• Advances in nano research
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• 제14권6호
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• pp.495-506
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• 2023

We study the bending wave, shear wave and longitudinal wave characteristics in the double nanobeams in this paper for the first time, in the process of research, based on the Reddy's higher-order shear deformation theory and considering shear layer stiffness, linear stiffness, inter-laminar stiffness, the pore volume fraction, temperature variation, functionally graded index influence on wave propagation, based on the nonlocal strain gradient theory and Hamilton variational principle, the wave equation of the double-nanometer beams are derived. Since there are three different motion states for the double nanobeams, which includes the cases of "in phase", "out of phase" and "one nanobeam fixed", the propagation characteristics of shear-, bending-, and longitudinal- waves in these three cases are discussed respectively, and some valuable conclusions are obtained.

• 한국정보과학회 언어공학연구회:학술대회논문집(한글 및 한국어 정보처리)
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• 한국정보과학회언어공학연구회 2019년도 제31회 한글 및 한국어 정보처리 학술대회
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• pp.93-96
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• 2019

최근 딥러닝 모델을 다양한 도메인에 적용하여 뛰어난 성능을 보여주고 있다. 하지만 딥러닝 모델은 정답으로 제시된 결과가 정상적으로 예측된 결과인지, 단순히 오버피팅에 의해 예측된 결과인지를 구분하기 어렵다. 이러한 불확실성(Uncertainty)을 측정 할 수 없다는 문제점을 해결하기 위해서 본 논문에서는 베이지안 딥러닝 방법 중 하나인 변분추론(Variational Inference)과 몬테카를로 Dropout을 오픈도메인(Open-Domain) 태스크에 적용하고, 예측 결과에 대한 불확실성을 측정하여 예측결과에 영향을 주는 모델의 성능을 측정해 효과성을 보인다.

• 대한수학회보
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• 제60권4호
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• pp.1101-1129
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• 2023

In this study we propose a model of optimal retirement, consumption and portfolio choice of an individual agent, which encompasses a large class of the models in the literature, and provide a methodology to solve the model. Different from the traditional approach, we consider the problems before and after retirement simultaneously and identify the difference in the dual value functions as the utility value of lifetime labor. The utility value has an option nature, namely, it is the maximized value of choosing the retirement time optimally and we discover it by solving a variational inequality. Then, we discover the dual value functions by using the utility value. We discover the value function and optimal policies by establishing a duality between the value function and the dual value function. The model and approach offer a significant advantage for computation of optimal policies for a large class of problems.

• Journal of applied mathematics & informatics
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• 제41권4호
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• pp.723-739
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• 2023

In this paper, we developed three theoretical models based on prey and predator that exhibit holling-type response functions. In both a fuzzy and a crisp environment, we have provided a mathematical formulation for the prey predator concept. We used the signed distance method to defuzzify the triangular fuzzy numbers using the alpha-cut function. We can identify equilibrium points for all three theoretical models using the defuzzification technique. Utilizing a variational matrix, stability is also performed with the two species model through three theoretical models. Results are presented, followed by discussion. MATLAB software is used to provide numerical simulations.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.349-361
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• 2022

In this paper, we study the following nonlinear problem: $$\{-\Delta_{p}^{3}(x)u\;=\;{\lambda}V_{1}(x){\mid}u{\mid}^{q(x)-2}u\;in\;{\Omega},\\u\;=\;{\Delta}u\;{\Delta}^{2}u\;=\;0\;on\;{\partial}\Omega, $$ under adequate conditions on the exponent functions p, q and the weight function V₁. We prove the existence and nonexistence of eigenvalues for p(x)-triharmonic problem with Navier boundary value conditions on a bounded domain in ℝ^N. Our technique is based on variational approaches and the theory of variable exponent Lebesgue spaces.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.405-432
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• 2022

Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that "absorbs" the boundary conditions at the cracks. Then the equations of motion are derived from the first principles using the Extended Hamilton's Principle, accounting for non-conservative forces. The variational formulation of the equations is stated in terms of the subdifferentials of the bending and axial potential energies. The equations are given in their abstract (weak), as well as in classical forms.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2023년도 춘계학술발표대회
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• pp.639-641
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• 2023

이미지 기반 폐기물 처리시스템에서 품목별 상이한 수집 난이도로 인해 발생하는 데이터 불균형으로 분류 모델 학습에 어려움이 따른다. 따라서 본 논문에서는 폐기물 분류 모델의 성능 비교를 통해 적합한 이미지 생성 모델을 탐색한다. 데이터의 불균형을 해결할 수 있도록 VAE(Variational Auto-Encoder), GAN(Generative Adversarial Networks) 및 Diffusion Model을 이용하여 이미지를 생성한다. 이후 각각의 생성 방법에 따라 학습데이터와 병합하여 객체 분류를 진행하였다. 정확도는 VAE가 84.41%로 3.3%의 성능 향상을, F1-점수는 Diffusion Model이 91.94%로 6.14%의 성능 향상을 이루었다. 이를 통해, 데이터 수집에서 나타나는 데이터 불균형을 해결하여 실 사용환경에 알맞은 시스템을 구축이 가능함을 확인하였다.

• 한국소음진동공학회논문집
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• 제13권3호
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• pp.172-179
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• 2003

Linear matrix Inequality based $H_\infty$ robust controller is designed to control the motion of a 4-axis unbalanced rigid asymmetric rotor supported and controlled by two active magnetic bearings in this paper. To this end, the equations of motion of the system are derived via Hamilton's variational principle and transformed to a state-space form for the standard $H_\infty$ control problem. LMI-based controller, which does not require additional assumptions beyond the usual stabilizability and detectability assumptions, is designed based upon the pole place weighting function and loopshaping technique. The obtained results are compared with those reported in the available literature and the efficiency of the proposed LMI-based $H_\infty$ control is revealed.

• 대한수학회논문집
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• 제38권4호
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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.

• 대한수학회보
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• 제61권2호
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• pp.541-556
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• 2024

In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain $-{\Delta}u+V(x)u-{\frac{u}{\sqrt{1-u^2}}}{\Delta}{\sqrt{1-u^2}}={\lambda}{\mid}u{\mid}^{p-2}u$, x ∈ ℝ^N, where 2 ≤ p < 2^*, N ≥ 3. By the Ekeland variational principle, the cut off technique, the change of variables and the L^∞ estimate, we study the existence of positive solutions. Here, we construct the L^∞ estimate of the solution in an entirely different way. Particularly, all the constants in the expression of this estimate are so well known.