• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권3호
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• pp.289-307
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• 2023

We prove some common fixed point theorems for β-non-decreasing mappings under contraction mapping principle on partially ordered metric spaces. We study the existence of solution for periodic boundary value problems and also give an example to show the degree of validity of our hypothesis. Our results improve and generalize various known results.

• 한국측량학회지
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• 제23권2호
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• pp.211-217
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• 2005

경계를 설정하기 위한 일반적인 방법은 등거리원칙이다. 등거리원칙은 각각의 기준선 또는 기준점의 경계에서 일정한 거리까지를 경계로 정하는 방법이다. 오랜 동안 해양의 공평한 경계를 정의하기 위한 노력이 진행되어, 모든 나라들이 적용할 수 있는 대양의 사용규제에 대한 단일협정인 유엔해양법협약이 채택되었다. 그 내용은 결국 당사국 간의 "공평"을 대원칙으로 한다는 것이다. 본 연구에서는 이러한 경계를 설정하는데 있어서의 한${\cdot}$일 양국의 실질적인 경계획선 방법에 대해 분석${\cdot}$비교하였다. 이를 위해 먼저 경계획선 과정에서의 기본이자 핵심이라 할 수 있는 양국의 측지계산 알고리즘을 분석하여 비교하였다. 양국의 실질적인 경계획선 알고리즘을 비교하기 위해 여러 가지 테스트를 수행하였다. 이에 향후 해양경계획정에 대비하여 효과적인 해양경계획선 알고리즘인 Three-Point 알고리즘을 제안한다. 또한 일본의 해양경계획선 알고리즘과의 비교를 통하여, 향후 경계분쟁에 대비한 기술적인 능력을 확보한다.

• 대한수학회보
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• 제36권4호
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• pp.637-647
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• 1999

In this paper, we consider a free boundary problem with Pushchino dynamics satisfying the Dirichlet boundary condition. We shall the stationary solutions ($v^{*}(x),s^{*}$) exist and the Hopf bifurcation occurs at a critical point when s $\in$ (1/3,1).

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.697-710
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• 2010

In this paper, we prove existence of infinitely many positive and concave solutions, by means of a simple approach, to $3^{th}$ order three-point singular boundary value problem {$x^{\prime\prime\prime}(t)=\alpha(t)f(t,x(t))$, 0 < t < 1, $x(0)=x'(\eta)=x^{\prime\prime}(1)=0$, (1/2 < $\eta$ < 1). Moreover with respect to multiplicity of solutions, we don't assume any monotonicity on the nonlinearity. We rely on a combination of the analysis of the corresponding vector field on the phase-space along with Knesser's type properties of the solutions funnel and the well-known Krasnosel'ski$\breve{i}$'s fixed point theorem. The later is applied on a new very simple cone K, just on the plane $R^2$. These extensions justify the efficiency of our new approach compared to the commonly used one, where the cone $K\;{\subset}\;C$ ([0, 1], $\mathbb{R}$) and the existence of a positive Green's function is a necessity.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1323-1329
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• 2010

In this paper, a new fixed point theorem in cone is applied to obtain the existence of at least one positive pseudo-symmetric solution for the second order three-point boundary value problem {x" + f(t, x, x')=0, t $\in$ (0, 1), x(0)=0, x(1)=x($\eta$), where f is nonnegative continuous function; ${\eta}\;{\in}$ (0, 1) and f(t, u, v) = f(1+$\eta$-t, u, -v).

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1273-1287
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• 2008

In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• International Journal of Internet, Broadcasting and Communication
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• 제11권1호
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• pp.39-46
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• 2019

This paper proposes an adaptive threshold watershed algorithm, which is the method used for image segmentation and boundary detection, which extends the region on the basis of regional minimum point. First, apply adaptive thresholds to determine regional minimum points. Second, it extends the region by applying adaptive thresholds based on determined regional minimum points. Traditional watershed algorithms create over-segmentation, resulting in the disadvantages of breaking boundaries between regions. These segmentation results mainly from the boundary of the object, creating an inaccurate region. To solve these problems, this paper applies an improved watershed algorithm applied with adaptive threshold in regional minimum point search and region expansion in order to reduce over-segmentation and breaking the boundary of region. This resulted in over-segmentation suppression and the result of having the boundary of precisely divided regions. The experimental results show that the proposed algorithm can apply adaptive thresholds to reduce the number of segmented regions and see that the segmented boundary parts are correct.

• 대한수학회보
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• 제58권1호
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• pp.71-111
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• 2021

We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence �� from the set of equivalent well-posed two-point boundary conditions to gl(4, ℂ). Using ��, we derive eigenconditions for the integral operator ��M for each well-posed two-point boundary condition represented by M ∈ gl(4, 8, ℂ). Special features of our eigenconditions include; (1) they isolate the effect of the boundary condition M on Spec ��M, (2) they connect Spec ��M to Spec ����,α,k whose structure has been well understood. Using our eigenconditions, we show that, for each nonzero real λ ∉ Spec ����,α,k, there exists a real well-posed boundary condition M such that λ ∈ Spec ��M. This in particular shows that the integral operators ��M, arising from well-posed boundary conditions, may not be positive nor contractive in general, as opposed to ����,α,k.

• 지적과 국토정보
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• 제45권2호
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• pp.101-116
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• 2015

경계점좌표 등록지역에서 지적공부 세계측지계 변환의 정확도는 기준점 측량성과에 의해 결정된다. 하지만 현재 기준점 측량성과는 등록 당시 측량기술과 방식의 한계로 인해 불균질한 성과를 나타내고 있으며, 사업지구별 특성이나 형성 시기에 따라 다양한 오차를 가지고 있다. 따라서 본 연구에서는 경계점좌표 등록지역 사례에 대해 사업지구 유형별 오차 원인을 규명하고, 세계측지계 변환과 검증측량을 통해 최적의 측지계 변환방법과 정확도의 향상 방안을 제시하였다.

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.269-284
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• 2016

In this paper, we firstly use Krasnosel'skii fixed point theorem to investigate positive solutions for the following three-point boundary value problems for p-Laplacian with a parameter $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+{\lambda}f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1), λ > 0 is a parameter. Then we use Leggett-Williams fixed point theorem to study the existence of three positive solutions for the fractional boundary value problem $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1).