• 대한수학회지
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• 제59권2호
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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.

• 대한수학회지
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• 제32권2호
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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 $H_nC$.

• 대한수학회논문집
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• 제9권2호
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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)

• 대한수학회지
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• 제32권3호
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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 $(\phi, \zeta, \eta, g)$.

• 대한수학회보
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• 제34권2호
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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.

• 대한수학회지
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• 제32권4호
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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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• 제20권10호
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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.

• 대한화학회지
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• 제24권4호
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• pp.302-309
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• 1980

니트로벤젠 및 1,2,4-트리클로로벤젠에서의 n-브롬화프로필의 溶解度를 19, 25, 40^{\circ}C$에서 브롬화갈륨이 있을 때와 없을 때에 각각 측정하여 보았다. 브롬화갈륨이 존재하지 않을때에 니트로벤젠에서의 n-브롬화프로필의 溶解度가 1,2,4-트리클로로벤젠에서보다 더 큰 점은 n-브롬화프로필과 니트로벤젠과의 상호작용이 1,2,4-트리클로로벤젠보다 더 강하다는 것을 나타낸다. 브롬화갈륨이 존재할 때에는 溶液內에서 n-브롬화프로필과 브롬화갈륨의 1:1 complex, $n-C_3H_7Br\cdotGaBr_3$가 형성된다. 이 complex의 instability constant K를 계산하였다. $$n-C_3H_7Br\cdotGaBr_3 \rightleftarrows n-C_3H_7Br ＋ \frac{1}{2Ga_2Br_6 }$$또한 이 complex의 解離에 대한 엔탈피, 자유에너지 및 엔트로피도 산출하였다. 브롬화갈륨과 브롬화알킨간의 complex의 안정도는 이들 알킬이온의 안정도와 상대적인 관계가 있다고 본다.

• 대한화학회지
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• 제15권5호
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• pp.228-235
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• 1971

니트로벤젠 및 1,2,4-트리클로로벤젠에서의 n-브롬화부틸의 溶解度를 $19^{\circ},\;25^{\circ},\;40^{\circ}C$에서 브롬화갈륨이 있을때와 없을때에 각각 測定하여 보았다. 브롬화갈륨이 存在하지 않을때에 니트로벤젠에서의 n-브롬화부틸의 溶解度가 1,2,4-트리클로로벤젠 보다 더 큰점은 n-브롬화부틸과 니트로벤젠과의 相互作用이 1,2,4-트리클로로벤젠 보다 더 강하다는 것을 나타낸다. 브롬화갈륨이 存在할 때에는 溶液內에서 n-브롬화부틸과 브롬화갈륨의 1:1 complex, $n-C_4H_9Br{\cdot}GaBr_3$가 형성된다. 이 complex의 instability constant K를 計算하였다. $n-C_4H_9Br{\cdot}GaBr_3{\\rightleftharpoons}n-C_4H_9Br+\frac{1}{2}Ga_2Br_6$ 또한 이 complex의 解離에 대한 엔탈피, 자유에너지 및 엔트로피도 산출하였다.

• Bulletin of the Korean Chemical Society
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• 제25권6호
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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.