• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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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 $n{\geq}1$.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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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).

• Journal of the Korean Applied Science and Technology
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• v.17 no.2
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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.

• Journal of the Korean Vacuum Society
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• v.6 no.S1
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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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• v.28 no.10
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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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.5
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• pp.1116-1121
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• 2014

Mesh structure is one of typical interconnection networks, and it is used in the part of VLSI circuit design. Torus and Hyper-Torus are advanced interconnection networks in the part of diameter and fault-tolerance of mesh structure. In this paper, we will analyze embedding between Torus and Hyper-Torus networks. We will show T(4k,2l) can be embedded into QT(m,n) with dilation 5, congestion 4, expansion 1. And QT(m,n) can be embedded into T(4k,2l) with dilation 3, congestion 3, expansion 1.

• Korean Journal of Crystallography
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• v.18 no.1_2
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• pp.21-25
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• 2007

When a $CH_2Cl_2$ solution of the dipyridyl species L' (N,N'-bis-(1-pyridin-4-yl-ethylidene)-naphthalene-1,5-diamine) was layered onto the top of a MeOH solution of $Co(NO_3)_2{\cdot}6H_2O$, a molecular cobalt compound [$CoL_2(MeOH)(NO_3)_2$] (1), not a coordination polymer, was formed. X-ray structural analysis of compound 1 revealed that it contains the pyridyl-amine ligand L (N1-(4-imino-1-methyl-but-2-enylidene)-naphthalene-1,5-diamine), instead of L'. Structure of compound 1 strongly suggests that the original ligand L' has been hydrolyzed to ligand L during the reaction.

• Journal of Species Research
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• v.6 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.41 no.2
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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.