• Kyungpook Mathematical Journal
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• 제63권3호
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• pp.413-424
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• 2023

The main purpose of this paper is to show that over a large class of bounded domains Ω ⊂ ℂ², for 1 < p < ∞, the Bergman projection 𝓟 is bounded from L^p(Ω, dV ) to the Bergman space A^p(Ω); from L^∞(Ω) to the holomorphic Bloch space BlHol(Ω); and from L¹(Ω, P(z, z)dV) to the holomorphic Besov space Besov(Ω), where P(ζ, z) is the Bergman kernel for Ω.

• 대한수학회보
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• 제61권3호
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• pp.671-697
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• 2024

In this paper, we formally introduce the notion of a general parametric digamma function Ψ(−s; A, a) and we find the Laurent expansion of Ψ(−s; A, a) at the integers and poles. Considering the contour integrations involving Ψ(−s; A, a), we present some new identities for infinite series involving Dirichlet type parametric harmonic numbers by using the method of residue computation. Then applying these formulas obtained, we establish some explicit relations of parametric linear Euler sums and some special functions (e.g. trigonometric functions, digamma functions, Hurwitz zeta functions etc.). Moreover, some illustrative special cases as well as immediate consequences of the main results are also considered.

• East Asian mathematical journal
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• 제40권3호
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• pp.319-328
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• 2024

We establish an existence result for a positive solution to the Schrödinger-type singular semipositone problem: $-{\Delta}u\,=\,V(x)u\,=\,{\lambda}{\frac{f(u)}{u^{\alpha}}}$ in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝ^N , N > 2, λ ∈ ℝ is a positive parameter, V ∈ L^∞(Ω), 0 < α < 1, f ∈ C([0, ∞), ℝ) with f(0) < 0. In particular, when ${\frac{f(s)}{s^{\alpha}}}$ is sublinear at infinity, we establish the existence of a positive solutions for λ ≫ 1. The proofs are mainly based on the sub and supersolution method. Further, we extend our existence result to infinite semipositone problems with mixed boundary conditions.

• 대한조선학회논문집
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• 제41권6호
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• pp.75-83
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• 2004

Ice rubble pieces broken by the bow impact load and side hull of an icebreaking vessel usually pass along the ship's bottom hull and may hit the propeller/rudder or other stern structures causing serious damage to ship's hull . Therefore it is important to estimate the size of broken ice pieces during the icebreaking process. The dynamic interaction process of icebreaker with infinite ice sheet is simplified as a wedge type beam of finite length supported by elastic foundation. The wedge type ice beam is leaded with vertical impact forces due to the inclined bow stem of icebreaking vessels. The numerical model provides locations of maximum dynamic bending moment where extreme tensile stress arises and also possible fracture occurs. The model can predict a failure length of broken ice sheet given design parameters. The results are compared to Nevel(1961)'s analytical solution for static load and observed pattern of ice sheet failure onboard an icebreaker. Also by comparing computed failure length with the characteristic length, the meaning of ice rubble sizes is discussed.

• 대한수학회논문집
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• 제29권1호
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• pp.155-161
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• 2014

Let M be a complete Riemannian manifold and let N be a Riemannian manifold of non-positive sectional curvature. Assume that $Ric^M{\geq}-\frac{4(p-1)}{p^2}{\mu}_0$ at all $x{\in}M$ and Vol(M) is infinite, where ${\mu}_0$ > 0 is the infimum of the spectrum of the Laplacian acting on $L^2$-functions on M. Then any p-harmonic map ${\phi}:M{\rightarrow}N$ of finite p-energy is constant Also, we study Liouville type theorem for p-harmonic morphism.

• 한국해안·해양공학회논문집
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• 제27권6호
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• pp.424-433
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• 2015

본 연구에서는 회절을 고려하여 반무한방파제 형식의 직립식 장대구조물에 작용하는 파력에 대해 검토하였다. 장대구조물에 작용하는 파력은 규칙파, 일방향 불규칙파 및 다방향 불규칙파를 대상으로 하였다. 방파제 전면 및 후면에서 발생하는 회절을 모두 고려하였다. 방파제의 상대길이(1/L)가 0인 경우 방파제에 작용하는 파력은 회절에 의해 0이 된다. 방파제의 상대길이가 1.0 이하인 경우에는 회절의 영향이 비교적 강하였으며, 방파제의 상대길이가 0.5 이상인 경우에는 방파제의 장대화 효과에 의해 작용 파력이 크게 감소하였다. 즉, 방파제의 상대길이가 1.0 이하인 경우에는 회절효과의 고려가 필요하며, 장대 방파제의 파력 감소효과를 얻기 위해서는 방파제의 상대길이가 최소 0.5 이상이어야 함을 알 수 있다.

• 한국수학사학회지
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• 제13권2호
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• pp.87-94
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• 2000

This paper investigates history and modern developments concerning spatial decay estimates for solutions in a semi-infinite cylinder or strip, in which model equations are defined with appropriate homogeneous lateral boundary conditions and initial conditions but left end boundary data are assumed. Our aim is to show this Saint-Venant type decay rate dependent critically on the Poincare constant resulting from characterizing variational principles.

• 한국수학사학회지
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• 제16권2호
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• pp.117-128
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• 2003

We investigate the origin and recent history for fuzzy equations. And we introduce the existence theorems of solutions for the fuzzy differential equation with infinite delays and fuzzy functional integral equations. We will also recent researches for controllability of sobolev-type semilinear integro-differential fuzzy system.

• 대한수학회지
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• 제43권3호
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• pp.677-690
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• 2006

We show that a group of three closure properties including the selectively Pytkeev property coincide on $C_k$(X) for a locally compact X. We also introduce a new game characterization of these properties for such spaces.

• Korean Journal of Mathematics
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• 제27권1호
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• pp.53-62
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• 2019

Recently, an infinite class of finitely based finite involution semigroups with non-finitely based semigroup reducts have been found. In contrast, only one example of the opposite type-non-finitely based finite involution semigroups with finitely based semigroup reducts-has so far been published. In the present article, a sufficient condition is established under which an involution semigroup is non-finitely based. This result is then applied to exhibit several examples of the desired opposite type.