• Journal of the Korean Society of Food Science and Nutrition
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• v.42 no.5
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• pp.832-836
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• 2013

To develop a predictive model for the shelf-life of fish cake, fish cake was stored at 30, 35, or $40^{\circ}C$ and populations of total aerobic bacteria were determined during storage. Gompertz model parameters were determined and their dependence on temperature formulated as a quadratic equation for applications toward shelf-life prediction. The predicted shelf-life values for fish cake used in this study were 6.9, 5.5, and 3.8 days at 0, 4, and $10^{\circ}C$, respectively. The shelf-life prediction equation was appropriate based on statistical analyses that reveal accuracy and bias factors. These results suggest that our prediction model is applicable for estimating the shelf-life of fish cake.

• Food Science and Biotechnology
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• v.16 no.2
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• pp.238-242
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• 2007

Square root models were developed for predicting the kinetics of growth of Listeria monocytogenes in sesame leaves as a function of temperature (4, 10, or $25^{\circ}C$). At these storage temperatures, the primary growth curves fit well ($R^2=0.898$ to 0.980) to a Gompertz equation to obtain lag time (LT) and specific growth rate (SGR). The square root models for natural logarithm transformations of the LT and SGR as a function of temperature were obtained by SAS's regression analysis. As storage temperature ($4-25^{\circ}C$) decreased, LT increased and SGR decreased, respectively. Square root models were identified as appropriate secondary models for LT and SGR on the basis of most statistical indices such as coefficient determination ($R^2=0.961$ for LT, 0.988 for SGR), mean square error (MSE=0.l97 for LT, 0.005 for SGR), and accuracy factor ($A_f=1.356$ for LT, 1.251 for SGR) although the model for LT was partially not appropriate as a secondary model due to the high value of bias factor ($B_f=1.572$). In general, our secondary model supported predictions of the effects of temperature on both LT and SGR for L. monocytogenes in sesame leaves.

• Journal of Korean Society of Forest Science
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• v.94 no.2 s.159
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• pp.121-126
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• 2005

This study was carried out to construct a single diameter and a single height model that could localize Chamaecyparis obtusa stand grown in 3 Southern regions of Korea. Dummy variables, which convert qualitative information such as geographical regions into quantitative information by means of a coding scheme (0 or 1), were used to localize growth models. In results, modified form of Gompertz equation, $Y_2={\exp}({\ln}(Y_1){\exp}(-{\beta}(T_2-T_1)+{\gamma}({T_2}^2-{T_1}^2))+({\alpha}+{\alpha}_1Al+{\beta}_1k_1+{\beta}_2k_2)(1-{\exp}(-{\beta}(T_2-T_1)+{\gamma}({T_2}^2-{T_1}^2))$, for diameter and height was successfully disaggregated to provide different projection equation for each of the 3 regions individually. The use of dummy variables on a single equation, therefore, provides potential capabilities for testing the justification of having different models for different sub-populations, where a number of site variables such as altitude, annual rainfall and soil type can be considered as possible variables to explain growth variation across regions.

• Journal of Microbiology and Biotechnology
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• v.18 no.6
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• pp.1130-1135
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• 2008

The effect of pH on anaerobic hydrogen production was investigated under various pH conditions ranging from pH 3 to 10. When the modified Gompertz equation was applied to the statistical analysis of the experimental data, the hydrogen production potential and specific hydrogen production rate at pH 5 were 1,182 ml and 112.5 ml/g biomass-h, respectively. In this experiment, the maximum theoretical hydrogen conversion ratio was 22.56%. The Haldane equation model was used to find the optimum pH for hydrogen production and the maximum specific hydrogen production rate. The optimum pH predicted by this model is 5.5 and the maximum specific hydrogen production rate is 119.6 ml/g VSS-h. These data fit well with the experimented data($r^2=0.98$).

• Journal of the Korean Society of Food Science and Nutrition
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• v.42 no.9
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• pp.1518-1523
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• 2013

To estimate the shelf life of red cabbage sprouts (stored at 4 and $10^{\circ}C$), the numbers of total aerobic bacteria were determined during storage. Parameters for the Gompertz model were determined and the shelf life was predicted using a modified Gompertz equation. The estimated shelf lives of red cabbage sprouts packed with polyolefin film and polyamide/polyamide/polyethylene (PA/PA/PE) film at $4^{\circ}C$ were 49.4 and 52.3 h, respectively, whereas those of red cabbage sprouts packed with polyolefin film and PA/PA/PE film at $10^{\circ}C$ were 19.7 and 22.6, respectively. The shelf life prediction equation was appropriate, based on the statistical analysis of the accuracy factor, bias factor, and mean square error. On the other hand, for red cabbage sprouts treated with aqueous $ClO_2$/fumaric acid and UV-C then packed with polyolefin film or PA/PA/PE film, the shelf life was predicted to be longer than 168 h. These results suggest that the combined treatment of aqueous $ClO_2$/fumaric acid and UV-C can be useful for improving microbial safety and extending the shelf life of red cabbage sprouts during storage.

• Journal of Food Hygiene and Safety
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• v.34 no.4
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• pp.374-379
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• 2019

This study developed predictive growth models of Salmonella enterica Serovar Typhimurium on lettuce washed with chlorine (100~300 ppm) and ultrasound (US, 37 kHz, 380 W) treatment and stored at different temperatures ($10{\sim}25^{\circ}C$) using a polynomial equation. The primary model of specific growth rate (SGR) and lag time (LT) showed a good fit ($R^2{\geq}0.92$) with a Gompertz equation. A secondary model was obtained using a quadratic polynomial equation. The appropriateness of the secondary SGR and LT model was verified by coefficient of determination ($R^2=0.98{\sim}0.99$ for internal validation, 0.97~0.98 for external validation), mean square error (MSE=-0.0071~0.0057 for internal validation, -0.0118~0.0176 for external validation), bias factor ($B_f=0.9918{\sim}1.0066$ for internal validation, 0.9865~1.0205 for external validation), and accuracy factor ($A_f=0.9935{\sim}1.0082$ for internal validation, 0.9799~1.0137 for external validation). The newly developed models for S. Typhimurium could be incorporated into a tertiary modeling program to predict the growth of S. Typhimurium as a function of combined chlorine and US during the storage. These new models may also be useful to predict potential S. Typhimurium growth on lettuce, which is important for food safety purposes during the overall supply chain of lettuce from farm to table. Finally, the models may offer reliable and useful information of growth kinetics for the quantification microbial risk assessment of S. Typhimurium on washed lettuce.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.53 no.5
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• pp.699-706
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• 2020

Predictive models in food microbiology are used for predicting microbial growth or death rates using mathematical and statistical tools considering the intrinsic and extrinsic factors of food. This study developed predictive growth models for Bacillus cereus on dried laver Pyropia pseudolinearis stored at different temperatures (5, 10, 15, 20, and 25℃). Primary models developed for specific growth rate (SGR), lag time (LT), and maximum population density (MPD) indicated a good fit (R²≥0.98) with the Gompertz equation. The SGR values were 0.03, 0.08, and 0.12, and the LT values were 12.64, 4.01, and 2.17 h, at the storage temperatures of 15, 20, and 25℃, respectively. Secondary models for the same parameters were determined via nonlinear regression as follows: SGR=0.0228-0.0069*T₁+0.0005*T₁²; LT=113.0685-9.6256*T₁+0.2079*T₁²; MPD=1.6630+0.4284*T₁-0.0080*T₁² (where T₁ is the storage temperature). The appropriateness of the secondary models was validated using statistical indices, such as mean squared error (MSE<0.01), bias factor (0.99≤B_f≤1.07), and accuracy factor (1.01≤A_f≤1.14). External validation was performed at three random temperatures, and the results were consistent with each other. Thus, these models may be useful for predicting the growth of B. cereus on dried laver.

• Korean Journal of Agricultural Science
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• v.44 no.3
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• pp.384-391
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• 2017

Growth curves in Hanwoo steers were estimated by Gompertz, Von Bertalanffy, Logistic, and Brody nonlinear models using growth data collected by the Hanwoo Improvement Center from a total of 6,973 Hanwoo (Bos taurus coreanae) steers 6 to 24 months old that were born between 1996 and 2015. The data included three parameters: A, mature size of body measurement; b, growth ratio; and, k, intrinsic growth rate. Nonlinear regression equations for wither height according to Gompertz, Von Bertalanffy, Logistic, and Brody models were $Y_t=144.7e^{-0.5869e^{-0.00301t}}$, $Y_t=145.3(1-0.1816e^{-0.00284t})^3$, $Y_t=143.1(1+0.7356e^{-0.00352t})^{-1}$, and $Y_t=146.8(1+0.4700e^{-0.00249t})^1$, respectively, while those for hip height were $Y_t=144.5e^{-0.5549e^{-0.00312t}}$, $Y_t=145.0(1-0.1724e^{-0.00295t})^3$, $Y_t=143.1(1+0.6863e^{-0.00360t})^{-1}$, and $Y_t=146.2(1+0.4501e^{-0.00263t})^1$, respectively. Equations for body length $Y_t=174.1e^{-0.8342e^{-0.00289t}}$, $Y_t=175.8(1-0.2500e^{-0.00265t})^3$, $Y_t=170.0(1+1.1548e^{-0.00363t})^{-1}$, and $Y_t=180.3(1+0.6077e^{-0.00215t})^1$, respectively, for the same models. Among the four models, the Brody model resulted in the lowest mean square error, with mean square errors of 31.79, 30.57, and 42.13, respectively, for wither height, hip height, and body length. Also, an estimated birth wither height, birth hip height, and birth body length (77.98, 80.57, and 70.97 cm, respectively) were lower in the Brody model than in other models. An inflection point was not observed during the growth phase of Hanwoo steer according to the growth curves calculated using Gompertz, Von Bertalanffy, and Logistic models. Based on the results, we concluded that the regression equation using the Brody model was the most appropriate among the four growth models. To obtain more accurate parameters, however, using data from a wider production period (from birth to shipping) would be required, and the development of a suitable model for body conformation traits would be needed.

• Journal of Korean Society of Forest Science
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• v.108 no.3
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• pp.364-371
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• 2019

This study was conducted to provide the basic information for a reasonable forest management plan and sustainable forest management by developing a dominant tree height growth model using diameter at breast height (DBH) and site index curves for Pinus densiflora and Chamaecyparis obtusa growing in Jeolla-do. The altitude, slope, orientation, soil type, height and DBH of a dominant tree, and the ages of trees were measured for 3055 Pinus densiflora trees (611 plots) and 3345 Chamaecyparis obtusa trees (699 plots), and these data were used to develop a customized afforestation map. In the dominant tree height growth model, the relationship to DBH was used in the Petterson, Michailow, and log equations. Also, a dominant tree height growth model in relationship to age used the Chapman-Richards, Schumacher, and Gompertz equations. The Petterson equation, which has a lower mean square error, was used to model dominant tree height growth in relationship to DBH. In the model of dominant tree height growth in relationship to age, three kinds of equations were considered to have little statistical difference. Therefore, the Chapman-Richards equation was chosen for modeling on the national level. Thirtyyears was used as the base age, which is an important factor for estimating the site index curves. In the results, a more varied range of site index family curves with 6-18 was developed for Pinus densiflora, and with 6-22 for Chamaecyparis obtusa. As the new site index curves indicated influences on growth of Pinus densiflora and Chamaecyparis obtusa, a reasonable forest management plan will be possible in the future for Jeolla-do.

• Environmental Engineering Research
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• v.24 no.1
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• pp.38-44
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• 2019

The Biochemical Methane Potential (BMP) of fresh leachate and domestic wastewaters codigestion was determined by laboratory Bach Tests at $35^{\circ}C$ over a period of 90 d using a wide range of leachates volumetric ratios from 0% to 100%. To simulate wastewaters plant treatment step, all the ratios were first air stripped for 48 h before anaerobic incubation. The kinetic of biogas production was assessed using modified Gompertz model and exponential equation. The results obtained showed that cumulative biogas production was insignificant in the case of wastewaters monodigestion while the codigestion significantly improves the BMP. Air stripping pretreatment had positive effect on both ammonium concentration and volatiles fatty acids with reduction up to 75% and 42%, respectively. According to the Modified Gompertz model, the optimal anaerobic co-digestion conditions both in terms of maximal biogas potential, start-up period and maximum daily biogas production rate, could be achieved within large leachate volumetric ratios from 25% to 75% with a maximum BMP value of 438.42 mL/g volatile solid at 50% leachate ratio. The positive effect of codigestion was attributed to a dilution effect of chemical oxygen demand and volatile fatty acid concentrations to optimal range that was between 11.7 to $32.3gO_2/L$ and 2.1 to 7.4 g/L, respectively. These results suggested that the treatment of fresh leachate by their dilution and co digestion at wastewaters treatment plants could be a promising alternative for both energetic and treatment purposes.