• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.733-743
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• 2012

For the "Hopf bundle" $S^1{\rightarrow}S^{2n,1}{\rightarrow}\mathbb{C}H^n$, horizontal lifts of simple closed curves are studied. Let ${\gamma}$ be a piecewise smooth, simple closed curve on a complete totally geodesic surface $S$ in the base space. Then the holonomy displacement along ${\gamma}$ is given by $$V({\gamma})=e^{{\lambda}A({\gamma})i}$$ where $A({\gamma})$ is the area of the region on the surface $S$ surrounded by ${\gamma}$; ${\lambda}=1/2$ or 0 depending on whether $S$ is a complex submanifold or not. We also carry out a similar investigation for the complex Heisenberg group $\mathbb{R}{\rightarrow}\mathcal{H}^{2n+1}{\rightarrow}\mathbb{C}^n$.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.1001-1015
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• 2010

Let M be a $C^{\infty}$ real hypersurface in $\mathbb{C}^{n+1}$, $n\;{\geq}\;1$, locally given as the zero locus of a $C^{\infty}$ real valued function r that is defined on a neighborhood of the reference point $P\;{\in}\;M$. For each k = 1,..., n we present a necessary and sufficient condition for there to exist a complex manifold of dimension k through P that is contained in M, assuming the Levi form has rank n - k at P. The problem is to find an integral manifold of the real 1-form $i{\partial}r$ on M whose tangent bundle is invariant under the complex structure tensor J. We present generalized versions of the Frobenius theorem and make use of them to prove the existence of complex submanifolds.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.265-275
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• 2001

In the previous paper we studied n-dimensional CR-submanifolds of (n-1) CR-dimension immersed in a complex projective space CP(sup)(n+p)/2, and especially determined such submanifolds under curvature conditions related to vertical direction; In the present article we determine such submanifolds under curvature conditions related to horizontal directions.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.575-586
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• 2001

The purpose of this paper is to study n-dimensional CR-submanifolds of (n-1) CR-dimension immersed in a complex projective space $CP^{(n+p)/2}$, and especially to determine such submanifolds under some curvature conditions.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.43-50
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• 2005

We introduce the Joint spectrum on the complex Banach space and on the complex Hilbert space and the tensor product spectrums on the tensor product spaces. And we will show ${\sigma}[P(T_1,T_2,{\ldots},T_n)]={\sigma}(T_1{\otimes}T_2{\otimes}{\cdots}{\otimes}T_n)$ on $X_1{\overline{\otimes}}X_2{\overline{\otimes}}{\cdots}{\overline{\otimes}}X_n$ for a polynomial P.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.327-332
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• 2002

In this paper we prove that if M is a J-invariant sub-manifold of codimension 2 in a complex projective space $P_{n+1}(C)$, and the second fundamental tensor is cyclic-parallel or M has harmonic curvature, then M is locally complex quadric Q$_n$(C) or P$_n$(C).

• Analytical Science and Technology
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• v.14 no.6
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• pp.535-539
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• 2001

One-dimensional coordination polymer of cadmium(II) complex, $[Cd(SCN)_2(C_4H_6N_2]_n$, has been prepared and characterized by X-ray single crystallography. Structure analysis reveals that each cadmium(II) atom is six-coordinated in distorted octahedral fashion with $CdS_2N_4$ composition. $CdS_2N_4$ composition contains two S and two N atoms from four thiocyanates and tow N atoms from two 4-methylimidazole ligands. Central cadmium(II) atoms are run in parallel to the a-axis and are doubly bridged with neighboring cadmium(II) atoms by the thiocyanate and isothiocyanate ligands. Thus, this complex has a one-dimensional polymer structure in which the 4-methylimidazole is in the trans conformation.

• Bulletin of the Korean Chemical Society
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• v.11 no.5
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• pp.367-371
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• 1990

The near-IR spectra of thioacetamide were recorded for the investigation of hydrogen bonding between thioacetamide (TA) and N,N-dimethylalkylamides (DMF, DMA, DMP) in chloroform over the range of 5$^{\circ}C$ to 55$^{\circ}C$. The ${\nu}_{\alpha}$ + amide II combination band has been resolved into contributions from monomeric TA, 1:1 hydrogen bonded complex and 1:2 complex by the parameterized matrix modeling method. The association constants ($K_c$) of the complex have been obtained at various temperatures and used to determine the thermodynamic parameters for the hydrogen bonding by the usual Van't Hoff method. It was found that N,N-dimethylalkylamide forms less stable hydrogen bonded complex with TA in chloroform than in carbon tetrachloride.

• Bulletin of the Korean Chemical Society
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• v.17 no.5
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• pp.428-432
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• 1996

Amino acid cobalt(Ⅲ) complexes of 1,3-diminopropane-N,N'-di-α-(β-methyl)-pentanoic acid (H2dpdmp), uns-cis-[Co(dpdmp)(aa)] (aa=glycine, S-alanine, R-aspartic acid, sarcosine) have been prepared from the reaction between the uns-cis-[Co(dpdmp)Cl2]- complex and the corresponding amino acid. In the reaction with the uns-cis-[Co(dpdmp)Cl2]- complex, glycine and S-alanine have yielded both merridional and facial isomers, while R-aspartic acid and sarcosine, only merridional isomers. The stereospecific substitution reaction of R-aspartic acid to racemic uns-cis-[Co(dpdmp)Cl2]- complex has yielded two merridional diastereomers; ΛR-uns-cis- and ΛR-uns-cis-[Co(dpdmp)(R-asp)]. It is of interest to note that this is one of the few CoⅢ(ONNO)(aa) type complex preparations, which gives only one isomer with stereospecificity. On the other hand, two merridional products obtained from the reaction of sarcosine with racemic uns-cis-[Co(dpdmp)Cl2]- are turned out to be mixtures of optical isomers.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.209-216
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• 2010

A spectrally arbitrary complex sign pattern A is a complex sign pattern of order n such that for every monic nth degree polynomial f(x) with coefficients from $\mathbb{C}$, there is a matrix in the qualitative class of A having the characteristic polynomial f(x). In this paper, we show a necessary condition for a spectrally arbitrary complex sign pattern and introduce a minimal spectrally arbitrary complex sign pattern $A_n$ all of whose superpatterns are also spectrally arbitrary for $n\;{\geq}\;2$. Furthermore, we study the minimum number of nonzero parts in a spectrally arbitrary complex sign pattern.