• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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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.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.48 no.10
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• pp.13-19
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• 2011

This study is to explore the causes for weak signal areas and suggest solutions for the problem of weak signal areas through the experiments for location error of satellite navigation system depending on the characteristics of locations. For kinematic point positioning, a moving object can have different number of satellite navigation systems available depending on its location. It has to receive location data from at least four satellite navigation systems for precise point positioning. However, drastic urbanization and poor surroundings have caused greater location error and weak signal areas. To reduce location error and remove the occurrence of weak signal areas, it is necessary to verify the characteristics of metropolitan surroundings. Therefore, experiments were conducted to measure location error and discover the causes for the occurrence of weak signal areas in metropolitan area, residential area, woods, ocean area, and open ground. In addition, this study suggests a point positioning algorithm with high precision suitable for local surroundings and an algorithm to remove weak signal areas.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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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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• v.31 no.6
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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.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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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.

• Proceedings of the KSR Conference
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• 2006.11b
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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.