• Honam Mathematical Journal
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• v.39 no.1
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• pp.101-113
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• 2017

Let G be a semialgebraic group which is not necessarily compact. Let X be a proper semialgebraic G-set whose orbit space has a semialgebraic structure. In this paper we prove that X has a finite open straight G-CW complex structure.

• Journal of the Korean Chemical Society
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• v.57 no.6
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• pp.721-725
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• 2013

Reaction between 2-pyridinecarboxylic acid (Hpic) and $K_3[Cr(O_2)_4]$ give complex $[Cr(pic)_3].H_2O$ (1) which is characterized by elemental analysis and spectroscopic methods (FT-IR, Raman) and X-ray crystallography. In the crystal structure of 1, chromium atom with coordinated by three nitrogen and three oxygen atoms has a distorted octahedral geometry. Also a water molecule is incorporated in crystal network. Each water molecule acts as hydrogen bond bridging and connects two adjacent complexes by two $O-H{\cdots}O$ hydrogen bonds.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.463-476
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• 2006

It is known that there are no real hypersurfaces with parallel Ricci tensor in a nonflat complex space form ([6], [9]). In this paper we investigate real hypersurfaces in a complex projective space $P_n\mathbb{C}$ using some conditions of the Ricci tensor S which are weaker than ${\nabla}S=0$. We characterize Hopf hypersurfaces of $P_n\mathbb{C}$.

• Korean Journal of Computational Design and Engineering
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• v.9 no.4
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• pp.294-305
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• 2004

Highly detailed geometric models are rapidly becoming commonplace in computer graphics and other applications. These complex models, which is often represented as complex1 triangle meshes, mainly suffer from the vast memory requirement for real-time manipulation of arbitrary geometric shapes without loss of data. Various techniques have been devised to challenge these problems in views of geometric processing, not a representation scheme. This paper proposes the new mesh structure for the compact representation and the efficient handling of the highly complex models. To verify the compactness and the efficiency, the memory requirement of our representation is first investigated and compared with other existing representations. And then we analyze the time complexity of our data structure by the most critical operation, that is, the enumeration of the so-called one-ring neighborhood of a vertex. Finally, we evaluate some elementary modeling functions such as mesh smoothing, simplification, and subdivision, which is to demonstrate the effectiveness and robustness of our mesh structure in the context of the geometric modeling and processing.

• Journal of the Korean Chemical Society
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• v.57 no.3
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• pp.352-356
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• 2013

In this work, a new cadmium complex $[Cd(L)(CH_3COO)_2].2H_2O$ (1) with the ligand L, N,N'-bis(2-pyridinecarboxalidene)-1,2-cyclohexanediamine was prepared and identified by elemental analysis, FT-IR, Raman, $^1H$ NMR spectroscopy and single-crystal X-ray diffraction. The cadmium atom in the crystal structure of 1 has distorted triangular dodecahedral geometry by coordination of the four nitrogen atoms of L and four oxygen atoms of the two acetate ions. Two water molecules are also incorporated in the crystal network. The $O-H{\cdots}O$ hydrogen bonds present in the crystal structure of 1. In this work, three structural surveys including coordination numbers of the cadmium atom, coordination modes of L and resonance in pyridine-2-ylmethanimine-based compounds are presented.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.307-326
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• 2007

We know that there are no real hypersurfaces with parallel Ricci tensor or parallel structure Jacobi operator in a nonflat complex space form (See [4], [6], [10] and [11]). In this paper we investigate real hypersurfaces M in a nonflat complex space form $M_n(c)$ under the condition that ${\nabla}_{\varepsilon}S=0\;and\;{\nabla}_{\varepsilon}R_{\varepsilon}=0,\;where\;S\;and\;R_{\varepsilon}$ respectively denote the Ricci tensor and the structure Jacobi operator of M in $M_n(c)$.

• East Asian mathematical journal
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• v.37 no.1
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• pp.41-77
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• 2021

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (��, ξ, η, g) in a complex space form Mn+1(c), c ≠ 0. We denote by Rξ = R(·, ξ)ξ and A(i) be Jacobi operator with respect to the structure vector field ξ and be the second fundamental form in the direction of the unit normal C(i), respectively. Suppose that the third fundamental form t satisfies dt(X, Y ) = 2��g(��X, Y ) for certain scalar ��(≠ 2c)and any vector fields X and Y and at the same time Rξ is ��∇ξξ-parallel, then M is a Hopf hypersurface in Mn(c) provided that it satisfies RξA(1) = A(1)Rξ, RξA(2) = A(2)Rξ and ${\bar{r}}-2(n-1)c{\leq}0$, where ${\bar{r}}$ denotes the scalar curvature of M.

• Bulletin of the Korean Chemical Society
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• v.32 no.5
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• pp.1745-1747
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• 2011

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.317-336
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• 1998

We study real hypersurfaces of a complex space form such that the Jacobi operator with respect to the structure vector field and the structure tensor $\phi$ on the real hypersurface commute.

• Bulletin of the Korean Chemical Society
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• v.24 no.3
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• pp.393-396
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• 2003