• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.435-441
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• 2016

Let G be a graph, and let g, f be two nonnegative integer-valued functions defined on V (G) with g(x) ≤ f(x) for each x ∈ V (G). A graph G is called a fractional (g, f, n)-critical graph if after deleting any n vertices of G the remaining graph of G admits a fractional (g, f)-factor. In this paper, we obtain a binding number condition for a graph to be a fractional (g, f, n)-critical graph, which is an extension of Zhou and Shen's previous result (S. Zhou, Q. Shen, On fractional (f, n)-critical graphs, Inform. Process. Lett. 109(2009)811-815). Furthermore, it is shown that the lower bound on the binding number condition is sharp.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.527-535
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• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies one pair of Torus-Sphere variational linking inequality. We show that I has at least two critical points when I satisfies one pair of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. We prove this result by use of the limit relative category and critical point theory on the manifold with boundary.

• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.3
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• pp.505-512
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• 1988

Since the propagation of a short fatigue crack is directly related to the large crack which causes the fracture of bulk specimen, the detailed study on the propagation of the short crack is essential to prevent the fatigue fracture. However, a number of recent studies have demonstrated that the short crack can grow at a low applied stress level which are predicted from the threshold condition of large crack. In present study, the threshold condition for the propagation of short fatigue crack is examined with respect to the microstructure and cyclic loading history. Specimens employed in this study were decarburized eutectoid steels which have various decarburized ferrite volume fraction. Rotating bending fatigue test was carried out on these specimens with the special emphasis on the '||'&'||'quot;critical non-propagating crack length.'||'&'||'quot; It is found that the reduction of the endurance limit of their particular microstructures can be due to the increase of the length of critical non-propagating crack, and the quantitative relationship between the threshold stress .DELTA. .sigma. $_{th}$ and the critical non-propagating crack length Lc can be written as .DELTA. .sigma. $_{th}$, Lc=C where m, C is constant. Further experiments were carried out on the effect of pearlitic structure and cyclic loading history on the length of critical non-propagating crack. It is shown that the length of critical non-propagating crack is closely related to both pearlite interlamellar spacing and cyclic loading history.ory. cyclic loading history.

• Proceedings of the Korea Water Resources Association Conference
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• 2018.05a
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• pp.149-149
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• 2018

Prediction on initial motion of sediment is crucial to evaluate sediment transport and channel stability. The condition of incipient movement of sediment is characterized by bed shear stress, which is generated from force of moving water against the bed of the channel, and by critical shear stress, which depends on force resisting motion of sediment due to the submerged weight of the grains. When the bed shear stress exceeds the critical shear stress, sediment particles begin rolling and sliding at isolated and random locations. In Mountain River, debris flow frequently occurs due to heavy rainfall and can lead some natural stones from mountain slope into the bed river. This phenomenon could add additional forces to sediment transport system in the bed of river and also affect or change direction and magnitude of sediment movement. In this paper, evaluations on incipient motion of uniform coarse gravel under falling spheres impacts using small scale flume channel were conducted. The drag force of falling spheres due to water flow and length movement of falling spheres were investigated. The experiments were carried out in flume channel made by glass wall and steel floor with 12 m long, 0.6 m wide, and 0.6 m deep. The bed slopes were selected with the range from 0.7% to 1.5%. The thickness of granular layer was at least 3 times of diameter of granular particle to meet grain placement condition. The sphere diameters were chosen to be 4cm, 6 cm, 8 cm, 10 cm. The spheres were fallen in to the bed channel for critical condition and under critical condition of motion particle. Based on the experimental results, the Shields curve of particles Reynold number and dimensionless critical shear stress were plotted. The relationship between with drag force and the length movement of spheres were plotted. The pathways of the bed material Under the impact of spheres falling were analyzed.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1805-1821
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• 2016

In this paper, we are concerned with the nonlinear elliptic equations of the p(x)-Laplace type $$\{\begin{array}{lll}-div(a(x,{\nabla}u))+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u) && in\;{\Omega}\\(a(x,{\nabla}u)\frac{{\partial}u}{{\partial}n}={\lambda}{\theta}g(x,u) && on\;{\partial}{\Omega},\end{array}$$ which is subject to nonlinear Neumann boundary condition. Here the function a(x, v) is of type${\mid}v{\mid}^{p(x)-2}v$ with continuous function $p:{\bar{\Omega}}{\rightarrow}(1,{\infty})$ and the functions f, g satisfy a $Carath{\acute{e}}odory$ condition. The main purpose of this paper is to establish the existence of at least three solutions for the above problem by applying three critical points theory due to Ricceri. Furthermore, we localize three critical points interval for the given problem as applications of the theorem introduced by Arcoya and Carmona.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.812-818
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• 2001

The drop type impact test and finite element analysis are established for examining the buckling behavior of a square tube under the lateral impact load. Based on these results, the effects by the boundary conditions for supporting the structure are reviewed, which are as follows. One is pinned condition by screw; the other is fixed by welding. The critical impact force and acceleration by test are nearly same between two cases. However, the critical impact velocity of the pinned condition is higher than that of the fixed case. Therefore, the dynamic buckling behavior of a pinned structure is better than the fixed condition in view of critical impact velocity. These test and analysis results will be adaptable for predicting the dynamic structural integrity of a tube structure not only the axial impact event but the lateral impact event.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.495-511
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• 2017

In this paper, we consider the system of three elliptic equations using two critical point theorem. We prove the existence of two solutions for suitable forcing terms, under a condition on the linear part which prevents resonance with eigenvalues of the operator.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.53-57
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• 2008

Let G be a graph, and let a, b, k be integers with $0{\leq}a{\leq}b,k\geq0$. Then graph G is called an (a, b, k)-critical graph if after deleting any k vertices of G the remaining graph of G has an [a, b]-factor. In this paper, the relationship between binding number bind(G) and (a, b, k)-critical graph is discussed, and a binding number condition for a graph to be (a, b, k)-critical is given.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.54 no.11
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• pp.507-517
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• 2005

This paper presents the results of critical contingency analysis for the Korean power system which is performed to identify the impact of the critical contingencies on the Korean power system and set up a short term system operation planning for the purpose of preventing large scale blackout. The static and dynamic simulation is carried out for each critical contingency and the simulation results for each contingency are shown under the peak load condition for the year 2005, 2007 and 2010.