• 대한수학회보
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• 제33권4호
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• pp.619-629
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• 1996

In studying smooth 4-manifolds the Donaldson invariant has played a central role. In [D1] Donaldson showed that non-vanishing Donaldson invariant of a smooth closed oriented 4-manifold X gives rise to the indecomposability of X. For instance, the complex algebraic suface X cannot decompose to a connected sum $X_1 #X_2$ with both $b_2^+(X_i) > 0$.

• 대한수학회보
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• 제47권5호
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• pp.951-960
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• 2010

We provide the set of left-invariant minimal unit vector fields on the semi-direct product $\mathbb{R}^n\;{\rtimes}_p\mathbb{R}$, where P is a nonsingular diagonal matrix and on the 7 classes of 4-dimensional solvable Lie groups of the form $\mathbb{R}^3\;{\rtimes}_p\mathbb{R}$ which are unimodular and of type (R).

• 대한수학회논문집
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• 제18권2호
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• pp.309-323
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• 2003

In this paper, We characterize a semi-invariant sub-manifold of codimension 3 satisfying ∇$\varepsilon$A = 0 in a complex projective space CP$\^$n+1/, where ∇$\varepsilon$A is the covariant derivative of the shape operator A in the direction of the distinguished normal with respect to the structure vector field $\varepsilon$.

• 대한수학회논문집
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• 제33권4호
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• pp.1331-1339
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• 2018

In this paper the decomposition of basic equations of $(LCS)_n$-manifolds is carried out into horizontal and vertical projections. Further, we study the integrability of the distributions $D,D{\oplus}[{\xi}]$ and $D^{\perp}$ totally geodesic of semi-invariant submanifolds of $(LCS)_n$-manifold.

• Kyungpook Mathematical Journal
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• 제53권4호
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• pp.515-540
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• 2013

Let $G=O(2){\times}O(2){\times}O(2)$. Then a closed G-invariant minimal hypersurface with constant scalar curvature in $S^5$ is a product of spheres, i.e., the square norm of its second fundamental form, S = 4.

• 충청수학회지
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• 제26권1호
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• pp.213-219
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• 2013

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, we compute the Galois actions of a class invariant from a generalized Weber function $g_1$ over imaginary quadratic number fields with discriminant $D{\equiv}64(mod72)$.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.385-395
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• 2013

To analyze the enzyme reaction on DNA knots and links, we study tangle embedding and the number of reaction. By using the quantum SU(3) invariant of knots and links we get a necessary condition for a tangle to be embedded in a knot or link. Moreover we give a relationship between the number of reactions and the changes of the value of quantum SU(3) invariant for the corresponding knots and links in a processive recombination.

• 충청수학회지
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• 제24권4호
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• pp.921-925
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• 2011

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}21$ (mod 36).

• East Asian mathematical journal
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• 제35권1호
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• pp.9-15
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• 2019

Kaavya introduce an involution on the set of partitions with crank 0 and studied the number of partitions of n which are invariant under Kaavya's involution. If a partition ${\lambda}$ with crank 0 is invariant under her involution, we say ${\lambda}$ is a self-conjugate partition with crank 0. We prove that the number of such partitions of n is equal to the number of partitions with rank 0 which are invariant under the usual partition conjugation. We also study arithmetic properties of such partitions and their q-theoretic implication.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.277-294
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• 2021

In this paper, we introduce the notions of Wijsman regularly invariant convergence types, Wijsman regularly (${\mathcal{I}}_{\sigma}$, ${\mathcal{I}}^{\sigma}_2$)-convergence, Wijsman regularly (${\mathcal{I}}^*_{\sigma}$, ${\mathcal{I}}^{{\sigma}*}_2$)-convergence, Wijsman regularly (${\mathcal{I}}_{\sigma}$, ${\mathcal{I}}^{\sigma}_2$) -Cauchy double sequence and Wijsman regularly (${\mathcal{I}}^*_{\sigma}$, ${\mathcal{I}}^{{\sigma}*}_2$)-Cauchy double sequence of sets. Also, we investigate the relationships among this new notions.