• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.635-648
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• 2022

We discuss the wellposedness of the Neumann problem on a half-space for the Kohn-Laplacian in the Heisenberg group. We then construct the Neumann function and explicitly represent the solution of the associated inhomogeneous problem.

• East Asian mathematical journal
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• v.39 no.3
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• pp.305-317
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• 2023

We establish the existence and uniqueness of Green functions in Lipschitz domains for stationary Stokes systems with Neumann boundary conditions. For the uniqueness, we impose a different normalization condition from that in Choi et al. (J. Math. Fluid Mech., 20(4):1745-1769, 2018).

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.65-71
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• 2019

This paper is concerned with the existence of positive solutions of the nonlinear Neumann boundary value problems $$\{u^{{\prime}{\prime}}+a(t)u={\lambda}b(t)f(u),\;t{\in}(0,1),\\u^{\prime}(0)=u^{\prime}(1)=0$$, where $a,b{\in}C[0,1]$ with $a(t)>0,\;b(t){\geq}0$ and the Green's function of the linear problem $$\{u^{{\prime}{\prime}}+a(t)u=0,\;t{\in}(0,1),\\u^{\prime}(0)=u^{\prime}(1)=0$$ may change its sign on $[0,1]{\times}[0,1]$. Our analysis relies on the Leray-Schauder fixed point theorem.

• Proceedings of the Acoustical Society of Korea Conference
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• 1998.06c
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• pp.261-264
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• 1998

본 논문에서는 MIT 머리전달함수(Head-Related Transfer Function; HRTF)와 Neumann의 머리전달함수를 이용하여 머리전달함수가 음성정위에 미치는 영향을 비교분석하였다. 이를 위하여 머리전달함수의 측정조건과 시간 및 주파수특성을 비교 분석하였고 청취실에 헤드폰 재생을 통하여 $10^{\circ}$간격으로 음상정위에 대한 주관평가들 실시하였으며, 주관평가 자료를 이용하여 개인과 전체 평균에 대한 방향 지각 에러(각도)를 계산하였다. 실험결과, MIT 머리전달함수에 비하여 Neumann 머리전달함수를 이용한 음상정위가 양호하게 나타났으며 음질에 대해서도 청취자들은 Neumann 머리전달함수에 의한 재생음이 보다 자연스럽고, 명확한 품질을 갖는다고 답하였다.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.509-518
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• 2001

The purpose of this paper is to propose a numerical algorithm for the problem of coefficient identification of the scalar wave equation based on a local observation on the boundary: Determine the unknown coefficient function with the knowledge of simultaneous Dirichlet and Neumann boundary values on a part of boundary. To find the unknown coefficient function, the unknown Neumann boundary value is also identified. We recast our inverse problem to variational problem. The gradient method is applied to find the minimizing functions. We confirm the effectiveness of our algorithm by numerical experiments.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.115-128
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• 2009

In this paper, we modify the axiom of infinity of von Neumann's axioms modified by Pinter([5]), and then discuss an existence of an unknowable class in the system and a relationship between the unknowable class and the axiom of choice.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.789-830
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• 2003

By forming completions of families of noncommutative polynomials, we define a notion of noncommutative continuous function and locally bounded Borel function that give a noncommutative analogue of the functional calculus for elements of commutative $C^{*}$-algebras and von Neumann algebras. These notions give a precise meaning to $C^{*}$-algebras defined by generator and relations and we show how they relate to many parts of operator and operator algebra theory.

• Kyungpook Mathematical Journal
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• v.20 no.1
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• pp.95-103
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• 1980

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.2
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• pp.1-10
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• 1987

The wave resistance of ships is calculated with the numerical solution of the Newmann-Kelvin problem. For the sake of the numerical evaluation of the Green function, Shen and Farell's method is used[7]. In particular, the contribution of the line integral term in the Neumann-Kelvin problem to the calculated values of the wave resistance is shown. For the Wigley's hull the calculated values of the wave resistance and the wave profiles at the hull surface are in fairly good agreement with the experimental data. However, for the series 60 hull and the practical hull, a 454,000 cubic feet reefer vessel, the calculated results of the wave resistance show definte hollows and humps considering the experimental result.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1805-1821
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• 2016

In this paper, we are concerned with the nonlinear elliptic equations of the p(x)-Laplace type $$\{\begin{array}{lll}-div(a(x,{\nabla}u))+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u) && in\;{\Omega}\\(a(x,{\nabla}u)\frac{{\partial}u}{{\partial}n}={\lambda}{\theta}g(x,u) && on\;{\partial}{\Omega},\end{array}$$ which is subject to nonlinear Neumann boundary condition. Here the function a(x, v) is of type${\mid}v{\mid}^{p(x)-2}v$ with continuous function $p:{\bar{\Omega}}{\rightarrow}(1,{\infty})$ and the functions f, g satisfy a $Carath{\acute{e}}odory$ condition. The main purpose of this paper is to establish the existence of at least three solutions for the above problem by applying three critical points theory due to Ricceri. Furthermore, we localize three critical points interval for the given problem as applications of the theorem introduced by Arcoya and Carmona.