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

• Geomechanics and Engineering
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• v.32 no.6
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• pp.553-566
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• 2023

A circular tank foundation resting on the ground and subjected to axisymmetric horizontal and vertical loads and moments is analyzed using the variational principles of mechanics. The circular foundation is assumed to behave as a Kirchhoff plate with in-plane and transverse displacements. The soil beneath the foundation is assumed to be a multi-layered continuum in which the horizontal and vertical displacements are expressed as products of separable functions. The differential equations of plate and soil displacements are obtained by minimizing the total potential energy of the plate-soil system and are solved using the finite element and finite difference methods following an iterative algorithm. Comparisons with the results of equivalent two-dimensional finite element analysis and other researchers establish the accuracy of the method.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1045-1061
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• 2023

Using variational methods, Krasnoselskii's genus theory and symmetric mountain pass theorem, we introduce the existence and multiplicity of solutions of a parameteric local equation. At first, we consider the following equation $$\{-div[a(x,{\mid}{\nabla}u{\mid}){\nabla}u]\,=\,{\mu}(b(x){\mid}u{\mid}^{s(x)-2}-{\mid}u{\mid}^{r(x)-2})u\;in\;{\Omega},\\u\,=0\,on\;{\partial}{\Omega},$$ where Ω⊆ ℝ^N is a bounded domain, µ is a positive real parameter, p, r and s are continuous real functions on ${\bar{\Omega}}$ and a(x, ξ) is of type |ξ|^p(x)-2. Next, we study boundedness and simplicity of eigenfunction for the case a(x, |∇u|)∇u = g(x)|∇u|^p(x)-2∇u, where g ∈ L^∞(Ω) and g(x) ≥ 0 and the case $a(x,\,{\mid}{\nabla}u{\mid}){{\nabla}u}\,=\,(1\,+\,{\nabla}u{\mid}^2)^{\frac{p(x)-2}{2}}{\nabla}u$ such that p(x) ≡ p.

• Coupled systems mechanics
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• v.13 no.1
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• pp.73-93
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• 2024

In this work, we propose combining an advanced optimal control algorithm with a geometrically exact beam model. For simplicity, the 2D Reissner beam model is chosen to represent large displacements and rotations. The difficulty pertains to the nonlinear nature of beam kinematics affecting the tangent stiffness matrix, making it non-constant, which compromises direct use of optimal control methods for linear problems. Thus, we seek to accommodate a time varying control using linear-quadratic regulator (LQR) algorithm with the proposed geometrically nonlinear beam model. We provide a detailed theoretical formulation and its numerical implementation in a variational format form. Several illustrative numerical examples are provided to confirm an excellent performance of the proposed methodology.

• Smart Structures and Systems
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• v.16 no.5
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• pp.781-806
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• 2015

A unified formulation of finite layer methods (FLMs), based on the Reissner mixed variational theorem (RMVT), is developed for the three-dimensional (3D) coupled electro-elastic analysis of simply-supported, functionally graded piezoelectric material (FGPM) plates with open- and closed-circuit surface conditions and under electro-mechanical loads. In this formulation, the material properties of the plate are assumed to obey an exponent-law varying exponentially through the thickness coordinate, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement components. The relevant orders used for expanding these variables in the thickness coordinate can be freely chosen as the linear, quadratic and cubic orders. Four different mechanical/electrical loading conditions applied on the top and bottom surfaces of the plate are considered, and the corresponding coupled electro-elastic analysis of the loaded FGPM plates is undertaken. The accuracy and convergence rate of the RMVT-based FLMs are assessed by comparing their solutions with the exact 3D piezoelectricity ones available in the literature.

• Bulletin of the Korean Chemical Society
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• v.24 no.6
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• pp.763-770
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• 2003

The $BH_5$ molecule, which is suggested as an intermediate of the acidolysis of $BH_4^-$, contains a weak two-electron-three-center bond and it requires extremely high-level of theories to calculate the energy and structure correctly. The structures and energies of $BH_5$ and the transition state for the hydrogen scrambling have been studied using recently developed multi-coefficient correlated quantum mechanical methods (MCCMs). The dissociation energies and the barrier heights agree very well with the previous results at the CCSD(T)/ TZ(3d1f1g, 2p1d) level. We have also calculated the potential energy curves for the dissociation of $BH_5$ to $BH_3$ and $H_2$. The lower levels of theory were unable to plot correct potential curves, whereas the MCCM methods give very good potential energy curves and requires much less computing resources than the CCSD(T)/ TZ(3d1f1g,2p1d) level. The potential energy of the $BH_5$ scrambling has been obtained by the multiconfiguration molecular mechanics algorithm (MCMM), and the rates are calculated using the variational transition state theory including multidimensional tunneling approximation. The rate constant at 300 K is 2.1 × $10^9s^{-1}$, and tunneling is very important.

• Korean Institute of Interior Design Journal
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• v.20 no.1
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• pp.89-97
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• 2011

Furniture design is no exception to human desire for pursuit of the nature. In various design fields, it has turned out nature-decorative method in the past, and also recently it has turned out bio-adaptive method which is more root design process using principal of generation in nature world. The purpose of this study is to analyze application methods and characteristics of fractal geometry and voronoi diagram which are most representative principals of generative design in nature by research on the example of furniture design using these principals. The results of having analyzed fumitures by generative design can be summarized as follows; design principals of fractal; superposition, scaling, repetition & gradation, deformation, distortion and voronoi diagram; individual speciation, variational patten, repetition gradation, ambiguous boundary create new design concept and emergent form in furniture design. Application methods are 'form emergence by algorithm', 'conventional process based on principals of generative design', and 'reproduction of pattern from generative design'. Biological reinterpretations and new explorations of principals of nature generation offer unbounded possibilities for furniture design.

• Journal of the Korea Institute of Military Science and Technology
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• v.26 no.5
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• pp.422-430
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• 2023

To build an automated system detecting toxic chemicals from Raman spectra, we have to obtain sufficient data of toxic chemicals. However, it usually costs high to gather Raman spectra of toxic chemicals in diverse situations. Tackling this problem, we develop methods to generate synthetic Raman spectra of DMMP and 2-CEES without actual experiments. First, we propose certain mathematical transforms to augment few original Raman spectra. Then, we train deep generative models to generate more realistic and diverse data. Analyzing synthetic Raman spectra of toxic chemicals generated by our methods through visualization, we qualitatively verify that the data are sufficiently similar to original data and diverse. For conclusion, we obtain a synthetic dataset of DMMP and 2-CEES with the proposed algorithm.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.40 no.4
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• pp.275-292
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• 2022

In order to detect climate changes using satellite imagery, the GCOS (Global Climate Observing System) defines requirements such as spatio-temporal resolution, stability by the time change, and uncertainty. Due to limitation of GK-2A sensor performance, the level-2 products can not satisfy the requirement, especially for spatial resolution. In this paper, we found the optimal pan-sharpening algorithm for GK-2A products. The six pan-sharpening methods included in CS (Component Substitution), MRA (Multi-Resolution Analysis), VO (Variational Optimization), and DL (Deep Learning) were used. In the case of DL, the synthesis property based method was used to generate training dataset. The process of synthesis property is that pan-sharpening model is applied with Pan (Panchromatic) and MS (Multispectral) images with reduced spatial resolution, and fused image is compared with the original MS image. In the synthesis property based method, fused image with desire level for user can be produced only when the geometric characteristics between the PAN with reduced spatial resolution and MS image are similar. However, since the dissimilarity exists, RD (Random Down-sampling) was additionally used as a way to minimize it. Among the pan-sharpening methods, PSGAN was applied with RD (PSGAN_RD). The fused images are qualitatively and quantitatively validated with consistency property and the synthesis property. As validation result, the GSA algorithm performs well in the evaluation index representing spatial characteristics. In the case of spectral characteristics, the PSGAN_RD has the best accuracy with the original MS image. Therefore, in consideration of spatial and spectral characteristics of fused image, we found that PSGAN_RD is suitable for GK-2A products.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.4
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• pp.1760-1778
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• 2018

For image segmentation with intensity inhomogeneity, many region-based level set methods have been proposed. Some of them however can't get the relatively ideal segmentation results under the severe intensity inhomogeneity and weak edges, and without use of the image gradient information. To improve that, we propose a new level set method combined with local direction gradient in this paper. Firstly, based on two assumptions on intensity inhomogeneity to images, the relationships between segmentation objects and image gradients to local minimum and maximum around a pixel are presented, from which a new pixel classification method based on weight of Euclidian distance is introduced. Secondly, to implement the model, variational level set method combined with image spatial neighborhood information is used, which enhances the anti-noise capacity of the proposed gradient information based model. Thirdly, a new diffusion process with an edge indicator function is incorporated into the level set function to classify the pixels in homogeneous regions of the same segmentation object, and also to make the proposed method more insensitive to initial contours and stable numerical implementation. To verify our proposed method, different testing images including synthetic images, magnetic resonance imaging (MRI) and real-world images are introduced. The image segmentation results demonstrate that our method can deal with the relatively severe intensity inhomogeneity and obtain the comparatively ideal segmentation results efficiently.