• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.379-385
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• 2014

For a bandlimited function with polynomial growth on the real line, we derive a nonuniform sampling expansion using a special bandlimited function which has polynomial decay on the real line. The series converges uniformly on any compact subsets of the real line.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.899-927
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• 2019

In this paper we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q)-th order and relative (p, q)-th lower order where p, q are any two positive integers and that of a special type of differential polynomial generated by one of the factors.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.379-391
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• 2015

We investigate the existence of solutions of the nonlinear biharmonic equation with variable coefficient polynomial growth nonlinear term and Dirichlet boundary condition. We get a theorem which shows that there exists a bounded solution and a large norm solution depending on the variable coefficient. We obtain this result by variational method, generalized mountain pass geometry and critical point theory.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.521-540
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• 2004

In this paper, we give a sharp estimate on the cardinality of the set generating the convex hull containing the image of harmonic maps with polynomial growth rate on a certain class of manifolds into a Cartan-Hadamard manifold with sectional curvature bounded by two negative constants. We also describe the asymptotic behavior of harmonic maps on a complete Riemannian manifold into a regular ball in terms of massive subsets, in the case when the space of bounded harmonic functions on the manifold is finite dimensional.

• Journal of the Korea institute for structural maintenance and inspection
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• v.10 no.3
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• pp.165-175
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• 2006

To analyze the deformation and failure of slopes, generally, two types of model, Polynomial model and Growth model, are applied. These two models are focused on the behavior of the slope by time. Therefore, this research is more focused on predicting of slope failure than analyzing the slope behavior by time. Generally, Growth model is used to analyze the soil slope, to the contrary, Polynomial model is used for rock slope. However, 3-degree polynomial($y=ax^3+bx^2+cx+d$) is suggested to combine two models in this research. The main trait of this model is having an asymptote. The fields to adopt this model are Gosujae Danyang(soil slope) and Youngduk slope(rock slope), which are the cut-slope near national road. Data from Gosujae are shown the failure traits of soil slope, to the contrary, those of Youngduk slope are shown the traits of rock slope. From the real-time monitoring data of the slope, 3-degree polynomial is proved as excellent system to analyze the failure and behavior of slope. In case of Polynomial model, even if the order of polynomials is increased, the $R^2$ value and shape of the curve-fitted graph is almost the same.

• Korean Journal of Food Science and Technology
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• v.37 no.2
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• pp.194-198
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• 2005

Growth curves of Listeria monocytogenes in modified surimi-based imitation crab (MIC) broth were obtained by measuring cell concentration in MIC broth at different culture conditions [initial cell numbers, $1.0{\times}10^{2},\;1.0{\times}10^{3}\;and\;1.0{\times}10^{4}$, colony forming unit (CFU)/mL; temperature, 15, 20, 25, 37, and $40^{\circ}C$] and applied to Gompertz model to determine microbial growth indicators, maximum specific growth rate constant (k), lag time (LT), and generation time (GT). Maximum specific growth rate of L. monocytogenes increased rapidly with increasing temperature and reached maximum at $37^{\circ}C$, whereas LT and GT decreased with increasing temperature and reached minimum at $37^{\circ}C$. Initial cell number had no effect on k, LT, and GT (p > 0.05). Polynomial and square root models were developed to express combined effects of temperature and initial cell number using Gauss-Newton Algorism. Relative coefficients of experimental k and predicted k of polynomial and square root models were 0.92 and 0.95, respectively, based on response surface model. Results indicate L. monocytogenes growth was mainly affected by temperature and square root model was more effective than polynomial model for growth prediction.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.17-51
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• 2019

In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative $_pL^*$-order, relative $_pL^*$-lower order and differential monomials, differential polynomials generated by one of the factors.

• 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.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.869-878
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• 2016

This paper presents an ecient fractional shifted Legendre polynomial method to solve the fractional Volterra's model for population growth model. The fractional derivatives are described based on the Caputo sense by using Riemann-Liouville fractional integral operator. The theoretical analysis, such as convergence analysis and error bound for the proposed technique has been demonstrated. In applications, the reliability of the technique is demonstrated by the error function based on the accuracy of the approximate solution. The numerical applications have provided the eciency of the method with dierent coecients of the population growth model. Finally, the obtained results reveal that the proposed technique is very convenient and quite accurate to such considered problems.