• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.153-167
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• 1996

In this paper we investigate the existence of solutions of a nonlinear wave equation $u_{tt} - u_{xx} = p(x, t, u)$$ in $H_0$, where $H_0$ is the Hilbert space spanned by eigenfunctions. If p satisfy condition $(p_1) - (p_3)$, this nonlinear gave equation has at least one solution.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.255-277
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• 2024

In this paper, we introduce the notion of stress-energy tensor Q of the traceless Ricci tensor for Riemannian manifolds (Mⁿ, g), and investigate harmonicity of Riemannian curvature tensor and Weyl curvature tensor when (M, g) satisfies some geometric structure such as critical point equation or vacuum static equation for smooth functions.

• Journal of Korean Association for Spatial Structures
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• v.20 no.4
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• pp.149-158
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• 2020

The governing equation for a dome-type shallow spatial truss subjected to a transverse load is expressed in the form of the Duffing equation, and it can be derived by considering geometrical non-linearity. When this model under constant load exceeds the critical level, unstable behavior is appeared. This phenomenon changes sensitively as the number of free-nodes increases or depends on the imperfection of the system. When the load is a periodic function, more complex behavior and low critical levels can be expected. Thus, the dynamic unstable behavior and the change in the critical point of the 3-free-nodes space truss system were analyzed in this work. The 4-th order Runge-Kutta method was used in the system analysis, while the change in the frequency domain was analyzed through FFT. The sinusoidal wave and the beating wave were utilized as the periodic load function. This unstable situation was observed by the case when all nodes had same load vector as well as by the case that the load vector had slight difference. The results showed the critical buckling level of the periodic load was lower than that of the constant load. The value is greatly influenced by the period of the load, while a lower critical point was observed when it was closer to the natural frequency in the case of a linear system. The beating wave, which is attributed to the interference of the two frequencies, exhibits slightly more behavior than the sinusoidal wave. And the changing of critical level could be observed even with slight changes in the load vector.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.215-219
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• 2003

Buckling and post-buckling Analysis of Ludwick type and modified Ludwick type elastic materials was carried out. Because the constitutive equation, or stress-strain relationship is different from that of linear elastic one, a new governing equation was derived and solved by $4^{th}$ order Runge-Kutta method. Considered as a special case of combined loading, the buckling under both point and distributed load was selected and researched. The final solution takes distinguished behavior whether the constitutive relation is chosen to be modified or non-modified Ludwick type as well as linear or non-linear. We also derived strain energy function for non-linear elastic constitutive relationship. By doing so, we calculated the criterion function which estimates the stability of the equilibrium solutions and determines critical buckling load for non-linear cases. We applied this theory to the constitutive relationship of fabric, which also is the non-linear equation between the applied moment and curvature. This results has both technical and mathematical significance.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.65-73
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• 2003

In this paper we seek a positive, radially symmetric and energy minimizing solution of an m-Laplacian equation, -div$($\mid${\nabla}u$\mid$^{m-2}$\mid${\nabla}u)\;=\;h(u)$. In the variational sense, the solutions are the critical points of the associated functional called the energy, $J(v)\;=\;\frac{1}{m}\;\int_{R^N}\;$\mid${\nabla}v$\mid$^m\;-\;\int_{R^N}\;H(v)dx,\;where\;H(v)\;=\;{\int_0}^v\;h(t)dt$. A positive, radially symmetric critical point of J can be obtained by solving the constrained minimization problem; minimize{$\int_{R^N}$\mid${\nabla}u$\mid$^mdx$\mid$\;\int_{R^N}\;H(u)d;=\;1$}. Moreover, the solution minimizes J(v).

• Clean Technology
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• v.17 no.1
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• pp.19-24
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• 2011

The bubble point pressures of binary mixtures of carbon dioxide ($CO_2$) and N,N-dimethylformamide (DMF) were measured by using a high-pressure experimental apparatus equipped with a variable-volume view cell, at various $CO_2$ compositions in the range of temperatures above the critical temperature of $CO_2$ and below the critical temperature of DMF. The experimental bubble point pressure data were correlated with the Peng-Robinson equation of state (PR-EOS) to estimate the corresponding dew point compositions at equilibrium with the bubble point compositions. The experimentally measured bubble point pressures gave good agreement with those calculated by the PR-EOS. The variable-volume view cell equipment was verified to be an easy and quick way to measure the bubble point pressures of high-pressure compressible fluid mixtures.

• Applied Chemistry for Engineering
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• v.20 no.1
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• pp.94-98
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• 2009

The bubble point pressures of dimethyl carbonate and carbon dioxide mixtures were measured by using a high-pressure experimental apparatus equipped with a variable-volume view cell, at various $CO_2$ compositions in the range of temperatures above the critical temperature of $CO_2$ and below the critical temperature of dimethyl carbonate. The experimental bubble point pressure data were correlated with the Peng-Robinson equation of state (PR-EOS) to estimate the corresponding dew point compositions at equilibrium with the bubble point compositions. The experimentally measured bubble point pressures gave good agreement with those calculated by the PR-EOS. The variable-volume view cell equipment was verified to be an easy and quick way to measure the bubble point pressures of high-pressure compressible fluid mixtures.

• Structural Engineering and Mechanics
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• v.81 no.4
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• pp.481-492
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• 2022

Cycloidal ball planetary transmission (CBPT) has many applications as precision reducer, such as precision machinery and automation drive systems etc. The traditional analytical model of CBPT cannot accurately describe the change of the normal force of meshing points, and thus cannot describe the precise transmission process of meshing pairs. In the paper, a method for deriving the normal force equation is put forward by using the non-linear relationship between force and deformation in elastic mechanics. The two-point contact analytical models of all the meshing pairs are established to obtain the micro-displacement analytical model of CBPT under axial pre-tightening. Then, the non-real-time two-point contact analytical models of all the meshing pairs are further constructed to obtain the normal force expression to determine the critical compression coefficients. Experimental investigations are performed to verify the analytical model using the critical compression coefficients.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.24 no.2
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• pp.129-135
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• 2012

Performance of various temperature-dependent vapor-pressure equations with two adjustable parameters is assessed. These are Antoine, Miller, Zia-Thodos, Mejbri-Bellagi and other 10 equations. The equations are fitted to correlate the data from NIST Chemistry WebBook for 43 pure substance refrigerants from the critical point to the triple point. It was found that the Mejbri-Bellagi equation yields the lowest average absolute deviation of 0.37% compared with that of 0.58% of the Miller equation which is known to give better fit to experimental data than the Antoine equation(1.42%) does.

• Progress in Superconductivity and Cryogenics
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• v.4 no.1
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• pp.73-77
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• 2002

The variation of critical current by the formation of crack in a high temperature super-conducting tape was studied by experimental and numerical analyses. The current-voltage relation of HTS tape is measured by the four-point measurement method. Numerical analyses are used to solve two dimensional heat conduction equation, considering the temperature distribution. By comparing current-voltage relation of experimental and numerical results, the validity of numerical method is verified.