• Korean Journal of Mathematics
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• 제11권1호
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• pp.9-15
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• 2003

We investigate change of the vector $S_{\omega}$ induced by the conformal change in 5-dimensional $g$-unified field theory. These topics will be studied for the second class in 5-dimensional case.

• East Asian mathematical journal
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• 제30권5호
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• pp.599-607
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• 2014

We study lightlike hypersurfaces M of an indefinite Kaehler manifold $\bar{M}$ of quasi-constant curvature subject to the condition that the curvature vector field of $\bar{M}$ belongs to the screen distribution S(TM). We provide several new results on such lightlike hypersurfaces M.

• Korean Journal of Mathematics
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• 제13권2호
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• pp.209-215
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• 2005

We investigate change of the vector $S_{\omega}$ induced by the conformal change in 7-dimensional $g$-unified field theory. These topics will be studied for the second class with the first category in 7-dimensional case.

• 대한수학회논문집
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• 제30권4호
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• pp.457-469
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• 2015

From the point of view of pseudohermitian geometry, we classify Legendre surfaces of Sasakian space forms with non-minimal ${\hat{C}}$-parallel mean curvature vector field for the Tanaka-Webster connection.

• 충청수학회지
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• 제36권1호
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• pp.55-64
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• 2023

In this paper, we propose a two-level overlapping domain decomposition preconditioner for three dimensional vector field problems posed in H(div). We introduce a new coarse component, which reduces the computational complexity, associated with the coarse vertices. Numerical experiments are also presented.

• 대한수학회지
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• 제61권3호
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• pp.495-513
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• 2024

In the paper, we show that for a generic C¹ vector field X on a closed three dimensional manifold M, any isolated transitive set of X is singular hyperbolic. It is a partial answer of the conjecture in [13].

• 대한수학회논문집
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• 제21권3호
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• pp.429-432
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• 2006

We use Cauchy's functional equation to construct a new non-measurable set which is a (vector) subspace of \mathbb{R}$ and is of a codimensiion 1, considering \mathbb{R}$, the set of real numbers, as a vector space over a field \mathbb{Q}$ of rational numbers. Moreover, we show that \mathbb{R}$ can be partitioned into a countable family of disjoint non-measurable subsets.

• Communications for Statistical Applications and Methods
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• 제19권5호
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• pp.655-662
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• 2012

Classification is an important research field in pattern recognition with high-dimensional predictors. The support vector machine(SVM) is a penalized feature selector and classifier. It is based on the hinge loss function, the non-convex penalty function, and the smoothly clipped absolute deviation(SCAD) suggested by Fan and Li (2001). We developed the algorithm for the multiclass SVM with the SCAD penalty function using the local quadratic approximation. For multiclass problems we compared the performance of the SVM with the $L_1$, $L_2$ penalty functions and the developed method.

• 대한수학회보
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• 제47권5호
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• pp.951-960
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• 2010

We provide the set of left-invariant minimal unit vector fields on the semi-direct product $\mathbb{R}^n\;{\rtimes}_p\mathbb{R}$, where P is a nonsingular diagonal matrix and on the 7 classes of 4-dimensional solvable Lie groups of the form $\mathbb{R}^3\;{\rtimes}_p\mathbb{R}$ which are unimodular and of type (R).

• 대한수학회논문집
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• 제38권1호
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• pp.235-242
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• 2023

In this paper, we studied several geometrical aspects of a perfect fluid spacetime admitting a Ricci ρ-soliton and an η-Ricci ρ-soliton. Beside this, we consider the velocity vector of the perfect fluid space time as a gradient vector and obtain some Poisson equations satisfied by the potential function of the gradient solitons.