• 대한수학회보
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• 제54권3호
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• pp.975-992
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• 2017

In this article, we consider a real hypersurface of complex two-plane Grassmannians $G_2({\mathbb{C}}^{m+2})$, $m{\geq}3$, admitting commuting ${\ast}$-Ricci and pseudo anti-commuting ${\ast}$-Ricci tensor, respectively. As the applications, we prove that there do not exist ${\ast}$-Einstein metrics on Hopf hypersurfaces as well as ${\ast}$-Ricci solitons whose potential vector field is the Reeb vector field on any real hypersurfaces.

• Journal of applied mathematics & informatics
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• 제41권4호
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• pp.811-819
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• 2023

In this research we have used the definition of standard fractional vector cross product to obtain fractional curl and fractional field of a standing wave, a travelling wave, a transverse wave, a vector field in xy plane, a complex vector field and an electric field. Fractional curl and fractional field for a complex order are also discussed. We have supported the study with calculation of impedance at γ = 0, 0 < γ < 1, γ = 1. The formula discussed in this paper are useful for study of polarization, reflection, impedance, boundary conditions where fractional solutions have applications.

• 지구물리와물리탐사
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• 제27권1호
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• pp.51-56
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• 2024

논문에서는 타원판의 벡터 중력과 중력 변화율 텐서 반응식을 유도하였다. 타원판의 벡터 중력은 이중 적분으로 표현한 타원판에 의한 중력 퍼텐셜을 각 축 방향으로 미분하여 유도한다. 이중 적분으로 정의된 타원판에 의한 벡터 중력은 복소 그린 정리를 이용하여 타원판 경계를 따라 폐곡선의 선적분으로 변형한다. 최종적으로 타원판 경계를 매개변수로 설정하여 1차원 수치적분을 통하여 타원판에 의한 벡터 중력을 유도한다. 타원판에 의한 중력 변화율 텐서의 xz, yz, zz성분은 타원판의 벡터 중력을 수직 방향으로 미분하여 구한다. xx, yy, xy성분은 이중 적분 형태의 벡터 중력의 수평 성분을 먼저 수평 방향으로 미분한 후 복소 그린 정리를 이용하여 유도한다.

• Journal of Electrical Engineering and Technology
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• 제13권4호
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• pp.1715-1723
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• 2018

This work investigates the performance of fully complex- valued radial basis function network(FC-RBF) and complex extreme learning machine (CELM) based neural approaches for classification of power quality disturbances. This work engages the use of S-Transform to extract the features relating to single and combined power quality disturbances. The performance of the classifiers are compared with their real valued counterparts namely extreme learning machine(ELM) and support vector machine(SVM) in terms of convergence and classification ability. The results signify the suitability of complex valued classifiers for power quality disturbance classification.

• East Asian mathematical journal
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• 제36권3호
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• pp.389-415
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• 2020

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 R_ξ and R'_X be the structure Jacobi operator with respect to the structure vector ξ and be R'_X = (∇_XR)(·, X)X for any unit vector field X on M, 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_ξ𝜙 = 𝜙R_ξ and at the same time R'_ξ = 0, then M is a Hopf real hypersurfaces of type (A), provided that the scalar curvature ${\bar{r}}$ of M holds ${\bar{r}}-2(n-1)c{\leq}0$.

• 대한수학회보
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• 제47권3호
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• pp.551-561
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• 2010

In this paper we give a new characterization of real hypersurfaces of type B, that is, a tube over a totally geodesic $\mathbb{Q}P^n$ in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$, where m = 2n, with the Reeb vector $\xi$ belonging to the distribution $\mathfrak{D}$, where $\mathfrak{D}$ denotes a subdistribution in the tangent space $T_xM$ such that $T_xM$ = $\mathfrak{D}{\bigoplus}\mathfrak{D}^{\bot}$ for any point $x{\in}M$ and $\mathfrak{D}^{\bot}=Span{\xi_1,\;\xi_2,\;\xi_3}$.

• 전기학회논문지
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• 제61권11호
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• pp.1601-1605
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• 2012

Three-phase voltage and current is applied to the three-phase alternating current motors which are commonly used in industry. Three phase variables of a, b, c are converted into d, q, 0 axis and the AC machines are modeled and analyzed. Basically the coordinate transformation or d-q transformation is used for convenience, a few steps are needed to analyze the motor performances - separating d and q components, establishing each equivalent circuit, and solving the differential equations of the circuits. In this study, a modeling technique of induction motor using complex vector is proposed and it can explain the induction motor physically. This method does not need the separating process of d and q components. With this technique, the model becomes simple, is easy to understand in physical, and can get the same results with those from the other models. These simulation results of the proposed model are compared with them for the conformation of the proposed method.

• Kyungpook Mathematical Journal
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• 제57권3호
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• pp.525-535
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• 2017

In this paper, we consider two kinds of derivatives for the shape operator of a real hypersurface in a $K{\ddot{a}}hler$ manifold which are named the Lie derivative and the covariant derivative with respect to the k-th generalized Tanaka-Webster connection ${\hat{\nabla}}^{(k)}$. The purpose of this paper is to study Hopf hypersurfaces in complex Grassmannians of rank two, whose Lie derivative of the shape operator coincides with the covariant derivative of it with respect to ${\hat{\nabla}}^{(k)}$ either in direction of any vector field or in direction of Reeb vector field.

• 대한수학회논문집
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• 제21권4호
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• pp.631-640
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• 2006

In this paper, we prove sufficient conditions of boundedness of maximal operators on the p-adic vector space. We also consider weighted Hardy-Littlewood averages on the p-adic vector space.

• 대한수학회논문집
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• 제14권1호
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• pp.211-216
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• 1999

We study the anti-linear involutions on a real algebraic vector bundle with bundle with a compact real algebraic group action.