• 대한수학회보
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• 제54권2호
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• pp.455-461
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• 2017

The Lie algebra analogue of Schur's result which is proved by Moneyhun in 1994, states that if L is a Lie algebra such that dimL/Z(L) = n, then $dimL_{(2)}={\frac{1}{2}}n(n-1)-s$ for some non-negative integer s. In the present paper, we determine the structure of central factor (for s = 0) and the factor Lie algebra $L/Z_2(L)$ (for all $s{\geq}0$) of a finite dimensional nilpotent Lie algebra L, with n-dimensional central factor. Furthermore, by using the concept of n-isoclinism, we discuss an upper bound for the dimension of $L/Z_n(L)$ in terms of $dimL_{(n+1)}$, when the factor Lie algebra $L/Z_n(L)$ is finitely generated and $n{\geq}1$.

• 대한수학회지
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• 제39권1호
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• pp.31-49
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• 2002

An R$^{n}$ -geometry (P$^{n}$ , L) is a generalization of the Euclidean geometry on R$^{n}$ (see Def. 1.1). We can consider some topologies (see Def. 2.2) on the line set L such that the join operation V : P$^{n}$ $\times$ P$^{n}$ \ $\Delta$ longrightarrow L is continuous. It is a notable fact that in the case n = 2 the introduced topologies on L are same and the join operation V : P$^2$ $\times$ P$^2$ \ $\Delta$ longrightarrow L is continuous and open [10, 11]. It is a fundamental topological property of plane geometry, but in the cases n $\geq$ 3, it is no longer true. There are counter examples [2]. Hence, it is a fundamental problem to find suitable topologies on the line set L in an R$^{n}$ -geometry (P$^{n}$ , L) such that these topologies are compatible with the incidence structure of (P$^{n}$ , L). Therefore, we need to study the topologies of the line set L in an R$^{n}$ -geometry (P$^{n}$ , L). In this paper, the relations of such topologies on the line set L are studied.

• 충청수학회지
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• 제26권4호
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• pp.793-798
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• 2013

Let ${\phi}$ be a map of a manifold M into another manifold N, L(N) the bundle of all linear frames over N, and ${\phi}^{-1}$(L(N)) the bundle over M which is induced from ${\phi}$ and L(N). Then, we construct a structure equation for the torsion form in ${\phi}^{-1}$(L(N)) which is induced from a torsion form in L(N).

• 한국응용과학기술학회지
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• 제17권2호
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• pp.99-104
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• 2000

Physical properties and performance characteristics of sodium salt of several pure N-acyl amino acids made from glycine, dl-alanine, sarcosine, dl-valine, l-leucine, l-aspartic acid and l-lysine seven long chain fatty acids are reported. The effect of acyl chain length and the differences in the structure of constituent amino acid of seven homologous series of amide intermediate linked carboxylate surfactant of this class on the properties are discussed.

• 한국진공학회지
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• 제6권S1호
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• pp.154-159
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• 1997

The crystal structure properties of TiN thin films deposited on SKD61 steel and Si(100) substrates by Ion Beam Assisted Deposition have been studied to clarify the thin film growth mechanism by using XRD, RBS, SEM, and AFM. The preferred orientation of TiN thin films changes from (111) to (100) as increasing the assisted energy. This tendency is independent of the substrate structure. The TiN thin film grow with (100) direction having surface free energy minimum as the assisted energy increases.

• Bulletin of the Korean Chemical Society
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• 제28권10호
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• pp.1781-1786
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• 2007

Two copper(II) complexes, [CuL3](ClO4)2 bearing one N-CH2CH2CONH2 group as well as one N-CH2CH2CN group and [CuL4](ClO4)2 bearing two N-CH2CH2CONH2 groups, have been prepared by the selective hydrolysis of [CuL2](ClO4)2 (L2 = C-meso-1,8-bis(cyanoethyl)-5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane). The complex [CuL5](ClO4)2 bearing one N-CH2CH2C(=NH)OCH3 and one N-CH2CH2CN groups has been prepared as the major product from the reaction of [CuL2](ClO4)2 with methanol in the presence of triethylamine. In acidic aqueous solution, the N-CH2CH2C(=NH)OCH3 group of [CuL5](ClO4)2 undergoes hydrolysis to yield [CuL6](ClO4)2 bearing both N-CH2CH2COOCH3 and N-CH2CH2CN groups. The crystal structure of [CuL5](ClO4)2 shows that the complex has a slightly distorted square-pyramidal coordination polyhedron with an apical Cu-N (N-CH2CH2C(=NH)OCH3 group) bond. The apical Cu-N bond distance (2.269(3) A) is ca. 0.06 A longer than the apical Cu-O (N-CH2CH2CONH2 group) bond of [CuL4](ClO4)2. The pendant amide group of [CuL3](ClO4)2 is involved in coordination. The carboxylic ester group of [CuL6](ClO4)2 is also coordinated to the metal ion in various solvents but is removed from the coordination sphere in the solid state.

• 한국정보통신학회논문지
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• 제18권5호
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• pp.1116-1121
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• 2014

메쉬 구조는 대표적인 상호연결망 중 하나로, VLSI 회로 설계 같은 분야에서 많이 이용되고 있다. 이러한 메쉬 구조에서 지름과 고장허용도를 개선한 연결망으로 토러스와 하이퍼-토러스 연결망이 있다. 본 논문에서는 토러스 구조 T(4k,2l)와 하이퍼-토러스 네트워크 QT(m,n) 사이의 임베딩을 분석한다. 토러스 T(4k,2l)는 QT(m,n)에 연장율 5, 밀집율 4, 확장율 1에 임베딩 가능하고, QT(m,n)은 T(4k,2l)에 연장율 3, 밀집율 3, 확장율 1에 임베딩 가능함을 보인다.

• 한국결정학회지
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• 제18권1_2호
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• pp.21-25
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• 2007

Dipyridyl 리간드 L'(N,N'-bis-(1-pyridin-4-yl-ethylidene)-naphthalene-1,5-diamine)을 함유한 $CH_2Cl_2$ 용액을 $Co(NO_3)_2{\cdot}6H_2O$을 함유한 MeOH 용액 위에 깔았을 때, 배위 고분자가 아닌, 분자성 코발트 화합물 [$CoL_2(MeOH)(NO_3)_2$] (1)이 형성되었다. 화합물 1의 X-ray 구조 분석 결과, 이 화합물은 pyridyl-amine 리간드 L(N1-(4-Imino-1-methyl-but-2-enylidene)-naphthalene-1,5-diamine)을 함유하고 있었다. 반응 중에 리간드 L'이 리간드 L로 가수분해되었다는 것을 화합물 1의 구조가 강하게 암시하고 있다.

• Journal of Species Research
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• 제6권2호
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• pp.190-194
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• 2017

Two new species of the genus Luffariella (Dictyoceratida: Thorectidae), L. tubula n. sp. and L. koreana n. sp. were collected from Jeju-do, Korea. These species differ significantly from the previously reported five species in terms of shape and skeletal structure. L. tubula n. sp. has two categories in thickness of secondary fibres which were different from other species. L. koreana n. sp. is very similar to L. variabilis from Tahiti in skeletal structure, but differs in sponge shape with irregular branching and indistinct surface conules. Primary fibres of the two new species are separated from secondary and tertiary fibres.

• 대한수학회지
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• 제41권2호
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• pp.369-378
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• 2004

A canonical Finsler connection Nr is defined by a generalized Finsler structure called a (G, N)-structure, where G is a generalized Finsler metric and N is a nonlinear connection given in a differentiable manifold, respectively. If NT is linear, then the(G, N)-structure has a linearity in a sense and is called Berwaldian. In the present paper, we discuss what it means that NT is with a vanishing hv-torsion: ${P^{i}}\;_{jk}\;=\;0$ and introduce the notion of a stronger type for linearity of a (G, N)-structure. For important examples, we finally investigate the cases of a Finsler manifold and a Rizza manifold.