• Korean Journal of Mathematics
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• v.19 no.4
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• pp.481-493
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• 2011

We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.679-692
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• 2006

On a compact oriented n-dimensional manifold $(M^n,\;g)$, it has been conjectured that a metric g satisfying the critical point equation (2) should be Einstein. In this paper, we prove that if a manifold $(M^4,\;g)$ is a 4-dimensional oriented compact warped product, then g can not be a solution of CPE with a non-zero solution function f.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.409-415
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• 2006

On a compact oriented smooth 3-dimensional manifold (M, g), we consider the critical point equation(CPE) defined as $z_g=s^{{\prime}*}_g(f)$. Under CPE, it is shown in [5] that every stable minimal hypersurface in M is contained in ${\varphi}^{-1}(0)$ for ${\varphi}{\in}$ ker $s^{{\prime}*}_g$. We study analytic and geometric conditions under which the stable minimal hypersurface in M does not exist.

• Proceedings of the Korean Vacuum Society Conference
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• 2000.02a
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• pp.83-83
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• 2000

MBE법으로 성장시킨 Cd1-xMgxTe 박막을 조성비 (x=0, 0.23, 0.32, 0.43)에 따라 타원편광 분석기로 측정하여 연구하였다. E0 critical point energy 아래에서 나타나는 간섭무늬를 제거하기 위해 multilayer calculation을 수행했고 ellipsometric data를 2번 미분하여 계산하는 Critical Point Parabolic Band(CPPB) model을 사용하여 E0, E0+Δ0, E1, E1,+Δ1, and E0'critical point energy 들을 구할 수 있었다. 특히 E2 peak region 에서는 종전의 고상시료 (bulk)에서 측정 발표된 값보다도 매우 높고 명확한 <$\varepsilon$2>값이 측정되어, E2와 E、0 peak가 명확하게 분리되는 것을 볼 수 있었다. 또한 Mg의 조성비에 따라 critical point energy 가 linear 하게 변화됨이 관측되었다.

• Applied Microscopy
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• v.50
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• pp.15.1-15.6
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• 2020

Sample preparation including dehydration and drying of samples is the most intricate part of scanning electron microscopy. Most current sample preparation protocols use critical-point drying with liquid carbon dioxide. Very few studies have reported samples that were dried using chemical reagents. In this study, we used hexamethyldisilazane, a chemical drying reagent, to prepare plant samples. As glandular trichomes are among the most fragile and sensitive surface structures found on plants, we used Millingtonia hortensis leaf samples as our study materials because they contain abundant glandular trichomes. The results obtained using this new method are identical to those produced via critical-point drying.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.437-445
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• 2008

We show the existence of at least four nontrivial critical points of the $C^{1,1}$ functional f on the Hilbert space $H=X_0{\oplus}X_1{\oplus}X_2{\oplus}X_3{\oplus}X_4$, $X_i$, i = 0, 1, 2, 3 are finite dimensional, with f(0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies $(P.S.)_c$ condition, and $f{\mid}_{X_0{\oplus}X_4}$ has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.

• Molecules and Cells
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• v.43 no.2
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• pp.182-187
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• 2020

When cells are stimulated by growth factors, they make a critical choice in early G₁ phase: proceed forward to S phase, remain in G₁, or revert to G₀ phase. Once the critical decision is made, cells execute a fixed program independently of extracellular signals. The specific stage at which the critical decision is made is called the restriction point or R-point. The existence of the R-point raises a major question: what is the nature of the molecular machinery that decides whether or not a cell in G₁ will continue to advance through the cell cycle or exit from the cell cycle? The R-point program is perturbed in nearly all cancer cells. Therefore, exploring the nature of the R-point decision-making machinery will provide insight into how cells consult extracellular signals and intracellular status to make an appropriate R-point decision, as well into the development of cancers. Recent studies have shown that expression of a number of immediate early genes is associated with the R-point decision, and that the decision-making program constitutes an oncogene surveillance mechanism. In this review, we briefly summarize recent findings regarding the mechanisms underlying the context-dependent R-point decision.

• Journal of ILASS-Korea
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• v.4 no.1
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• pp.55-61
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• 1999

The first maximum point in the stability curve of liquid jet, i.e., the critical point is associated with the critical Reynolds number. This critical Reynolds number should be predicted by simple means. In this work, the critical Reynolds number in the stability curve of liquid jet are predicted using the empirical correlations and the experimental data reported in the literatures. The critical Reynolds number was found to be a function of the Ohnesorge number, nozzle lengh-to-diameter ratio, ambient Weber number and nozzle inlet type. An empirical correlation for the critical Reynolds number as a function of the Ohnesorge number and nozzle length-to-diameter ratio is newly proposed here. Although an empirical correlation proposed in this work may not be universal because of excluding the effects of ambient pressure and nozzle inlet type, it has reasonably agrees with the measured critical Reynolds number.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.113-121
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• 2003

This paper is concerned with some properties of stable domains and limit functions. Using the relationship between cycles of periodic stable domains and orbits of critical points and using the Sullivan theorem [19], we prove that the value of a constant limit function in some stable domain for a rational function f of degree at least two lies in the closure of the set of critical orbits of f.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.471-478
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• 2024

The aim of this paper is to investigate some properties of the critical points equations on the statistical manifolds. We obtain some geometric equations on the statistical manifolds which admit critical point equations. We give a relation only between potential function and difference tensor for a CPE metric on the statistical manifolds to be Einstein.