• Korean Journal of Mathematics
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• 제25권3호
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• pp.437-453
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• 2017

A new class of sets, called generalized (${\Lambda}$, b)-closed sets, has been introduced and studied. Also, several properties of generalized (${\Lambda}$, b)-closed sets are investigated. Some characterizations of ${\Lambda}_b$-regular spaces and ${\Lambda}_b$-normal spaces are discussed.

• 대한수학회보
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• 제55권6호
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• pp.1891-1908
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• 2018

In this paper, we investigate the existence of an S-shaped connected component in the set of positive solutions of the Dirichlet problem of the one-dimension Minkowski-curvature equation $$\{\(\frac{u^{\prime}}{\sqrt{1-u^{{\prime}2}}}\)^{\prime}+{\lambda}a(x)f(u)=0,\;x{\in}(0,1),\\u(0)=u(1)=0$$, where ${\lambda}$ is a positive parameter, $f{\in}C[0,{\infty})$, $a{\in}C[0,1]$. The proofs of main results are based upon the bifurcation techniques.

• 대한수학회보
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• 제59권6호
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• pp.1471-1493
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• 2022

The goal of this paper is to establish the boundedness of bilinear Calderón-Zygmund operator BT and its commutator [b₁, b₂, BT] which is generated by b₁, b₂ ∈ BMO(ℝⁿ) (or ${\dot{\Lambda}}_{\alpha}$(ℝⁿ)) and the BT on generalized variable exponent Morrey spaces 𝓛^p(·),𝜑(ℝⁿ). Under assumption that the functions 𝜑₁ and 𝜑₂ satisfy certain conditions, the authors proved that the BT is bounded from product of spaces 𝓛^{p₁(·),𝜑₁}(ℝⁿ)×𝓛^{p₂(·),𝜑₂}(ℝⁿ) into space 𝓛^p(·),𝜑(ℝⁿ). Furthermore, the boundedness of commutator [b₁, b₂, BT] on spaces L^p(·)(ℝⁿ) and on spaces 𝓛^p(·),𝜑(ℝⁿ) is also established.

• 대한수학회보
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• 제59권4호
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• pp.961-977
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• 2022

In this paper, we consider the following Kirchhoff type equation on the whole space $$\{-(a+b{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}\;{\mid}{\nabla}u{\mid}^2dx){\Delta}u=u^5+{\lambda}k(x)g(u),\;x{\in}{\mathbb{R}}^3,\\u{\in}{\mathcal{D}}^{1,2}({\mathbb{R}}^3),$$ where λ > 0 is a real number and k, g satisfy some conditions. We mainly investigate the existence of ground state solution via variational method and concentration-compactness principle.

• Kyungpook Mathematical Journal
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• 제46권4호
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• pp.553-563
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• 2006

Let A be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of A is the set ${\sigma}_{B{\omega}}(A)$ of all ${\lambda}{\in}\mathbb{C}$ such that $A-{\lambda}I$ is not a B-Fredholm operator of index 0. Let E(A) be the set of all isolated eigenvalues of A. Recently in [6] Berkani showed that if A is a hyponormal operator, then A satisfies generalized Weyl's theorem ${\sigma}_{B{\omega}}(A)={\sigma}(A)$\E(A), and the B-Weyl spectrum ${\sigma}_{B{\omega}}(A)$ of A satisfies the spectral mapping theorem. In [51], H. Weyl proved that weyl's theorem holds for hermitian operators. Weyl's theorem has been extended from hermitian operators to hyponormal and Toeplitz operators [12], and to several classes of operators including semi-normal operators ([9], [10]). Recently W. Y. Lee [35] showed that Weyl's theorem holds for algebraically hyponormal operators. R. Curto and Y. M. Han [14] have extended Lee's results to algebraically paranormal operators. In [19] the authors showed that Weyl's theorem holds for algebraically p-hyponormal operators. As Berkani has shown in [5], if the generalized Weyl's theorem holds for A, then so does Weyl's theorem. In this paper all the above results are generalized by proving that generalizedWeyl's theorem holds for the case where A is an algebraically ($p,\;k$)-quasihyponormal or an algebarically paranormal operator which includes all the above mentioned operators.

• 대한화학회지
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• 제34권1호
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• pp.1-9
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• 1990

콜레스테릴 펜타노에이트의 결정은 사방정계에 속하며 a = 21.930(3), b = 21.404(3), c = 6.419(5) $\AA$이며 단위세포안에 4개의 분자가 있다. 1.0 $\sigma$ (I)보다 큰 강도를 가진 1,520개의 회절 반점에 대한 최종 R값은 0.086이다. 직접법에 의하여 구조를 풀었으며 C-H 결합길이와 메틸기는 길이를 고정시켜 이상적인 기하학적 구조에 맞춰 cascade diagonal least-squares refinement에 의하여 정밀화하였다. 테트라시클로 고리는 정상적인 구조를 하고 있으나 에스텔과 곁사슬 부분은 열적효과에 의하여 정상적인 길이와 각도의 값에서 변화를 보이고 있으며 에스텔의 끝부분이 굽어져 치켜들고 있다. 분자는 비결합성 van der waals힘에 의하여 서로 쌓여져 있고 가장 짧은 분자간 거리는 3.529 $\AA$이다.

• Bulletin of the Korean Chemical Society
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• 제11권5호
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• pp.427-430
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• 1990

Cholesteryl aniline ($C_{33}H_{51}N$) is monoclinic, space group $P2_1$, with a = 9.020(3), b = 6.000(1), c = 27.130(9)${\AA},\;{\beta} = 98.22(2)^{\circ}$, Z = 2, Dc = 1.06 g/cm$^3$ and Dm = 1.04 g/cm$^3$. A diffraction data set was collected with Mo-$K_{\alpha}$ radiation (${\lambda} = 0.7107 {\AA}$) on a diffractometer with a graphite monochromator to a maximum 2${\theta}$ value of 50$^{\circ}$, by the ${\omega}-2{\theta}$ scan technique. The coordinates of the non-hydrogen atoms and their anisotropic temperature factors were refined by full-matrix least-squares methods to final R of 0.058. In cholesteryl group, bond distances were normal except in tail part, where high thermal vibration resulted in apparent shortening of the C-C distances. The crystal structure consists of bilayers of thickness $d_{001} = 27.13 {\AA}$, in each of which there is the tail to tail arrangement of molecules aligned in the unit cell with their long axes approximately parallel to the [104] axis. The two halves of the double layer are related to each other by the screw axis.