• Honam Mathematical Journal
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• v.2 no.1
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• pp.37-44
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• 1980

우리는 먼저 Principal G-bundle와 성질을 살피고 representation of G over C를 irreducible CG-space의 direct sum으로 표시하여 Schur's Lemma를 이용하면 E가 임의의 CG-space, ${\sigma}E=Hom_c(E{\sigma},E)$라 할 때 ${\oplus}_{\sigma}(E_{\sigma}{\otimes}{\sigma}E){\rightarrow}E$ 가 G-ismorphism이 됨을 알아본다. 본 논문의 목적은 이러한 결과를 이용하여 K(X)와 $K_G(X)$의 관계를 구명하는데 있다.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1411-1440
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• 2017

We study free actions of finite groups on 3-dimensional nil-manifolds with the first homology ${\mathbb{Z}}^2{\oplus}{\mathbb{Z}}_p$. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal nilpotent subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.1 no.1
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• pp.43-53
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• 1988

The main result of this paper is a characterization of almost projective modules over art in algebras by means of irreducible maps and almost split sequences. A module X is an almost projective module if and only if it has a presentation $0{\longrightarrow}L{\longrightarrow^{\alpha}}P{\longrightarrow}X{\longrightarrow}0$ with projective module P and irreducible maps ${\alpha}$. Let X be an injective almost projective non simple module and $0{\rightarrow}Dtr(x){\rightarrow}E{\rightarrow}X{\rightarrow}0$ be an almost split sequence. If $E=E_1{\oplus}E_2$ is a direct decomposition of indecomposable modules then ${\ell}(X)=3$.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.9-23
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• 2002

For a closed densely defined linear operator T on a Hilbert space H, let ${\prod}$ denote the function which corresponds to T, the orthogonal projection from $H{\oplus}H$ onto the graph of T. We extend some ordinary norm ineqralites comparing ${\parallel}{\Pi}(A)-{\Pi}(B){\parallel}$ and ${\parallel}A-B{\parallel}$ to the Schatten p-norm where A and B are bounded operators on H.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.455-467
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• 2014

In this paper, we consider the additive set-valued functional equation $nf(\sum_{i=1}^{n}x_i)=\sum_{i=1}^{n}f(x_i){\oplus}\sum_{1{\leq}i<j{\leq}n}f(x_i+x_j)$ where $n{\geq}2$ is an integer, and prove the Hyers-Ulam stability of the functional equation.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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• pp.365-381
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• 2019

We study free actions of finite nonabelian groups on 3-dimensional nilmanifolds with the first homology ${\mathbb{Z}}^2{\oplus}{\mathbb{Z}}_2$, up to topological conjugacy. We show that there exist three kinds of nonabelian group actions in ${\pi}_1$, two in ${\pi}_2$ or ${\pi}_{5,i}$(i = 1, 2, 3), one in the other cases, and clarify what those groups are.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.81-89
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• 2021

In this paper, we introduce the notions of a distance function, Alexandrov topology and ⊖-upper (⊕-lower) approximation operator based on complete co-residuated lattices. Under various relations, we define (⊕, ⊖)-fuzzy rough set on complete co-residuated lattices. Moreover, we study their properties and give their examples.

• Journal for History of Mathematics
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• v.25 no.3
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• pp.29-39
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• 2012

As a product of modern proof theory, linear logic is a new form of logic developed for the purpose of enhancing programming language by Professor Jean-Yves Girard of Marseille University (France) in 1987 by supplementing intuitionist logic in a sophisticated manner. Thus, linear logic' s connectives can be explained using information processing terms such as sequentiality and parallel computation. For instance, A${\otimes}$B shows two processes, A and B, carried out one after another. A&B is linked to an internal indeterminate, allowing an observer to select either A or B. A${\oplus}$B is an external indeterminate, and as such, an observer knows that either A or B holds true, but does not know which process will be true. A ${\wp}$ B signifies parallel computation of process A and process B; linear negative exhibits synchronization, that is, in order for the process A to be carried out, both A and $A^{\bot}$ have to be accomplished simultaneously. Since the field of linear logic is not very active in Korea at present, this paper deals only with syntax aspect of linear logic in order to arouse interest in the subject, leaving semantics and proof nets for future studies.

• Analytical Science and Technology
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• v.8 no.3
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• pp.249-258
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• 1995

The polymers, polyazine, polyazomethine ( I ) and polyazomethine ( II ) were prepared by the condensation of p-benzoquinone with hydrazine hydrate, p-phenylenediamine and diaminomaleonitrile in DMSO, respectively. The IR spectra of these polymers showed a characteristic peak of schiff base (-C=N-) at about $1600cm^{-1}$. These polymers dissolved in concentrated sulfuric acid showed UV/VIS absorption near 300nm indicatiog the presence of iminium ion(>$C\limits^{\small\oplus}=NH-$). Another UV/VIS absorption band in the region of 350~415nm was shown presumably due to the charge transfer transition in the molecule. The electrical conductivities of polyazine, polyazomethine ( I ) and ( II ) were measured. The self-electrical conductivity of these was found to be about $10^{-14}{\sim}10^{-11}{\Omega}^{-1}cm^{-1}$ and these polymers doped with $I_2$ showed the maximum conductivity of about $10^{-2}{\Omega}^{-1}cm^{-1}$.