• Journal of Plant Biology
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• v.37 no.3
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• pp.301-308
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• 1994

The individual and combined effects of acidic rain, Mg deficiency (-Mg) and Al surplus (＋Al) on the growth of shoots and roots of pitch pine seedlings and the effect of humic substances (Lit) on Al toxicity were investigated. The growth of height and dry matter were not significantly less for pitch pine seedlings sprayed with simulated acid rain (SAR) of pH 3.5 than for those sprayed with SAR of pH 5.6. But treatments of Al and ＋Al-Mg in soil solution reduced the growth of seedlings in terms of height of shoots, and dry matter of shoots or roots. Effect of Mg deficiency on the growth of seedlings was apparent only when Al was treated simutaneously. The growth of seedlings, regardless of rain pH, decreased in the following order: control=-Mg>Lit＋Al>＋Al>＋Al-Mg. Treatments of Al and ＋Al-Mg in soil solution reduced the total length of secondary and teritary roots of seedlings regardless of rain pH, and decreased in the following order: the primary root

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.323-334
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• 2010

We give a theorem for the existence of at least three solutions for the fourth order elliptic boundary value problem with the square growth variable coefficient nonlinear term. We use the variational reduction method and the critical point theory for the associated functional on the finite dimensional subspace to prove our main result. We investigate the shape of the graph of the associated functional on the finite dimensional subspace, (P.S.) condition and the behavior of the associated functional in the neighborhood of the origin on the finite dimensional reduction subspace.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.819-829
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• 2016

In this paper, we study the order of growth of solutions to the non-homogeneous linear differential equation $$f^{(k)}+A_{k-1}e^{az}f^{(k-1)}+{\cdots}+A_1e^{az}f^{\prime}+A_0e^{az}f=F_1e^{az}+F_2e^{bz}$$, where $A_j(z)$ (${\not\equiv}0$) ($j=0,1,{\cdots},k-1$), $F_j(z)$ (${\not\equiv}0$) (j = 1, 2) are entire functions and a, b are complex numbers such that $ab(a-b){\neq}0$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.419-431
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• 2021

In this paper we discuss the classical problem of finding conditions on the entire coefficients A(z) and B(z) guaranteeing that all nontrivial solutions of f" + A(z)f' + B(z)f = 0 are of infinite order. We assume A(z) is an entire function of completely regular growth and B(z) satisfies three different conditions, then we obtain three results respectively. The three conditions are (1) B(z) has a dynamical property with a multiply connected Fatou component, (2) B(z) satisfies T(r, B) ~ log M(r, B) outside a set of finite logarithmic measure, (3) B(z) is extremal for Denjoy's conjecture.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.137-161
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• 2022

In this article, we study the existence and multiplicity of homoclinic solutions for the following fourth-order differential equation (1) u⁽⁴⁾(x) + ωu''(x) + a(x)u(x) = f(x, u(x)), ∀x ∈ ℝ where a(x) is not required to be either positive or coercive, and F(x, u) = ∫^u₀ f(x, v)dv is of subquadratic or superquadratic growth as |u| → ∞, or satisfies only local conditions near the origin (i.e., it can be subquadratic, superquadratic or asymptotically quadratic as |u| → ∞). To the best of our knowledge, there is no result published concerning the existence and multiplicity of homoclinic solutions for (1) with our conditions. The proof is based on variational methods and critical point theory.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.149-157
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• 2020

Some basic properties in connection with generalized relative order and generalized relative lower order of analytic functions in the unit disc have been dicussed in this article.

• Biotechnology and Bioprocess Engineering:BBE
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• v.7 no.2
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• pp.117-120
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• 2002

The effect of cell density on cell growth was investigated in a suspension batch culture of hybridoma cells. The specific growth rate was found to increase with increasing initial cell density and then to decrease with further increases in initial cell density. In order to quantitatively describe the dependence of specific growth rate on cell density, a kinetic model is proposed, which satisfactorily represents the experimental data.

• Journal of Information Technology Applications and Management
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• v.25 no.1
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• pp.105-124
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• 2018

The usage level of SMEs' win-win payment system is still lower than originally expected. In order to find the answer, we studied SMEs' usage performance of win-win payment system and analyzed the influencing factors of SMEs' usage level of win-win payment system. This study found that the more SMEs utilize win-win payment system, the higher they achieve the desired performance in finance, customer, process, learning and growth perspective. And this study found that usage level of win-win payment system is high in order of large corporations' pressure, government policy, and SMEs' readiness. This study is expected to improve win-win growth by increasing usage level of win-win payment system between large corporations and SMEs, while establishing desirable ecosystems.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.11 no.4
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• pp.166-169
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• 2001

6H-SiC bulk crystals were grown by sublimation method with different conditions in term of gaseous pressures ad source temperatures. In order to optimize the growth rate, pressure at growth period and source and substrate temperatures were investigated as experimental variables. the results were compared with each other and finally the optimum growth conditions were discussed. Furthermore the relation of the growth steps and defects formation was evaluates in the point of reducing the micropipes. Subsequently the growth steps and defects formation was evaluated in the point of reducing the micropipes. Subsequently the growth steps were observed leading to the lower step height with the lower growth rate.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.20 no.3
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• pp.117-124
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• 2010

For Ar=5, Pr=1.18, Le=0.15, Pe=2.89, Cv=1.06, $P_B$=20 Torr, the effects of impurity $(N_2)$ on thermally and solutally buoyancy-driven convection ($Gr_t=3.46{\times}10^4$ and $Gr_s=6.02{\times}10^5$, respectively) are theoretically investigated for further understanding and insight into an essence of thermo-solutal convection occurring in the vapor phase during the physical vapor transport. For $10K{\leq}{\Delta}T{\leq}50K$, the crystal growth rates are intimately related and linearly proportional to a temperature difference between the source and crystal region which is a driving force for thermally buoyancy-driven convection. Moreover, both the dimensionless Peclet number (Pe) and dimensional maximum velocity magnitudes are directly and linearly proportional to ${\Delta}T$. The growth rate is second order-exponentially decayed for $2{\leq}Ar{\leq}5$. This is related to a finding that the effects of side walls tend to stabilize the thermo-solutal convection in the growth reactor. Finally, the growth rate is found to be first order exponentially decayed for $10{\leq}P_B{\leq}200$ Torr.