13565, ATCC14458, ATCC23235, ATCC27664, and NCCP10826). The inoculated samples were then stored at $4^{\circ}C$ (1440 h), $15^{\circ}C$ (288 h), $25^{\circ}C$ (72 h), and $30^{\circ}C$ (48 h), and the growth of all bacteria and of S. aureus were enumerated on tryptic soy agar and mannitol salt agar, respectively. The Baranyi model was fitted to the growth data of S. aureus to calculate growth rate (${\mu}_{max}$; ${\log}CFU{\cdot}g^{-1}{\cdot}h^{-1}$), lag phase duration (LPD; h), lower asymptote (log CFU/g), and upper asymptote (log CFU/g). The growth parameters were further analyzed using the square root model as a function of temperature. The model performance was validated with observed data, and the root mean square error (RMSE) was calculated. At $4^{\circ}C$, S. aureus cell growth was not observed on either processed cheese, but S. aureus growth on the mozzarella and cheddar cheeses was observed at $15^{\circ}C$, $25^{\circ}C$, and $30^{\circ}C$. The ${\mu}_{max}$ values increased, but LPD values decreased as storage temperature increased. In addition, the developed models showed acceptable performance (RMSE = 0.3500-0.5344). This result indicates that the developed kinetic model should be useful in describing the growth pattern of S. aureus in processed cheeses.

Follow-up Study of Children with Anthracycline Cardiotoxicity (소아 Anthracycline 심독성의 추적 관찰)

  • Kwon, Hyok Joo;Song, Young Hwan;Kang, Soo Jung;Kang, Hyoung Jin;Choi, Hyoung Soo;Bae, Eun Jung;Shin, Hee Young;Noh, Chung Il;Yun, Yong Soo;Ahn, Hyo Seop
    • Clinical and Experimental Pediatrics
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    • v.46 no.3
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    • pp.242-249
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    • 2003
  • Purpose : We studied the relationship between anthracycline cumulative dose and anthracycline cardiotoxicity in childhood cancer and followed up 40 children with anthracycline cardiotoxicity. Methods : A retrospective study was performed in 154 children who received anthracycline chemotherapy between January 1995 to December 2000. Cardiotoxicity was defined when the left ventricular fractional shortening(FS) was below 26%; it was divided into two groups, mild and severe cardiotoxicity, according to the FS. We followed up survivors with cardiotoxicity, and checked their present cardiac function by physical activity, echocardiography, electrocardiography(EKG) and chest X-ray. Results : Of the 154 children treated with anthracyclines, forty(26.0%) were diagnosed as cardiotoxicity. The incidence of cardiotoxicity increased in exponential fashion with increases in the cumulative dose of anthracyclines. There was minimal increase of incidence until a dose of $300mg/m^2$ after which the incidence increased rapidly. After mean $3.8{\pm}1.8year$ follow-up of 23 survivors with cardiotoxicity, FS increased significantly. EKG and chest X-rays were not helpful for the diagnosis of cardiotoxicity because of their low sensitivity and specificity. Conclusion : Although convenient, non-invasive and inexpensive, EKG and chest X-rays were not helpful for the follow-up of anthracycline cardiotoxicity. Almost all survivors with anthracycline cardiotoxicity have improved in both physical activity and echocardiographic findings after discontinuation of anthracyclines.

The Expression of Oncogenes on the Radiation-induced Apoptosis in SCK Mammary Adenocarcinoma Cell Line (SCK 선암세포주에서 방사선 조사에 의해 유도되는 Apoptosis에 미치는 암유전자의 발현)

  • Lee Hyung Sik;Park Hong Kyu;Moon Chang Woo;Yoon Seon Min;Hur Won Joo;Jeong Su Jin;Jeong Min Ho;Lee Sang Hwa
    • Radiation Oncology Journal
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    • v.17 no.1
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    • pp.70-77
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    • 1999
  • Purpose : The expression of p53, P211WAF/CIP, Bcl-2, and Bax underlying the radiation-induced apoptosis in different pH environments using SCK mammary adenocarcinoma cell line was investigated. Materials and Methods Mammary adenocarcinoma cells of hi) mice (SCK cells) in exponential growth phase were irradiated with a linear accelerator at room temperature. The cells were irradiated with 12 Gy and one hour later, the media was replaced with fresh media at a different pHs. After Incubation at 37Microbioiogy, College of Medicine Dong A University for 0$\~$48 h, the extort of apoptosis was determined using agarose gel electrophoresis and flow cytometry. The progression of cells through the cell cycle after irradiation in different pHs was also determined with flow cytometry. Western blot analysis was used to monitor p53, p211WAFfCIP, Bcl-2, and Bu protein levels. Results : The induction of apoptosis by irradiation in pH 6.6 medium was markedly less than that in pH 7.5 medium. The radiation-induced G2IM arrest in pH 6.6 medium lasted markedly longer than that in pH 7.5 medium. Considerable amounts of p53 and p21 proteins already existed at pH 7.5 and increased the level of p53 and p21 significantly after 12 Gy X-irradiation. An incubation at pH 6.6 after 12 Gy X-irradiation did not change the level of p53 and p21 protein levels significantly. Bcl-2 proteins were not significantly affected by radiation and showed no correlation with cell susceptibility to radiation-induced apoptosis in different pHs. An exposure to 12 Gy of X-rays increased the level of Bax protein at pH 7.5 but at pH 6.6, it was slight. Conclusions : The molecular mechanism underlying radiation-induced apoptosis in dinerent pH environments using SCK mammary adenocarcinoma cell line was dependent of the expression p53 and P211YVAF/CIP proteins. We may propose following hypothesis that an acidic stress augments the radiation-induced G2iM arrest, which inhibiting the irradiated cells undergo post-mitotic apoptosis. The effects of environmental acidity on anti-apoptotic and pro-apoptotic function of Bcl-2 family was unclear in SCK mammary adenocarcinoma cell line.

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Weathering Sensitivity Characterization for Rock Slope, Considering Time Dependent Strength Changes (시간에 따른 강도변화를 고려한 암반사면의 풍화민감특성 분석)

  • Lee Jeong-Sang;Bae Seong-Ho;Yu Yeong-Il;Oh Joung-Bae;Lee Du-Hwa;Park Joon-Young
    • Tunnel and Underground Space
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    • v.16 no.2 s.61
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    • pp.109-134
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    • 2006
  • Rocks undergo weathering processes influenced by changing in pressure-temperature condition, atmosphere, underground water, and rainfall. The weathering processes change physical and chemical characteristics of the rocks. Once the rocks are weathered, the characteristics of them are changed and, because of the changing, several disadvantages such as rock slope failures and underground water spouts are can occur. Before we cut a large rock slope, therefore, we must analyze current weathering conditions of rocks and predict weathering processes in the future. Through the results of such analyses, we can judge reinforcement works. In order to comply with such requests, chemical weathering sensitivity analysis which was analyzed from chemical weathering velocities and other characteristics of rocks has been applied in several prior construction works in Korea. But, It is defective to use directly in engineering fields because it was developed for soils(not rocks), it has too mny factors must be considered and the relationships between the factors are not clear, and it is hard to explain the weathering processes in engineering time range. Besides above, because it has been used for isotropic rocks, this method is hard to apply to anisotropic rocks such as sedimentary rocks. Acceding to studies from morphologists (e.g. Oguchi et al., 1994; Sunamura, 1996; Norwick and Dexter, 2002), time dependent strength reduction influenced by weathering shows a negative exponential function form. Appling this relation, one can synthesize the factors which influence the weathering processes to the strength reduction, and get meaningful estimates in engineering viewpoint. We suggest this weathering sensitivity characterization method as a technique that can explain time dependent weathering sensitivity characteristics through strength changes and can directly applied the rock slope design.

Estimation of Groundwater Recharge by Considering Runoff Process and Groundwater Level Variation in Watershed (유역 유출과정과 지하수위 변동을 고려한 분포형 지하수 함양량 산정방안)

  • Chung, Il-Moon;Kim, Nam-Won;Lee, Jeong-Woo
    • Journal of Soil and Groundwater Environment
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    • v.12 no.5
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    • pp.19-32
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    • 2007
  • In Korea, there have been various methods of estimating groundwater recharge which generally can be subdivided into three types: baseflow separation method by means of groundwater recession curve, water budget analysis based on lumped conceptual model in watershed, and water table fluctuation method (WTF) by using the data from groundwater monitoring wells. However, groundwater recharge rate shows the spatial-temporal variability due to climatic condition, land use and hydrogeological heterogeneity, so these methods have various limits to deal with these characteristics. To overcome these limitations, we present a new method of estimating recharge based on water balance components from the SWAT-MODFLOW which is an integrated surface-ground water model. Groundwater levels in the interest area close to the stream have dynamics similar to stream flow, whereas levels further upslope respond to precipitation with a delay. As these behaviours are related to the physical process of recharge, it is needed to account for the time delay in aquifer recharge once the water exits the soil profile to represent these features. In SWAT, a single linear reservoir storage module with an exponential decay weighting function is used to compute the recharge from soil to aquifer on a given day. However, this module has some limitations expressing recharge variation when the delay time is too long and transient recharge trend does not match to the groundwater table time series, the multi-reservoir storage routing module which represents more realistic time delay through vadose zone is newly suggested in this study. In this module, the parameter related to the delay time should be optimized by checking the correlation between simulated recharge and observed groundwater levels. The final step of this procedure is to compare simulated groundwater table with observed one as well as to compare simulated watershed runoff with observed one. This method is applied to Mihocheon watershed in Korea for the purpose of testing the procedure of proper estimation of spatio-temporal groundwater recharge distribution. As the newly suggested method of estimating recharge has the advantages of effectiveness of watershed model as well as the accuracy of WTF method, the estimated daily recharge rate would be an advanced quantity reflecting the heterogeneity of hydrogeology, climatic condition, land use as well as physical behaviour of water in soil layers and aquifers.

Analysis of Heterogeneous Tree-Ring Growths of Pinus densiflora with Various Topographical Characteristics in Mt. Worak Using GIS (GIS 기법을 이용한 지형적 특성에 따른 월악산 소나무 연륜생장의 이질성 규명)

  • 서정욱;김재수;박원규
    • The Korean Journal of Ecology
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    • v.23 no.1
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    • pp.25-32
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    • 2000
  • To analyze the relationship between climatic factors (monthly temperatures and precipitations) and the radial growths or Pinus densiflora with different topographical settings in Worak National Park, Korea, 20 stands were chosen and 10 trees were selected from each stand. After crossdating, each ring-width series was double detrended (standardized) by fitting first a negative exponential or straight regression line and secondly a 60-year cubic spline. The growth patterns coud be categorized by four groups using cluster analysis. Cluster Ⅰ stand has north aspect, but others have south or southwest aspects. Cluster Ⅰ (one), cluster Ⅱ (ten), and cluster Ⅲ (two) stands are located in lower. elevation (305∼580 m), however, cluster Ⅳ (seven) stands are located in higher elevation, mostly in 560~870 m. Cluster Ⅱ and Ⅲ stands are located at similar elevation with the same aspect, however, cluster Ⅱ stands are located on more rocky and stiff slope with shallow soil depth. The response functions were used to examine the difference in the relationships between climatic factors and tree growths among the 4 cluster chronologies. The climatic factors are not limiting the growth in the cluster Ⅰ stand as highly as in other cluster plots because of rather mesic conditions in the north slope. The precipitation in the spring appears to be the main limiting factor in the cluster Ⅱ stands. The topographical characteristics of the sites of cluster Ⅱ, shallow soil depths on the rocky slope in the south aspect at lower elevation, may enhance the sensitivity of growth to moisture stress. In cluster Ⅲ and cluster Ⅳ, winter and spring temperature prior to the growth become more important than for cluster Ⅱ. This pattern is com-mon for Pinus densiflora trees growing in higher. elevation (equation omitted 800 m) in South Korea. It nay be re-lated with preconditioning effects of temperature as the temperature decreases with increasing elevation (cluster Ⅳ) or in the valley (cluster Ⅲ). The results obtained by tree-ring analysis were digitalized by GIS and spatio-temporal information on tree-ring data and topographic setting were analyzed and displayed simultaneously. The results of this study can be used to predict the future change of Pinus densiflora ecosystem to climate change expected in central Korea.

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Population Ecological Study of Cultured Sea Squirt (Halocynthia roretzi) and Management Implications (양식 우렁쉥이(Halocynthia roretzi)의 자원 생태학적 분석 및 적정관리 방안)

  • Zhang Chang Ik;Lim Hyun Sig
    • Journal of Aquaculture
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    • v.3 no.1
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    • pp.49-63
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    • 1990
  • A population ecological study was carried out to estimate survival and growth rates, biomass, biological production and turnover ratio of cultured sea squirt, Halocynthia roretzi, by growth stages, using data from in situ culture experiment off Hansando in the southern part of Korea from February 1985 to July 1986. The squirt population followed an exponential decay function and the instantaneous coefficient of total mortality (Z) was estimated to be 0.0614 $month^{-1}$(Var (Z) = 0.000126). Growths in total weight and meat weight of squirts were expressed as linear functions during the period of culture experiment. The growth of squirts showed a negative correlation with the water temperature. The mean biomass per string ranged from 2.14 kg for March of the first year to 16.26 kg for March of the next year. The biological production per string was estimated to range from 3.28 kg for the first summer (June - July) to 6.46kg for the first late winter (February-March). The peak of turnover ratio occurred in the late winter (February-March) as 3.013 and the ratios sharply declined thereafter. Based on the results of this study, management implications for culturing sea squirts were also suggested. The optimum harvest time ($t_{mb}$) when the peak biomass in terms of total weight occurred was estimated to be late June of the second year, which corresponded to 16.7 months after the main hanging. However, the time when the peak biomass in terms of meat weight was occurred was early July of the second year. The maximum harvest biomass was 17.4 kg per string in terms of total weight and 6.3 kg per string in terms of meat weight. In conclusion, the process of culture should be conducted on the basis of the knowledge of population ecological theories as shown in this study.

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Changes of Heart Rate During Marathon Running (장거리 (마라톤)선수에서의 전 경기중 심박동수의 변화)

  • Kim, In-Kyo;Lee, Jung-Woo;Hah, Jong-Sik;Ryu, Yun-Hee;Choi, Jung-Ok;Kim, Ki-Ho
    • The Korean Journal of Physiology
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    • v.13 no.1_2
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    • pp.1-12
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    • 1979
  • To evaluate the present status of physical fittness of Korean long distance runners, body fat, pulmonary functions, maximal oxygen intake and oxygen debt were measured in 5 elite marathoners (A group), 6 college student runners (B group) and 3 middle school student runners (C group). After laboratory tests, full course marathon running was performed in 2 elite marathoners during which their heart rates were monitored continuously. The results are summerized as follows: 1) Total body fat in all three groups are in the range of 13-15% of their body weight. 2) In all three groups, average values of various pulmonary functions were within the normal limits, but those of tidal volume were higher and respiratory rate were lower in comparison to normal values. These phenomena may represent respiratory adaptations against training. The average resting oxygen consumptions in A,B and C were $322{\pm}23$, $278{\pm}14$ and $287{\pm}16$m1/min, respectively. 3) In all three groups, resting blood pressures were in the normal range, but the resting heart rate was slightly lower in groups A $(56{\pm}3\;beats/min)$ and B $(64{\pm}2\;beats/min)$ and higher in group C $(82{\pm}9\;beats/min)$ in comparison to normal values. These changes in cardiovascular functions in marathoners may also represent adaptive phenomena. 4) During treadmill running the minute ventilation and oxygen consumption of the runners increased lineally with work load in all three groups. When the oxygen consumption was related to heart rate, it appeared to be a exponential function of the heart rate in all three groups. 5) The average maximal heart rates during maximal work were $196{\pm}3$, $191{\pm}3$ and $196{\pm}5\;beats/min$ for groups A,B and C, respectively. Maximal oxygen intakes were $84.2{\pm}3.3\;ml/min/kg$ in group A, $65.2{\pm}1.1\;ml/min/kg$ in group B and $58.7{\pm}0.4\;ml/min/kg$ in group C. 6) In all three groups, oxygen debts and the rates of recovery of heart rate after treadmill running were lower than those of long ditsance runners reported previously. 7) The 40 km running time in 2 elite marathoners was recorded to be $2^{\circ}42'25'$, and their mean speed was 243 m/min (ranged 218 to 274 m/min). The heart rate appeared to increase lineally with running speed, and the total energy expenditure during 40 km running was approximately 1360.2 Calories. From these it can be speculated that if their heart rates were maintained at 166 beats/min during the full course of marathon running, their records would be arround $2^{\circ}15'$. Based on these results, we may suspect that a successful long distance running is, in part, dependent on the economical utilization of one's aerobic capacity.

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