• 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.

• 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.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.31 no.6_2
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• pp.577-583
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• 2013

Recently, massive archives of ground information imagery from new sensors have become available. To establish a functional relationship between the image and the ground space, sensor models are required. The rational functional model (RFM), which is used as an alternative to the rigorous sensor model, is an attractive option owing to its generality and simplicity. To determine the rational polynomial coefficients (RPC) in RFM, however, we encounter the problem of obtaining a stable solution. The design matrix for solutions is usually ill-conditioned in the experiments. To solve this unstable solution problem, regularization techniques are generally used. In this paper, we describe the effective determination of the optimal regularization parameter in the regularization technique during RPC derivation. A brief mathematical background of RFM is presented, followed by numerical approaches for effective determination of the optimal regularization parameter using the Euler Method. Experiments are performed assuming that a tilted aerial image is taken with a known rigorous sensor. To show the effectiveness, calculation time and RMSE between L-curve method and proposed method is compared.

• Journal of Food Hygiene and Safety
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• v.26 no.2
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• pp.120-124
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• 2011

Predictive mathematical models were developed for predicting the kinetics of growth of Listeria monocytogenes in smoked salmon, which is the popular ready-to-eat foods in the world, as a function of temperature (4, 10, 20 and $30^{\circ}C$). At these storage temperature, the primary growth curve fit well ($r^2$=0.989~0.996) to a Gompertz equation to obtain specific growth rate (SGR) and lag time (LT). The Polynomial model for natural logarithm transformation of the SGR and LT as a function of temperature was obtained by nonlinear regression (Prism, version 4.0, GraphPad Software). Results indicate L. monocytogenes growth was affected by temperature mainly, and SGR model equation is $365.3-31.94^*Temperature+0.6661^*Temperature^{\wedge^2}$ and LT model equation is $0.1162-0.01674^*Temperature+0.0009303^*Temperature{\wedge^2}$. As storage temperature decreased $30^{\circ}C$ to $4^{\circ}C$, SGR decreased and LT increased respectively. Polynomial model was identified as appropriate secondary model for SGR and LT on the basis of most statistical indices such as bias factor (1.01 by SGR, 1.55 by LT) and accuracy factor (1.03 by SGR, 1.58 by LT).

• Computers and Concrete
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• v.5 no.1
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• pp.75-88
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• 2008

This paper presents a mathematical model for strength and porosity of mortars made with ternary blends of ordinary Portland cement (OPC), ground rice husk ash (RHA) and classified fly ash (FA). The mortar mixtures were made with Portland cement Type I containing 0-40% FA and RHA. FA and RHA with 1-3% by weight retained on a sieve No. 325 were used. Compressive strength and porosity of the blended cement mortar at the age of 7, 28 and 90 days were determined. The use of ternary blended cements of RHA and FA produced mixes with good strength and low porosity of mortar. A mathematical analysis and two-parameter polynomial model were presented for the strength and porosity estimation with FA and RHA contents as parameters. The computer graphics of strength and porosity of the ternary blend were also constructed to aid the understanding and the proportioning of the blended system.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.485-494
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• 2023

Let Y be the quintic del Pezzo 4-fold defined by the linear section of Gr(2, 5) by ℙ⁷. In this paper, we describe the locus of double lines in the Hilbert scheme of coincs in Y. As a corollary, we obtain the desigularized model of the moduli space of stable maps of degree 2 in Y. We also compute the intersection Poincaré polynomial of the stable map space.

• Current Optics and Photonics
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• v.6 no.1
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• pp.69-78
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• 2022

A high-resolution camera is a precise optical system. Its vibrations during transportation and launch, together with changes in temperature and gravity field in orbit, lead to different degrees of defocus of the camera. Thermal refocusing is one of the solutions to the problems related to in-orbit defocusing, but there are few relevant thermal refocusing mathematical models for systematic analysis and research. Therefore, to further research thermal refocusing systems by using the development of a high-resolution micro-nano satellite (CX6-02) super-resolution camera as an example, we established a thermal refocusing mathematical model based on the thermal elasticity theory on the basis of the secondary mirror position. The detailed design of the thermal refocusing system was carried out under the guidance of the mathematical model. Through optical-mechanical-thermal integration analysis and Zernike polynomial calculation, we found that the data error obtained was about 1%, and deformation in the secondary mirror surface conformed to the optical index, indicating the accuracy and reliability of the thermal refocusing mathematical model. In the final ground test, the thermal vacuum experimental verification data and in-orbit imaging results showed that the thermal refocusing system is consistent with the experimental data, and the performance is stable, which provides theoretical and technical support for the future development of a thermal refocusing space camera.

• Journal of IKEEE
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• v.25 no.1
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• pp.88-94
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• 2021

Public-key cryptographic algorithms such as RSA and ECC, which are currently in use, have used mathematical problems that would take a long time to calculate with current computers for encryption. But those algorithms can be easily broken by the Shor algorithm using the quantum computer. Lattice-based cryptography is proposed as new public-key encryption for the post-quantum era. This cryptographic algorithm is performed in the Polynomial Ring, and polynomial multiplication requires the most processing time. Therefore, a hardware model module is needed to calculate polynomial multiplication faster. Number Theoretic Transform, which called NTT, is the FFT performed in the finite field. The logic verification was performed using HDL, and the proposed design at the transistor level using Hspice was compared and analyzed to see how much improvement in delay time and power consumption was achieved. In the proposed design, the average delay was improved by 30% and the power consumption was reduced by more than 8%.

• Journal of Distribution Science
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• v.10 no.12
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• pp.19-24
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• 2012

Purpose - This paper discusses the heterogeneous fixed fleet vehicle routing problem with pick-up and delivery (HFFVRPPD), for vehicles with different capacities, fixed costs, and travel costs. Research Design, data, methodology - This paper made nine assumptions for establishing a mathematical model to describe HFFVRPPD. It established a practical mathematical model, and because of the non-deterministic polynomial-time hard (NP-hard), improved the traditional simulated annealing algorithm and tested a new algorithm using a certain scale model. Result - We calculated the minimum cost of the heterogeneous fixed fleet vehicle routing problem (HFFVRP) with a single task and, on comparing the results with the actual HFFVRP for the single task alone, observed that the total cost of HFFVRPPD reduced significantly by 46.7%. The results showed that the new algorithm provides better solutions and stability. Conclusions - This paper, by comparing the HFFVRP and HFFVRPPD results, highlights certain advantages of using HFFVRPPD in physical distribution enterprises, such as saving distribution vehicles, reducing logistics cost, and raising economic benefits.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.2 no.2
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• pp.29-38
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• 1982

Nonlinear hydrological model containing the nonlinearity of effective rainfall, lag time and runoff is presented. In the evaluation of rainfall excess, the polynomial fitting method for total rainfall, 5 day antecedant rainfall and direct runoff is developed. In the application to actual watershed, the estimated model parameters of nonlinear lag model reflecting the nonlinearity of lag time are compared with the parameters, by both the fitting method and the correlation, model which are the modified version of the storage function model. The Successive Approximation Method in mathematical solution and Newton-Rhapson method in numerical solution are found to be superior to the conventional numerical graphic method in the analysis of nonlinear processes.