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

• Wind and Structures
• /
• v.5 no.5
• /
• pp.393-406
• /
• 2002

Aerodynamic pressures and forces were measured on a model of a solar panel containing six slender, parallel modules. Of particular importance to system design is the aerodynamically induced torque. The peak system torque was generally observed to occur at approach wind angles near the diagonals of the panel ($45^{\circ}$, $135^{\circ}$, $225^{\circ}$ and $315^{\circ}$) although large loads also occurred at $270^{\circ}$, where wind is in the plane of the panel, perpendicular to the individual modules. In this case, there was strong vortex shedding from the in-line modules, due to the observation that the module spacing was near the critical value for wake buffeting. The largest loads, however, occurred at a wind angle where there was limited vortex shedding ($330^{\circ}$). In this case, the bulk of the fluctuating torque came from turbulent velocity fluctuations, which acted in a quasi-steady sense, in the oncoming flow. A simple, quasi-steady, model for determining the peak system torque coefficient was developed.

• Korean Journal of Mathematics
• /
• v.17 no.3
• /
• pp.283-291
• /
• 2009

We investigate the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+g_1(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}),\\{\eta}_t=-L{\eta}+g_2(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}).\end{array}$$ We show the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system when the nonlinearity $g^{\prime}_1,\;g^{\prime}_2$ are bounded and $3g^{\prime}_1(-{\infty})+g^{\prime}_2(-{\infty})<{\lambda}_1,\;{\lambda}_n<3g^{\prime}_1(+{\infty})+g^{\prime}_2(+{\infty})<{\lambda}_{n+1}$.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.20 no.11
• /
• pp.977-982
• /
• 2007

The realization of the photoresist(PR) removal method with vaporized water and ozone gas mixture has been studied for the LCD TFT array manufacturing. The developed PR stripper uses the water boundary layer control method based on the high concentration ozone production technology. We develop the prototype of PR stripper and experiment to find the optimal process parameter condition like as the ozone gas flow/concentration, process reaction time and thin boundary layer formation. As a results, we realize the LCD PR strip rate over the 0.4 ${\mu}m/min$ and this PR removal rate is more than 5 times higher than the conventional immersion type ozonized water process.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.23 no.1
• /
• pp.56-64
• /
• 2013

Turbulent boundary layer noise is already a significant contributor to sonar self noise. For developing acoustic window of sonar system to reduce self noise, a parametric study of design factors of acoustic window is presented. Distance of sensor array from acoustic window, materials of acoustic window and characteristics of damping layer are studied as design factors to influence in the characteristics of the transfer function of self noise. As the result, these design factors make change the characteristics of transfer function slightly. Among design factors the location of sensor array is most important parameter in the self noise reduction

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2005.11b
• /
• pp.97-100
• /
• 2005

Precise prediction of resonance frequency has been the subject of numerous papers related to Helmholtz resonator design because of its high performance at the frequency. The resonance frequency is dependent upon not only the internal dimensions of resonator but also the external boundary conditions such as the existence of other resonators in Helmholtz resonator array panel. However, the latter effect, which changes the external end correction of resonator, has not been well studied. We propose a formula to calculate the radiation impedance (or external end correction) of Helmhoitz resonator array panel. Any distance between adjacent resonators and any angle of Incidence can be allowed in the method. Numerical examples show how and how much the distance affects the resonance frequency of the panel. It is also found that the maximum absorption of the panel varies with the resonator arrangement.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.16 no.7 s.112
• /
• pp.677-682
• /
• 2006

In the case of aeroacoustic test in windtunnel, measurement accuracy is reduced by not only Doppler effects but also by the microphone self noise due to airflow and high turbulence in the wall boundary layer. Microphone array measurements can be easily utilized for the solutions of these problems. In this paper, geometrical optics approach and diagonal term elimination of cross spectral matrix was introduced to the de-dopplerization and self noise reduction methods for the microphone array measurement. For the validation, beamforming tests for sinusoidal point source were performed in the closed type test section of windtunnel, and their performances of beam width and sidelobe rejection were significantly improved.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2005.11a
• /
• pp.822-825
• /
• 2005

In the case of aeroacoustic test in windtunnel, measurement accuracy is reduced by not only Doppler effects but also by the microphone self noise due to airflow and high turbulence in the wall boundary layer. Microphone array measurements can be easily utilized for the solutions of these problems. In this paper, geometrical optics approach and diagonal term elimination of cross spectral matrix was introduced to the de-dopplerization and self noise reduction methods for the microphone array measurement. For the validation, beamforming tests for sinusoidal point source were performed in the closed type test section of windtunnel, and their performances of beam width and sidelobe rejection were significantly improved.

• Journal of the Korean Mathematical Society
• /
• v.59 no.5
• /
• pp.911-926
• /
• 2022

Let u be a function on a locally finite graph G = (V, E) and Ω be a bounded subset of V. Let 𝜀 > 0, p > 2 and 0 ≤ λ < λ₁(Ω) be constants, where λ₁(Ω) is the first eigenvalue of the discrete Laplacian, and h : V → ℝ be a function satisfying h ≥ 0 and $h{\not\equiv}0$. We consider a perturbed Yamabe equation, say $$\{\begin{array}{lll}-{\Delta}u-{\lambda}u={\mid}u{\mid}^{p-2}u+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω and ∂Ω denote the interior and the boundary of Ω, respectively. Using variational methods, we prove that there exists some positive constant 𝜀₀ > 0 such that for all 𝜀 ∈ (0, 𝜀₀), the above equation has two distinct solutions. Moreover, we consider a more general nonlinear equation $$\{\begin{array}{lll}-{\Delta}u=f(u)+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ and prove similar result for certain nonlinear term f(u).

• Journal of the Korean Institute of Telematics and Electronics D
• /
• v.34D no.4
• /
• pp.100-105
• /
• 1997

3-dimensional finite element mehtod (FEM) elecrical field analysis was performed to obtain electric fields on a field emission display (FED) tip in an array form. Because, unlike a single tip structure, there is no azimuthal symmetry for a tip aary, 3D analysis is necessary. To reduce memory requriement the simulatio was performed by applying the neumann boundary condition to the intermediate plane between tips to take the effect of the array on the electric field into account and corresponding current was calculated. To verify our algorithm, comparison between simulation resutls and experimental data from another paper was made and the difference was discussed.