• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1327-1345
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• 2021

In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation of Chern-Simons-Higgs type $$u(x)=\vec{\;l\;}+C_{\ast}{{\displaystyle\smashmargin{2}{\int\nolimits_{\mathbb{R}^n}}}\;{\frac{(1-{\mid}u(y){\mid}^2){\mid}u(y){\mid}^2u(y)-\frac{1}{2}(1-{\mid}u(y){\mid}^2)^2u(y)}{{\mid}x-y{\mid}^{n-{\alpha}}}}dy.$$ Here u : ℝⁿ → ℝ^k is a bounded, uniformly continuous function with k ⩾ 1 and 0 < α < n, $\vec{\;l\;}{\in}\mathbb{R}^k$ is a constant vector, and C_* is a real constant. We prove that ${\mid}\vec{\;l\;}{\mid}{\in}\{0,\frac{\sqrt{3}}{3},1\}$ if u is the finite energy solution. Further, if u is also a differentiable solution, then we give a Liouville type theorem, that is either $u{\rightarrow}\vec{\;l\;}$ with ${\mid}\vec{\;l\;}{\mid}=\frac{\sqrt{3}}{3}$, when |x| → ∞, or $u{\equiv}\vec{\;l\;}$, where ${\mid}\vec{\;l\;}{\mid}{\in}\{0,1\}$.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.661-678
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• 1995

In this paper we will estimate from above and below the values of the Bergman, Caratheodory and Kobayashi metrics for a vector X at z, where z is any point near a given point $z_0$ in the boundary of pseudoconvex domains in $C^n$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.35-43
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• 2009

We say that an isometric immersed hypersurface x : $M^n\;{\rightarrow}\;{\mathbb{R}}^{n+1}$ is of $L_k$-finite type ($L_k$-f.t.) if $x\;=\;{\sum}^p_{i=0}x_i$ for some positive integer p < $\infty$, $x_i$ : $M{\rightarrow}{\mathbb{R}}^{n+1}$ is smooth and $L_kx_i={\lambda}_ix_i$, ${\lambda}_i\;{\in}\;{\mathbb{R}}$, $0{\leq}i{\leq}p$, $L_kf=trP_k\;{\circ}\;{\nabla}^2f$ for $f\;{\in}\'C^{\infty}(M)$, where $P_k$ is the kth Newton transformation, ${\nabla}^2f$ is the Hessian of f, $L_kx\;=\;(L_kx^1,\;{\ldots},\;L_kx^{n+1})$, $x=(x^1,\;{\ldots},\;x^{n+1})$. In this article we study the following(hyper)surfaces in ${\mathbb{R}}^{n+1}$ from the view point of $L_1$-finiteness type: totally umbilic ones, generalized cylinders $S^m(r){\times}{\mathbb{R}}^{n-m}$, ruled surfaces in ${\mathbb{R}}^{n+1}$ and some revolution surfaces in ${\mathbb{R}}^3$.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.03a
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• pp.257-260
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• 1997

The high precision of the products manufatured by press forming requires the high stiffness of press machines. In this study, the C-frame type press is analyzed to provide the basic idea on the C-frame press design, especially on the frame design. The finite element method is applied for the analysis and the isotropic propertics of the frame material is also considered. The results are summarized in terms of stresses and displacement distributions. Also, the openback angle of the presses is compared with two different models. The CS-150 and ECS-150 models, which are presses model having 150 ton frame capacity relatively and produced by SSangYong precision Co. LTD, are applied for the analysis.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.18 no.3
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• pp.122-126
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• 2017

The aim of this study was to develop a device for solving the heating problem of living space using heated air, utilizing a simple air heater type collector for solar energy. At the present time, this study assessed the possibility of a development system through theoretical calculations for the amount of available energy according to the size change of the air-heated solar energy collector. To produce and supply hot water using the heat energy of the sun, hot water at $100^{\circ}C$ or less was produced using a flat or vacuum tube type collector. The purpose of this study was to research the air heating type solar collector that utilizes heating energy with heating air above $75^{\circ}C$, by designing and manufacturing an air piping type solar collector that is a simpler type than a conventional solar collector system. The analysis results were obtained for the generated air temperature ($^{\circ}C$) and the production of air (kg/h) to determine the performance of air heating by an air-heated solar collector according to the heat transfer characteristics in the collector of the model when a specified amount of heat flux was dropped into a solar collector of a certain size using PHOENICS, which is a heat flow analysis program applying the Finite Volume Method. From the analysis result, the temperature of the air obtained was approximately $40.5^{\circ}C$, which could be heated using an air heating tube with an inner diameter of 0.1m made of aluminum in a collector with a size of $1.2m{\times}1.1m{\times}0.19m$. The production of air was approximately 161 m3/h. This device can be applied to maintain a suitable environment for human activity using the heat energy of the sun.

• Structural Engineering and Mechanics
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• v.57 no.3
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• pp.457-471
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• 2016

To analyze laminated composite and sandwich beams under temperature loads, a $C^0$-type Reddy's beam theory considering transverse normal strain is proposed in this paper. Although transverse normal strain is taken into account, the number of unknowns is not increased. Moreover, the first derivatives of transverse displacement have been taken out from the in-plane displacement fields, so that the $C^0$ interpolation functions are only required for the finite element implementation. Based on the proposed model, a three-node beam element is presented for analysis of thermal responses. Numerical results show that the proposed model can accurately and efficiently analyze the thermoelastic problems of laminated composites.

• Journal of Dental Rehabilitation and Applied Science
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• v.21 no.2
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• pp.153-167
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• 2005

The purpose of this study was to compare the v-shape thread with the square shape thread of fixture in the view of stress distribution pattern using finite element stress analysis. The finite element model was designed with the parallel placement of two standard fixtures(4.0 mm diameter ${\times}$ 11.5 mm length) on the region of mandibular 1st and 2nd molars. Three dimensional finite element model was created with the components of the implant and surrounding bone. This study simulated loads of 200 N at the central fossa in a axial direction (load A), 200 N at the buccal offset load that is 2 mm apart from central fossa in a axial direction (load B), 200 N at the buccal offset load that was 4 mm apart from central fossa in a axial direction (load C). These forces of load A',B',C' were applied to a $15^{\circ}$ inward oblique direction at that same site with 200 N. Von Mises stress values were recorded and compared in the supporting bone, fixture, and abutment screw. The following results have been made based on this study : 1. The highest stress concentration occurred at the cervical region of the implant fixture. 2. Von Mises stress value of off-site region was higher than that of central fossa region. 3. Square shape thread type showed more even stress distribution in the vertical and oblique force than V-shape thread type. 4. Stress distribution was the most effective in the case of buccal offset load (2, 4 mm distance from central fossa) in the square shape thread type. 5. V-shape thread type revealed higher von Mises stress value than square shape thread type in all environmental condition. The results from numerical analyses concluded that square shape thread type had the lower destructive stress and more stress distribution between the fixture and bone interface than V-shape thread type. Therefore, square shape thread type was regarded as optimal thread configuration in biomechanical concepts.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.387-388
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• 2006

This article provides a dynamic analysis model for huge marine engine that examined analytically variation effects of frequency response by fitting of transverse stays such as hydraulic type. First, vibration analysis using the three dimensional finite element models for the huge marine engine has performed in order to find out the dynamic characteristics. Second, three dimensional finite elements model for the huge marine engine was modifued so that generate forcing nodes in crosshead part and top bracing nodes in cylinder frame part. Third, a system matrix and output matrix was derived for the general siso(single input single out) state space model. Finally, developed state space model for the three dimensional finite elements model for the huge marine engine without the additional modifying process.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.553-569
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• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.447-456
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• 2015

In this paper, we investigate the differential-difference equation $(f(z+c)-f(z))^2+P(z)^2(f^{(k)}(z))^2=Q(z)$, where P(z), Q(z) are nonzero polynomials. In addition, we also investigate Fermat type q-difference differential equations $f(qz)^2+(f^{(k)}(z))^2=1$ and $(f(qz)-f(z))^2+(f^{(k)}(z))^2=1$. If the above equations admit a transcendental entire solution of finite order, then we can obtain the precise expression of the solution.