• Korean Journal of Mathematics
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• v.18 no.1
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• pp.87-96
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• 2010

We consider the semilinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the semilinear biharmonic boundary value problem. We show this result by using the critical point theory, the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

• Bulletin of the Korean Chemical Society
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• v.7 no.4
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• pp.283-288
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• 1986

A nonlinear analysis is presented for the treatment of fluctuations near the critical point in the presence of diffusion in the Schlogl models. The two time scaling method is used to obtain an evolution equation for the amplitude of fluctuations. It is shown that the fluctuations decay to zero in the stable region and they are enhanced to a finite value as time goes to infinity in the unstable region.

• 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.

• Journal of ILASS-Korea
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• v.26 no.4
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• pp.171-181
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• 2021

This study presents a prediction methodology of thermodynamic properties by using RK-PR Equation of State in a wide range of temperature and pressure conditions including both sub-critical and super-critical regions, in order to obtain thermophysical properties for hydrocarbon aviation fuels and their products resulting from endothermic reactions. The density and the constant pressure specific heat are predicted in the temperature range from 300 to 1000 K and the pressure from 0.1 to 5.0 MPa, which includes all of the liquid and gas phases and the super-critical region of three representative hydrocarbon fuels, and then compared with those data obtained from the NIST database. Results show that the averaged relative deviations of both predicted density and constant pressure specific heat are below 5% in the specified temperature and pressure conditions, and the major sources of the errors are observed near the saturation line and the critical point of each fuel.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.8
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• pp.2524-2539
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• 1996

A design process and an axisymmetric boundary integral equation method for precise structural analysis of the aircraft gas turbine rotor disk were developed. This axisymmetric boundary integral equation method for stress and steady-state thermal analysis was improved in solution accuracy by appling an implicit technique for Cauchy principal value evaluation, a subelement technique for weak singular integral evaluation and a double exponentical integral technoque for internal point solution near boundary surfaces. Stresses, temperatures, low cycle fatigue lifes and critical speeds for the turbine rotor disk of the thrust 1421 N class turbojet engine were analysed in a pratical calculation model problem.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1087-1094
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• 2016

On a compact n-dimensional manifold M, it has been conjectured that a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, is Einstein. In this paper, after derivng an interesting curvature identity, we show that the conjecture is true in dimension three and four when g is weakly Einstein. In higher dimensional case $n{\geq}5$, we also show that the conjecture is true under an additional Ricci curvature bound. Moreover, we prove that the manifold is isometric to a standard n-sphere when it is n-dimensional weakly Einstein and the kernel of the linearized scalar curvature operator is nontrivial.

• Journal of the Korean Chemical Society
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• v.45 no.4
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• pp.293-297
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• 2001

The existing vapor pressure measurements reported in the literature for parahydrogen between the triple point and the critical point have been employed to establish the constants and exponent of the following equation in the form of reduced vapor pressure and reduced temperature: ln $lnP_r=2.64-{\frac{2.75}{T_r}}+1.48129lnT_r+0.11T^5_r$Only the normal boiling point ($T_b$= 20.268K), the critical pressure ($P_c$= 1292.81 kPa), and the critical temperature ($T_c$= 32.976K) are necessary to calculate the vapor pressure for an overall average deviation of 0.21% for 153 experimental vapor pressure data.

• Proceedings of the Korea Institute of Applied Superconductivity and Cryogenics Conference
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• 2002.02a
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• pp.249-252
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• 2002

The change of critical current with a crack formation in a Bi-2223/Ag tape was studied by experimental and numerical analyses. Critical current of Bi-2223/Ag tape was measured with a continuous DC-power supply. The current-voltage relation of a Bi-2223/Ag tape is measured by the four point method. Numerical method is used to solve two dimensional heat conduction equation. By comparing the experimental and numerical results, the validity of numerical method is verified.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.309-322
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• 2008

We prove the existence of infinitely many solutions of the nonlinear higher order elliptic equation with Dirichlet boundary condition $(-{\Delta})^mu=q(x,u)$ in ${\Omega}$, where $m{\geq}1$ is an integer and ${\Omega}{\subset}{R^n}$ is a bounded domain with smooth boundary, when q(x,u) satisfies some conditions.

• Korean Journal of Mathematics
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• v.15 no.1
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• pp.1-11
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• 2007

It is well known that a suspension bridge may display certain oscillations under external aerodynamic forces. Under the action of a strong wind, in particular, a narrow and very flexible suspension bridge can undergo dangerous oscillations. So it would be very contributive to determine under what conditions a similar situation cannot occur, and find out safe parameters of the bridge construction. In this paper, we investigate relations between the multiplicity of solutions and nonlinear terms in this suspension bridge equation using critical point theorem and linking theorem.