• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.421-434
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• 2016

The main aim of this paper is to discuss the difference between the Euler-Maruyama's approximate solutions and the accurate solution to stochastic differential delay equation. To make the theory more understandable, we impose the non-uniform Lipschitz condition and weakened linear growth condition. Furthermore, we give the pth moment continuous of the approximate solution for the delay equation.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.491-498
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• 2013

This note is concerned with the uniform $L^p$-continuity of solution for the stochastic differential equations under Lipschitz condition and linear growth condition. Furthermore, uniform $L^p$-continuity of the solution for the stochastic functional differential equation is given.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.491-506
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• 2019

In this paper, we show the existence and uniqueness of solution to stochastic differential equations under weakened $H{\ddot{o}}lder$ condition and a weakened linear growth condition. Furthermore, the properties of their solutions investigated and estimate for the error between Picard iterations $x_n(t)$ and the unique solution x(t) of SDEs.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.229-241
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• 2020

For a second order linear differential equation f" + A(z)f' + B(z)f = 0, with A(z) and B(z) being transcendental entire functions under some restrictions, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions, with a condition, have exponent of convergence of zeros equal to infinity. Also, we have extended these results to higher order linear differential equations.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.507-519
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• 2009

We give a theorem of the existence of the multiple solutions of the Hamiltonian system with the square growth nonlinearity. We show the existence of m solutions of the Hamiltonian system when the square growth nonlinearity satisfies some given conditions. We use critical point theory induced from the invariant function and invariant linear subspace.

• Korean Chemical Engineering Research
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• v.59 no.1
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• pp.138-151
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• 2021

The effect of a reactant ratio on the growth of a buoyancy-driven instability in an irreversible A+B→C reaction system is analyzed theoretically and numerically. Taking a non-stoichiometric reactant ratio into account, new linear stability equations are derived without the quasi-steady state assumption (QSSA) and solved analytically. It is found that the main parameters to explain the present system are the Damköhler number, the dimensionless density difference of chemical species and the ratio of reactants. The present initial grow rate analysis without QSSA shows that the system is initially unconditionally stable regardless of the parameter values; however, the previous initial growth rate analysis based on the QSSA predicted the system is unstable if the system is physically unstable. For time evolving cases, the present growth rates obtained from the spectral analysis and pseudo-spectral method support each other, but quite differently from that obtained under the conventional QSSA. Adopting the result of the linear stability analysis as an initial condition, fully nonlinear direct numerical simulations are conducted. Both the linear analysis and the nonlinear simulation show that the reactant ratio plays an important role in the onset and the growth of the instability motion.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.53-63
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• 2019

In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.

• International journal of advanced smart convergence
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• v.9 no.1
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• pp.132-140
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• 2020

It is very important to use appropriate nutrition water for crop growth in hydroponic farming facilities. However, in many cases, the supply of nutrition water is not designed with a precise plan, but is performed in a conventional manner. We proposes a forecasting technique for nutrition water requirements based on a data analysis for optimal strawberry production. To do this, the proposed forecasting technique uses linear regression for correlating strawberry production, soil condition, and environmental parameters with nutrition water demand for the actual two-stage strawberry production soil. Also, it includes predicting the optimal amount of nutrition water requires according to the heterogeneous cultivation environment and variety by comparing the amount of nutrition water needed for the growth and production of different kinds of strawberries. We suggested study uses two types of section beds that are compared to find out the best section bed production of strawberry growth. The dataset includes 233 samples collected from a real strawberry greenhouse, and the four predicted variables consist of the total amounts of nutrition water, average temperature, humidity, and CO₂ in the greenhouse.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.29-40
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• 2009

Motivated by [Linear Algebra and its Appl. 420(2007), 218-227] and [Linear Algebra and its Appl. 425(2007), 171-183], we, in this paper, study the solvability of periodic boundary value problems of higher order nonlinear functional difference equations with p-Laplacian. Sufficient conditions for the existence of at least one solution of this problem are established.

• Environmental Engineering Research
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• v.23 no.2
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• pp.216-222
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• 2018

The growth characteristics of Spirulina platensis were investigated using four photo-bioreactors with $CO_2$-mixed air flows. Each reactor was operated under a specific condition: 3% $CO_2$ at 50 mL/min, 3% $CO_2$ at 150 mL/min, 6% $CO_2$ at 50 mL/min, and 6% CO2 at 150 mL/min. The 3% $CO_2$ at 150 mL/min condition produced the highest algal growth rate, while the 6% $CO_2$ at 150 mL/min conditioned produced the lowest. The algal growth performance was suitably assessed by the linear growth curve rather than the exponential growth. The medium pH decreased from 9.5 to 8.7-8.8 (3% $CO_2$) and 8.4-8.5 (6% $CO_2$), of which trends were predicted only by the pH-carbonate equilibrium and the reaction kinetics between dissolved $CO_2$ and $HCO_3{^-}$. Based on the stoichiometry between the nutrient amounts and cell elements, it was predicted that depleted nitrogen (N) at the early stage of the cultivation would reduce the algal growth rates due to nutrient starvation. In this study, use of the photobioreactors capable of good light energy distribution, proper ranges of $CO_2$ in bubbles and medium pH facilitated production of high amounts of algal biomass despite N limitation.