• 충청수학회지
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• 제22권3호
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• pp.557-569
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• 2009

We present a new regularity criterion for suitable weak solutions of the steady-state Navier-Stokes equations near boundary in dimension five. We show that suitable weak solutions are regular up to the boundary if the scaled $L^{\frac{5}{2}}$-norm of the solution is small near the boundary. Our result is also valid in the interior.

• 대한수학회지
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• 제53권3호
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• pp.597-621
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• 2016

We present regularity conditions for suitable weak solutions of the Navier-Stokes equations with slip boundary data near the curved boundary. To be more precise, we prove that suitable weak solutions become regular in a neighborhood boundary points, provided the scaled mixed norm $L^{p,q}_{x,t}$ with 3/p + 2/q = 2, $1{\leq}q$ < ${\infty}$ is sufficiently small in the neighborhood.

• 대한수학회지
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• 제44권2호
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• pp.443-453
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• 2007

We study the equation of a membrane with strong viscosity. Based on the variational formulation corresponding to the suitable function space setting, we have proved the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.

• 대한수학회논문집
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• 제36권1호
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• pp.51-62
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• 2021

Variational method has played an important role in solving problems of uniqueness and existence of the nonlinear works as well as analysis. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations economy, optimization, game theory and medicine. Recently, the existence of infinitely many weak solutions for some non-local problems of Kirchhoff type with Dirichlet boundary condition are studied [14]. Here, a suitable method is presented to treat the elliptic partial derivative equations, especially (p(x), q(x))-Laplacian-like systems. This kind of equations are used in the study of fluid flow, diffusive transport akin to diffusion, rheology, probability, electrical networks, etc. Here, the existence of infinitely many weak solutions for some boundary value problems involving the (p(x), q(x))-Laplacian-like operators is proved. The method is based on variational methods and critical point theory.

• 대한수학회보
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• 제56권2호
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• pp.479-489
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• 2019

In this paper, we show the existence of a weak solution for a stochastic differential equation driven by an additive fractional Brownian sheet with Hurst parameters H, H' > 1/2, and a drift coefficient satisfying the linear growth condition. The result is obtained using a suitable Girsanov theorem for the fractional Brownian sheet.

• 대한전자공학회논문지TC
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• 제48권10호
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• pp.13-19
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• 2011

이 논문은 위성항법시스템을 이용한 위치측위에서 지역별 특성에 따른 위치오차실험을 통하여, 음영지역 발생 원인과 해결 방법을 제안하기 위한 연구이다. 동적측위에서 이동체는 이동 위치에 따라 사용할 수 있는 위성항법시스템의 수가 변화한다. 정확한 위치측위를 위해서는 4개 이상의 위성항법시스템으로부터 위치정보데이터를 수신 받아야 한다. 하지만 급격한 산업화와 열악한 지역 환경으로 위치오차가 커지고 음영지역이 발생한다. 이러한 위치오차를 줄이고 음영지역 발생을 해소하기 위해서는 대도시의 환경과 지역 환경 특성에 따른 원인을 파악하는 것이 중요하다. 따라서 본 논문에서는 대도시, 주택 지역, 숲 지역, 바다 지역, 대지 등을 선정하여 위치오차와 음영지역 발생 원인을 실험하였다. 그리고 이 논문을 기반으로 지역 환경에 따른 적합한 고정밀 측위 알고리즘을 제안하고, 음영지역해소 알고리즘을 제안하려고 한다.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.709-730
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• 2022

We consider the nonlinear matrix equation (NMEs) of the form 𝓤 = 𝓠 + Σ^k_i=1 𝓐^*_iℏ(𝓤)𝓐_i, where 𝓠 is n × n Hermitian positive definite matrices (HPDS), 𝓐₁, 𝓐₂, . . . , 𝓐_m are n × n matrices, and ~ is a nonlinear self-mappings of the set of all Hermitian matrices which are continuous in the trace norm. We discuss a sufficient condition ensuring the existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME 𝓤 = 𝓠 + 𝓐^*₁(𝓤²/900)𝓐₁ + 𝓐^*₂(𝓤²/900)𝓐₂ + 𝓐^*₃(𝓤²/900)𝓐₃. In order to do this, we define 𝓕𝓖_w-contractive conditions and derive fixed points results based on aforesaid contractive condition for a mapping in extended Branciari b-metric distance followed by two suitable examples. In addition, we introduce weak well-posed property, weak limit shadowing property and generalized Ulam-Hyers stability in the underlying space and related results.

• Bulletin of the Korean Chemical Society
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• 제31권6호
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• pp.1561-1567
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• 2010

In this study, we have developed a new detection method using Si field effect transistor (FET)-type biosensors, which enables the direct monitoring of antigen-antibody binding within very high-ionic-strength solutions such as 1$\times$PBS and human serum. In the new method, as no additional dilution or desalting processes are required, the FET-type biosensors can be more suitable for ultrasensitive and real-time analysis of raw sample solutions. The new detection scheme is based on the observation that the strength of antigen-antibody-specific binding is significantly influenced by the ionic strength of the reaction solutions. For a prostate specific antigen (PSA), in some conditions, the binding reaction between PSA and anti-PSA in a low-ionic strength reaction solution such as 10 ${\mu}M$ phosphate buffer is weak (reversible), while that in high-ionic strength reaction solutions such as 1$\times$PBS or human serum is strong.

• 대한수학회지
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• 제57권6호
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• pp.1347-1372
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• 2020

We study bifurcation for the following fractional Schrödinger equation $$\{\left.\begin{eqnarray}(-{\Delta})^su+V(x)u&=&{\lambda}f(u)&&{\text{in}}\;{\Omega}\\u&>&0&&{\text{in}}\;{\Omega}\\u&=&0&&{\hspace{32}}{\text{in}}\;{\mathbb{R}}^n{\backslash}{\Omega}\end{eqnarray}\right$$ where 0 < s < 1, n > 2s, Ω is a bounded smooth domain of ℝⁿ, (-∆)^s is the fractional Laplacian of order s, V is the potential energy satisfying suitable assumptions and λ is a positive real parameter. The nonlinear term f is a positive nondecreasing convex function, asymptotically linear that is $\lim_{t{\rightarrow}+{\infty}}\;{\frac{f(t)}{t}}=a{\in}(0,+{\infty})$. We discuss the existence, uniqueness and stability of a positive solution and we also prove the existence of critical value and the uniqueness of extremal solutions. We take into account the types of Bifurcation problem for a class of quasilinear fractional Schrödinger equations, we also establish the asymptotic behavior of the solution around the bifurcation point.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2006년도 추계학술대회 논문집
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• pp.1326-1331
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• 2006

The precast concrete deck is one of suitable solutions for replacement and new construction in urban area. However, the precast concrete deck could be a weak point of the steel plate girder bridges structurally due to the connections between precast panels in the longitudinal direction. Thereafter, it is necessary for improvement of durability and load carrying capacity to introduce the prestress force in the longitudinal direction Some cracks of connections at the precast concrete deck may be occurred due to live loads, the difference of temperature and long-term effects. The shrinkage and creep of concrete may significantly affect long-term behaviors which occur tensile stresses at the precast concrete deck of steel plate girder bridges. In this study, the time-dependant analysis program has been developed to determine the initial prestress force in the longitudinal direction considering loss of stress at the precast concrete deck. Also it has been estimated the initial prestress force by construction stages and shapes of girder.