• Journal of Food Hygiene and Safety
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• v.26 no.1
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• pp.25-30
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• 2011

In this study, predictive mathematical models were developed to predict the kinetics of Listeria monocytogenes growth in the mixed fresh-cut vegetables, which is the most popular ready-to-eat food in the world, as a function of temperature (4, 10, 20 and $30^{\circ}C$). At the specified storage temperatures, the primary growth curve fit well ($r^2$=0.916~0.981) with a Gompertz and Baranyi equation to determine the specific growth rate (SGR). The Polynomial model for natural logarithm transformation of the SGR as a function of temperature was obtained by nonlinear regression (Prism, version 4.0, GraphPad Software). As the storage temperature decreased from $30^{\circ}C$ to $4^{\circ}C$, the SGR decreased, respectively. Polynomial model was identified as appropriate secondary model for SGR on the basis of most statistical indices such as mean square error (MSE=0.002718 by Gompertz, 0.055186 by Baranyi), bias factor (Bf=1.050084 by Gompertz, 1.931472 by Baranyi) and accuracy factor (Af=1.160767 by Gompertz, 2.137181 by Baranyi). Results indicate L. monocytogenes growth was affected by temperature mainly, and equation was developed by Gompertz model (-0.1606+$0.0574^*Temp$+$0.0009^*Temp^*Temp$) was more effective than equation was developed by Baranyi model (0.3502-$0.0496^*Temp$+$0.0022^*Temp^*Temp$) for specific growth rate prediction of L.monocytogenes in the mixed fresh-cut vegetables.

• Korean Journal of Soil Science and Fertilizer
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• v.43 no.3
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• pp.356-362
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• 2010

This research studied the bio-methane potential of several waste biomass materials as alternative sources for biogas production, and the laboratory procedure for measuring the biochemical methane potential was described. The wastes from four agro-industries (sewage, livestock, food wastewater treatment sludge and cattle rumen substance generating in slaughter house) were evaluated as substrates for the assay of biochemical methane potential. In order to estimate the ultimate methane yield, two empirical equations (modified Gompertz equation and exponential equation) was investigated. The ultimate methane yield of sewage, livestock, food sludge and lumen substance estimated by the modified Gompertz equation were 0.086, 0.147, 0.146, and 0.121 L $CH_{4}\;g^{-1}\;VS_{added}$, respectively. The ultimate methane yield estimated by the exponential equation were 0.109, 0.246 and 0.174 L $CH_{4}\;g^{-1}\;VS_{added}$ in sewage, livestock sludge and lumen substance. And the ultimate methane yield estimated by the exponential equation showed more high values in the range of 26.7 ~67.3% than the ultimate methane yield estimated by the modified Gompertz equation.

• Proceedings of the Korean Institute of Building Construction Conference
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• 2023.11a
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• pp.149-150
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• 2023

This study proposes the most suitable strength prediction model equation for UHPC by calculating the apparent activation energy of UHPC according to the curing temperature and deriving the integrated temperature and compressive strength prediction equation. The results are summarized as follows. The apparent activation energy was calculated using the Arrhenius function, which was calculated as 21.09 KJ/mol. A model equation suitable for UHPC was calculated, and when the Flowman model equation was used, it was confirmed that it was suitable for the properties of UHPC using a condensation promoting super plasticizing agent.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.521-528
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• 2014

A stochastic Gompertz diffusion model for tumor growth is a topic of active interest as cancer is a leading cause of death in Korea. The direct maximum likelihood estimation of stochastic differential equations would be possible based on the continuous path likelihood on condition that a continuous sample path of the process is recorded over the interval. This likelihood is useful in providing a basis for the so-called continuous record or infill likelihood function and infill asymptotic. In practice, we do not have fully continuous data except a few special cases. As a result, the exact ML method is not applicable. In this paper we proposed a method of parameter estimation of stochastic Gompertz differential equation via Markov chain Monte Carlo methods that is applicable for several data structures. We compared a Markov transition data structure with a data structure that have an initial point.

• Journal of Forest and Environmental Science
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• v.8 no.1
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• pp.35-49
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• 1992

Three theoretical growth equations, i.e., the Mitscherlich, the Gompertz, and the Logistic equation, were applied to the radical stem growth of 50 jack pines (Pinus banksiana Lamb.). For the determination of the parameters in these equations, NELDER-MEAD's method was used, which is one of the direct-search methods of optimization. It has been known to be very convenient in dealing with the issues related to optimization, specifically where the number of parameters are less than 6. It was found that although all the equations did not appropriately work as expected, the Mitscherlich equation revealed the least discrapancy from the obsered value among three. Using these equations and the first certain period data, i. e., 35, 55, 75 years, the predection of radius of age 95 was investigated. Comparing to the observed value, the most valid equation was the Mitscherlich, and the next were the Gompertz and the Logistic, in order.

• Korean Journal of Food Science and Technology
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• v.37 no.5
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• pp.850-855
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• 2005

Model was developed to predict the growth of Listeria monocytogenes in raw pork. Experiment condition for model development was full 5-by-7 factorial arrangements of temperature (0, 5, 10, 15, and $20^{\circ}C$) and time (0, 1, 2, 3, 18, 48, and 120 hr). Gompertz values A, C, B, and M, and growth kinetics, exponential growth rate (EGR), generation time (GT), lag phase duration (LPD), and maximum population density (MPD) were calculated based on growth increased data. GT and LPD values gradually decreased, whereas EGR value gradually increased with increasing temperature. Response surface analysis (RSA) was carried out using Gompertz B and M values, to formulate equation with temperature being main control factor. This equation was applied to Gompertz equation. Experimental and predictive values for GT, LPD, and EGR, compared using the model, showed no significant differences (p<0.01). Proposed model could be used to predict growth of microorganisms for exposure assessment of MRA, thereby allowing more informed decision-making on potential regulatory actions of microorganisms in raw pork.

• Biotechnology and Bioprocess Engineering:BBE
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• v.11 no.3
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• pp.223-229
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• 2006

In this study, we have conducted kinetics and modelling studies of Centella asiatica cell growth and substrate uptake, in an attempt to evaluate cell growth for a better understanding and control of the process. In our bioreactor cultivation experiment, we observed a growth rate of 0.18/day, a value only 20% higher than was seen in the shake flask cultivation trial. However, the observed maximum cell dry weight in the shake flask, 10.5g/L, was 14% higher than was achieved in the bioreactor. Ninety seven percentage confidence was achieved via the fitting of three unstructured growth models; the Monod, Logistic, and Gompertz equations, to the cell growth data. The Monod equation adequately described cell growth in both cultures. The specific growth rate, however, was not effectively predicted with the Logistic and Gompertz equations, which resulted in deviations of up to 73 and 393%, respectively. These deviations in the Logistic and Gompertz models may be attributable to the fact that these models were developed for substrate-independent growth and fungi growth, respectively.

• Korean Journal of Agricultural Science
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• v.43 no.4
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• pp.623-633
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• 2016

A total of 6,973 steer growth records of Hanwoo breeding bull's progeny test data collected from 1989 to 2015 were analyzed to identify the most appropriate growth curve among three growth curve models (Gompertz, Logistic and von Bertalanffy). The Gompertz growth curve model equation was $W_t=990.5e^{{-2.7479e}^{-0.00241t}}$, the Logistic growth curve model equation was $W_t=772(1+8.3314e^{-0.00475t})^{-1}$, and the von Bertalanffy growth curve model equation was $W_t=1,196.4(1-0.646e^{-0.00162t})^3$. The Gompertz model parameters A, b, and k were estimated to be $990.5{\pm}10.27$, $2.7479{\pm}0.0068$, and $0.00241{\pm}0.000028$, respectively. The inflection point age was estimated to be 421 days and the weight of inflection point was 365.3 kg. The Logistic model parameters A, b, and k were estimated to be $772.0{\pm}4.12$, $8.3314{\pm}0.0453$, and $0.00475{\pm}0.000033$, respectively. The inflection point age was estimated to be 445 days and the weight of inflection point was 385.0 kg. The von Bertalanffy model parameters A, b, and k were estimated to be $1196.4{\pm}18.39$, $0.646{\pm}0.0010$, and $0.00162{\pm}0.000027$, respectively. The inflection point age was estimated to be 405 days and the weight of inflection point was 352.0 kg. Mature body weight of the von Bertalanffy model was 1196.4 kg, the Gompertz model was 990.5 kg, and the Logistic model was 772.0 kg. The difference between actual and estimated weights was similar in the Logistic model and the von Bertalanffy model. The difference between market weight and estimated market weight was the lowest in the Gompertz model. The growth curve using the von Bertalanffy model showed the lowest mean square error.

• Journal of Korean Society of Forest Science
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• v.90 no.2
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• pp.210-216
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• 2001

Pinus densiflora S. et Z. has widely been distributed, and is one of the important main foret resources in Korea. Diameter and height growth patterns were estimated using non-linear algebraic difference equation, which requires two-measurement times $T_1$ and $T_2$. To maximize data use, all possible measurement interval data were derived using Lag and Put statements in the SAS. In results, of the algebraic difference equations applied, the Schumacher and the Gompertz polymorphic equations for diameter and height, respectively showed the higher precision of the fitting. In order to allow more precise estimation of growth than those of the basic Schumacher and the Gompertz, further refinement that combine biological realism as input into the equation would be necessary.

• Journal of Animal Science and Technology
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• v.44 no.5
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• pp.519-522
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• 2002

Body weight-age data from 60 bulls and 60 steer of Hanwoo in the Korean Native Cattle Improvement Center was used to determine the growth curve parameters with Gompertz equation. Estimated growth curve functions were as follows; Bul l : $W_t$ = 906.1.exp{－3.956.exp(－0.0034t)} Steer : $W_t$ = 823.1.exp{－3.301.exp(－0.0027t} Mature weight estimated with Gompertz equation of bull is higher than earlier studies. And the major factor raising differences from the other is feeding level. Relative body weights of steer to bull were rapidly decreased to 79.2% until 19.5 months of age, and then increased slowly. The ratio was 90.8% at mature state. Body weight was under-estimated for bull at birth, but over-estimated for steer, and the body weight variations of bull were larger than the steer.