• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.229-257
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• 2022

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, 𝜉, 𝜂, g) in a complex space form M_n+1(c), c ≠ 0. We denote by A and R_𝜉 the shape operator in the direction of distinguished normal vector field and the structure Jacobi operator with respect to the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(< 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_𝜉A = AR_𝜉 and at the same time ∇_𝜉R_𝜉 = 0 on M, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.85-89
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• 2003

Let V be a localizing infinite-dimensional complex Banach space. Let X be a flag manifold of finite flags either of finite codimensional closed linear subspaces of V or of finite dimensional linear subspaces of V. Let E be a holomorphic vector bundle on X with finite rank. Here we prove that E is uniform, i.e. that for any two lines $D_1$ R in the same system of lines on X the vector bundles E$\mid$D and E$\mid$R have the same splitting type.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.319-335
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• 2011

We classify equivariant topoligical complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most) three points are sufficient to classify equivariant vector bundles over real projective plane except one case. To do it, we relate the problem to classification on two-sphere through the covering map because equivariant vector bundles over two-sphere have been already classified.

• Bulletin of the Korean Chemical Society
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• v.14 no.1
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• pp.21-29
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• 1993

For the study of relaxation processes in complex spin system, a general master equation, which can be used to simulate a vast range of pulse experiments, has been formulated using the Liouville representation of quantum mechanics. The state of a nonequilibrium spin system in magnetic field is described by a density vector in Liouville space and the time evolution of the system is followed by the application of a linear master operator to the density vector in this Liouville space. In this master equation the nuclear spin relaxation due to intramolecular dipolar interaction or randomly fluctuating field interaction is explicitly implemented as a relaxation supermatrix for a strong coupled two-spin (1/2) system. The whole dynamic information inherent in the spin system is thus contained in the density vector and the master operator. The radiofrequency pulses are applied in the same space by corresponding unitary rotational supertransformations of the density vector. If the resulting FID is analytically Fourier transformed, it is possible to represent the final nonstationary spectrum using a frequency dependent spectral vector and intensity determining shape vector. The overall algorithm including relaxation interactions is then translated into an ANSIFORTRAN computer program, which can simulate a variety of two dimensional spectra. Furthermore a new strategy is tested by simulation of multiple quantum signals to differentiate the two relaxation interaction types.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.425-443
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• 2006

The aim of this paper is to obtain several results in approximation by Jackson-type generalizations of complex Picard, Poisson-Cauchy and Gauss-Weierstrass singular integrals in terms of higher order moduli of smoothness. In addition, these generalized integrals preserve some sufficient conditions for starlikeness and univalence of analytic functions. Also approximation results for vector-valued functions defined on the unit disk are given.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.819-835
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• 1998

The main purpose of this paper is to prove that if a real hypersurfaces M of a complex space form satisfies ${\nabla}_{\xi}S$=0 and $S{\xi}=\sigma\xi$ for some constant on $\sigma$ on M, then the structure vector field $\xi$ is principal, where S denotes the Ricci tensors of M.

• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.343-351
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• 2008

By supervised learning with p predictors, we frequently obtain a prediction function of the form $y\;=\;f(x_1,...,x_p)$. When $p\;{\geq}\;3$, it is not easy to understand the inner structure of f, except for the case the function is formulated as additive. In this study, we propose to use p simple graphs for visual understanding of complex prediction functions produced by several supervised learning engines such as LOESS, neural networks, support vector machines and random forests.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.11
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• pp.1089-1096
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• 2010

The relation between the vibration induced from machinery and the radiated sound is complicated. Acoustic intensity method is widely used to obtain the accuracy of noise measurement and noise identification. In this study, as groundwork, the complex acoustic intensity method is performed to identify noise source and transmission path on different free space point source fields. As an industrial application, the complex acoustic intensity method is applied to HVAC to identify sound radiation characteristics in the near field. Experimental complex acoustic intensity method was applied to HVAC, it is possible to identify noise sources in complicated sound field characteristics which noise sources are related with each other, and certificate the validity of complex acoustic intensity. Especially, it can be seen that complex acoustic intensity method using both of active and reactive intensity is vital in devising a strategy for identification of noise. Also, the vector flow of acoustic intensity was investigated to identify sound intensity distributions and energy flow in the near field of HVAC.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.107-118
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• 2017

In this paper we study CR-submanifolds of maximal CR-dimension by investigating extrinsic behaviors of integral curves of characteristic vector field on them. Also we consider the notion of ruled CR-submanifold of maximal CR-dimension which is a generalization of that of ruled real hypersurface and find some characterizations of ruled CR-submanifold of maximal CR-dimension concerning extrinsic shapes of integral curves of the characteristic vector field and those of CR-Frenet curves.

• Journal of the Korea Society of Computer and Information
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• v.16 no.5
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• pp.101-107
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• 2011

The optimum weight vector is studied to remove interference and jamming signals in adaptive array antenna system. The optimum weight vector is calculated to apply a minimum variance algorithm and cost function in linearly constrained conditions, and accurately estimates target's signal. Adaptive array antenna system is the system which improves signal to noise ratio(SNR) and decreases interference and jammer power. Adaptive array antenna system delays at tap output of antenna array element. Each tap finally makes the complex signal of one in multiplier complex weight. In order to obtain optimum's weight calculation, optimum weight vector is used in this paper. After simulation, resolution is increased below $3^{\circ}$, and sidelobe is decreased about 10 dB.