• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.1 s.71
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• pp.85-92
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• 2006

This paper investigates critical loads of the tapered Beck's columns with clamped and spring supports, subjected to a subtangential follower force. The linearly tapered columns with the solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck's columns is derived using the Bemoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters: the taper type, the subtangential parameter and the spring stiffness.

• Journal of the Korean Applied Science and Technology
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• v.23 no.1
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• pp.54-62
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• 2006

Kelvin equation is revisited, which accounts for important phenomena observed frequently in nano-dispersion systems. They include vapor pressure increase for curved interfaces, nucleation, capillary condensation, Ostwald ripening and so on. The smaller the radius of curvature is, the more significant Kelvin equation becomes. Therefore, its meaning, curvature effect, and importance are examined and discussed.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.29 no.1
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• pp.92-96
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• 1996

To elucidate the flow properties of carboxymethyl chitin (CM-chitin), the critical concentration and flow equation of aqueous CM-chitin solution were investigated. The concentration of $0.8\%$ appeared to be the critical concentration. So interaction occurred between polymer chains in the CM-chitin solutions had the higher concentration than $0.8\%$ but not in lower than $0.8\%.\;0.5\%$ CM-chitin solution was revealed as a newtonian flow but $1.0\%$ CM-chitin solution showed a pseudoplastic flow. Flow constants of $3.0\%$ CH-chitin solution were 0.0908cp for $\eta_\infty$, 770cp for $\eta_0$, 0.81 for $\beta$ and 0.36 for n. Therefore, flow equation of $3.0\%$ CM-chitin solution was as follow; $$\eta=0.1+\{{770/(1+0.81D^{0.36})\}$$.

• Nuclear Engineering and Technology
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• v.5 no.2
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• pp.115-131
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• 1973

L.S. Pontryagin's maximum principle is applied to the minimum critical mass problem without any restriction on the ranges of uranium enrichment. For the analysis, two group diffusion equation is adopted for a cylindrical reactor neglecting the vertical axis consideration. The result shows that the three-zoned reactor turns out to be most optimal: the inner and outer zones with the minimum enrichment ; whereas the middle 3one with the maximum enrichment. With the given three-zoned reactor, critical condition is derived, which leads to the calculation of the determinant. By finding the roots of the determinant the numerical calculation of the minimum critical mass is carried out for the case of Kori reactor geometry changing the minimum or the maximum enrichment. It is found from many computed values that the least possible critical mass turns out to be the case of 1.2% maximum enrichment for the middle zone and 0.65% minimum enrichment for the inner and out zones.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.117-123
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• 2004

It has been conjectured that, on a compact orient able manifold M, a critical point of the total scalar curvature functional restricted the space of unit volume metrics of constant scalar curvature is Einstein. In this paper we show that if a manifold is a 3-dimensional warped product, then (M, g) cannot be a critical point unless it is isometric to the standard sphere.

• 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.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.299-314
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• 2009

We investigate the multiple nontrivial solutions of the asymmetric beam equation $u_{tt}+u_{xxxx}=b_1[{(u + 2)}^+-2]+b_2[{(u + 3)}^+-3]$ with Dirichlet boundary condition and periodic condition on t. We reduce this problem into a two-dimensional problem by using variational reduction method and apply the Mountain Pass theorem to find the nontrivial solutions of the equation.

• Proceedings of the Korea Water Resources Association Conference
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• 2021.06a
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• pp.141-141
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• 2021

This study proposed an equation for Rainfall Threshold for Flood Warning (RTFW) for urban areas based on computer simulations. First, a coupled 1D-2D dual-drainage model was developed for nine watersheds in Seoul, Korea. Next, the model simulation was repeated for a total of 540 combinations of the synthetic rainfall events and watershed imperviousness (9 watersheds × 4 NRCS Curve Number (CN) values × 15 rainfall events). Then, the results of the 101 simulations with the critical flooded depth (0.25m-0.35m) were used to develop the equation that relates the value of RTFW to the rainfall event temporal variability (represented as coefficient of variation) and the watershed Curve Number. The results suggest that 1) the rainfall with greater temporal variability causes critical floods with less amount of total rainfall; and that 2) the greater imperviousness requires less rainfall to have critical floods. For validation, the proposed equation was applied for the flood warning system with two storm events occurred in 2010 and 2011 over 239 watersheds in Seoul. The results of the application showed high performance of the warning system in issuing the flood warning, with the hit, false and missed alarm rates at 68%, 32% and 7.4% respectively for the 2010 event and 49%, 51% and 10.7% for the event in 2011.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.547-572
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• 2010

We study existence of positive solutions of the classical nonlinear Schr$\ddot{o}$dinger equation $-{\Delta}u\;+\;V(x)u\;-\;f(x,\;u)\;-\;H(x)u^{2*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$. In fact, we consider the following more general quasi-linear Schr$\ddot{o}$odinger equation $-div(|{\nabla}u|^{m-2}{\nabla}u)\;+\;V(x)u^{m-1}$ $-f(x,\;u)\;-\;H(x)u^{m^*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$, where m $\in$ (1, n) is a positive number and $m^*\;:=\;\frac{mn}{n-m}\;>\;0$, is the corresponding critical Sobolev embedding number in $\mathbb{R}^n$. Under appropriate conditions on the functions V(x), f(x, u) and H(x), existence and non-existence results of positive solutions have been established.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.77-85
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• 2002

The statistical testing methods have been widely recognized to determine the plain and cipher texts. In fact, the randomness for a sequence from an encryption algorithm is necessary to guarantee security and reliance of cipher algorithm. Thus, the statistical randomness tests are used to discover cipher text. In this paper, we would provide the critical value for an approximate entropy test by estimating the nonlinear regression equation when the number of sequence and the level of significance are given. Thus, we can discern plan and cipher text for real problem with given number of sequence and the level of significance. Also, we confirm the fitness of the estimated critical values from the rate of success for plain or cipher text.