• 대한수학회보
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• 제34권4호
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• pp.653-665
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• 1997

We define an almost quaternionic Kaehler product manifold and study its submanifolds. Moreover we construct the curvature tensor of the product manifold of two quaternionic forms.

• Journal of the Korean Data and Information Science Society
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• 제25권1호
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• pp.19-26
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• 2014

다항 로지스틱 회귀모형의 설명변수가 연속형과 범주형을 모두 포함할 때 범주형 설명변수는 직합을 적용하고 연속형 설명변수는 텐서곱을 적용하는 모형을 제안한다. 변수선택의 기준으로 BIC를 사용하고, 제안된 모형의 알고리즘을 구현하였다. 구현된 알고리즘을 실제 자료에 적용하여 기존의 방법과 비교하여 제안된 모형이 더 좋은 분류율을 보임을 확인하였다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권1호
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• pp.1-19
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• 2024

In this paper, the notions of strong Connes amenability for certain products of Banach algebras and module extension of dual Banach algebras is investigated. We characterize χ ⊗ η-strong Connes amenability of projective tensor product ${\mathbb{K}}{\hat{\bigotimes}}{\mathbb{H}}$ via χ ⊗ η-σwc virtual diagonals, where χ ∈ 𝕂_* and η ∈ ℍ_* are linear functionals on dual Banach algebras 𝕂 and ℍ, respectively. Also, we present some conditions for the existence of (χ, θ)-σwc virtual diagonals in the θ-Lau product of 𝕂 ×_θ ℍ. Finally, we characterize the notion of (χ, 0)-strong Connes amenability for module extension of dual Banach algebras 𝕂 ⊕ 𝕏, where 𝕏 is a normal Banach 𝕂-bimodule.

• 수학
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• 제3권1호
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• pp.8-11
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• 1966

• Kyungpook Mathematical Journal
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• 제31권1호
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• pp.119-130
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• 1991

• East Asian mathematical journal
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• 제6권2호
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• pp.193-198
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• 1990

• Kyungpook Mathematical Journal
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• 제29권1호
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• pp.104-113
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• 1989

• Korean Journal of Mathematics
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• 제26권1호
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• pp.75-85
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• 2018

In this paper, we study nonconstant warping functions on an Einstein warped product manifold $M=B{\times}_{f^2}F$ with a warped product metric $g=g_B+f(t)^2g_F$. And we consider a 2-dimensional base manifold B with a metric $g_B=dt^2+(f^{\prime}(t))^2du^2$. As a result, we prove the following: if M is an Einstein warped product manifold with a 2-dimensional base, then there exist generally nonconstant warping functions f(t).

• 대한수학회지
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• 제51권5호
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• pp.1089-1104
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• 2014

An operator $T{\in}L(H)$, is said to belong to k-quasi class $A_n^*$ operator if $$T^{*k}({\mid}T^{n+1}{\mid}^{\frac{2}{n+1}}-{\mid}T^*{\mid}^2)T^k{\geq}O$$ for some positive integer n and some positive integer k. First, we will see some properties of this class of operators and prove Weyl's theorem for algebraically k-quasi class $A_n^*$. Second, we consider the tensor product for k-quasi class $A_n^*$, giving a necessary and sufficient condition for $T{\otimes}S$ to be a k-quasi class $A_n^*$, when T and S are both non-zero operators. Then, the existence of a nontrivial hyperinvariant subspace of k-quasi class $A_n^*$ operator will be shown, and it will also be shown that if X is a Hilbert-Schmidt operator, A and $(B^*)^{-1}$ are k-quasi class $A_n^*$ operators such that AX = XB, then $A^*X=XB^*$. Finally, we will prove the spectrum continuity of this class of operators.

• 대한수학회보
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• 제34권4호
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• pp.525-533
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• 1997

We analysis spectral subspaces of $C^*$-algebras for a compacr group action. And we prove the condition that the fixed point algebra of the product action is the tensor product of the fixed point algebras.