• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.379-405
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• 2022

We introduce the notions of Koszul N-complex, Čech N-complex and telescope N-complex, explicit derived torsion and derived completion functors in the derived category D_N (R) of N-complexes using the Čech N-complex and the telescope N-complex. Moreover, we give an equivalence between the categories of cohomologically 𝖆-torsion N-complexes and cohomologically 𝖆-adic complete N-complexes, and prove that over a commutative Noetherian ring, via Koszul cohomology, via RHom cohomology (resp. ⊗ cohomology) and via local cohomology (resp. derived completion), all yield the same invariant.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.161-170
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• 1995

A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. Takagi [12] and Berndt [2] classified all homogeneous real hypersufaces of $P_nC$ and $H_nC$.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.369-383
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• 1994

A complex n-dimensional Kahler manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_{n}$ (c). A complete and simply connected complex space form consists of a complex projective space $P_{n}$ C, a complex Euclidean space $C^{n}$ or a complex hyperbolic space $H_{n}$ C, according as c > 0, c = 0 or c < 0.(omitted)

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.471-482
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• 1995

A complex n-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a comples space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form consists of a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. The induced almost contact metric structure of a real hypersurface M of $M_n(c)$ is denoted by $(\phi, \zeta, \eta, g)$.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.173-184
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• 1997

An n-dimensional complex space form $M_n(c)$ is a Kaehlerian manifold of constant holomorphic sectional curvature c. As is well known, complete and simply connected complex space forms are a complex projective space $P_n C$, a complex Euclidean space $C_n$ or a complex hyperbolic space $H_n C$ according as c > 0, c = 0 or c < 0.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.835-848
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• 1995

Let $M_n$(c) be an n-dimensional complete and simply connected Kahlerian manifold of constant holomorphic sectional curvature c, which is called a complex space form. Then according to c > 0, c = 0 or c < 0 it is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$.

• Bulletin of the Korean Chemical Society
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• v.20 no.10
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• pp.1200-1204
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• 1999

The reactions of Ru(tpy)Cl3 (tpy = 2,2';6',2"-terpyridine) with new N,N,C-terdentate ligands, 3,2'-annulated-6-(2"-pyridyl)-2-phenylpyridines (1, HL) and the properties of their Ru(II) complexes are described. The distribution ratio of the two possible Ru(II) complexes, a pentaaza-coordinated complex [Ru(tpy)(1-N,N')Cl]+ and a cycloruthenated complex [Ru(tpy)(La-N,N',C)]+ are highly dependent on the length of the polymethylene unit. The trimethylene bridge of the N,N,C-terdentate in pentaaza-coordinated complex is rigid enough to induce an asymmetry in the complex.

• Journal of the Korean Chemical Society
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• v.24 no.4
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• pp.302-309
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• 1980

The solubilities of n-propyl bromide in nitrobenzene and in 1,2,4-trichlorobenzene have been measured at 19, 25 and $40^{\circ}C$ in the presence and absence of gallium bromide. When gallium bromide does not exist in the system, the solubility of n-propyl bromide in nitrobenzene is greater than in 1,2,4-trichlorobenzene, indicating a stronger interaction of n-propyl bromide with nitrobenzene than with 1,2,4-trichlorobenzene. In the presence of gallium bromide, 1: 1 complex $n-C_3H_7Br\cdotGaBr_3$ is formed in the solution. The instability constant K of the complex was evaluated. $$n-C_3H_7Br\cdotGaBr_3 \rightleftarrows n-C_3H_7Br ＋ \frac{1}{2Ga_2Br_6 }$$The change of enthalpy, free energy and entropy for the dissociation of the complex were also calculated. It seems that the stabilities of the complex, gallium bromide with alkyl bromide, are relatively concerned with the stabilities of the alkyl ion.

• Journal of the Korean Chemical Society
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• v.15 no.5
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• pp.228-235
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• 1971

The solubilities of n-butyl bromide in nitrobenzene and in 1,2,4-trichlorobenzene have been measured at $19^{\circ},\;25^{\circ},\;and\;40^{\circ}C$ in the presence and absence of gallium bromide. When gallium bromide does not exist in the system, the solubility of n-butyl bromide in nitrobenzene is greater than in 1,2,4-trichlorobenzene, indicating a stronger interaction of n-butyl bromide with nitrobenzene than with 1,2,4-trichlorobenzene. In the presence of gallium bromide, complex of n-butyl bromide with gallium bromide, 1:1 complex, $n-C_4H_9Br{\cdot}GaBr_3$, is formed in the solution. The instability constant K of the complex was evaluated. $n-C_4H_9Br{\cdot}GaBr_3{\rightleftharpoons}n-C_4H_9Br+\frac{1}{2}Ga_2Br_6$ The changes of enthalpy, free energy and entropy for the dissociation of the complex were also calculated.

• Bulletin of the Korean Chemical Society
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• v.25 no.6
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• pp.796-800
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• 2004

The structure of [Cu(tpen)]$(ClO_4)_2$ (tpen = N,N,N',N'-tetrakis(2-pyridylmethyl)-1,2-ethanediamine) has been identified by X-ray crystallography. The copper(II) ion is surrounded by two amine N atoms and three pyridine N atoms of the ligand, making a distorted trigonal-bipyramid. Among the six potential N donor atoms (two amine N and four pyridine N atoms), only one pyridine N atom remains uncoordinated. We examined structural changes on addition of $Cl^-$ to $[Cu(tpen)]^{2+}$(1). The addition of $Cl^-$ in methanol resulted in the formation of a novel dinuclear copper(II) complex $[Cu_2Cl_2(tpen)](ClO_4)_2{\cdot}H_2O$. The structure of the dinuclear complex was verified by X-ray crystallography. Each copper(II) ion in the dinuclear complex showed a distorted square planar geometry with two pyridine N atoms, one amine N atom and one $Cl^-$ ion.