• East Asian mathematical journal
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• v.38 no.5
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• pp.549-581
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• 2022

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

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.133-166
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• 2022

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form M_n+1(c) for c ≠ 0. We denote by S and R_𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain 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 S𝜉 = g(S𝜉, 𝜉)𝜉, then M is a real hypersurface in M_n(c) (⊂ M_n+1(c)) provided that $\bar{r}-2(n-1)c{\leq}0$, where $\bar{r}$ denotes the scalar curvature of M.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1705-1723
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• 2008

Let n be a 2-step nilpotent Lie algebra which has an inner product <, > and has an orthogonal decomposition $n\;=z\;{\oplus}v$ for its center z and the orthogonal complement v of z. Then Each element z of z defines a skew symmetric linear map $J_z\;:\;v\;{\longrightarrow}\;v$ given by <$J_zx$, y> = for all x, $y\;{\in}\;v$. In this paper we characterize Jacobi fields and calculate all conjugate points of a simply connected 2-step nilpotent Lie group N with its Lie algebra n satisfying $J^2_z$ = A for all $z\;{\in}\;z$, where S is a positive definite symmetric operator on z and A is a negative definite symmetric operator on v.

• The Journal of Engineering Research
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• v.1 no.1
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• pp.5-14
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• 1997

The purpose of thesis is to analyze the radiation characteristics of an offset gregorian antenna in order to design the satellite-loaded antenna. In order to compute the radiation pattern of the sub-reflector, the reflected wave is obtained by GO(Geometric Optics) at an arbitrary shaped sub-reflector. Then the total radiation EM wave is obtained by summing the diffracted fields obtained by UTD(Uniform Geometrical Theory of Diffraction) and the GO fields. In order to calculate the far field radiation pattern of the main reflector, the radiation integral equation is derived from the induced current density on reflector surface using PO(Physical Optics). The kernel is expanded in terms of Jacobi-Bessel series for increasing the computational efficiency, then the modified radiation integral is represented as the double integral equation independent of observation points. When the incident fields are assumed to be x-or y-polarized field, the characteristics of radiation patterns in the gregorian antenna is analyzed in case of the main reflector having the focal length of 62.4$\lambda$, diameter of 100$\lambda$, and offset height of 75$\lambda$, and the sub-reflector having the eccentricity of 0.501, the inter focal length og 32.8$\lambda$, the horn axis angle of $9^{\circ}$ and the half aperture angle of $15.89^{\circ}$. The cross-polarized level and side lobe level in the offset geogorian reflector are reduced by 30dB and 10dB, respectively, in comparison with those of the offset parabolic antenna.

• The Journal of Engineering Research
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• v.3 no.1
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• pp.159-169
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• 1998

The purpose of this study is to analyze the radiation characteristics of the shaped Cassegrainian antenna. Radiation pattern of the sub-reflector is calculated by GTD (Geometrical Theory of Diffraction) The complete radiation patterns are obtained by summing the reflect field from the surface and the diffracted fields from the edge. The first and the second derivative on the sub-reflector are calculated by the local interpolation technique. The Radiation characteristics of the main-reflector are obtained by integrating the surface current density, which is derived from PO approximation. The radiation integral is expanded by the Jacobi-Bessel series for the purpose of reducing the computation time.

• East Asian mathematical journal
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• v.40 no.1
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• pp.1-23
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• 2024

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). We denote by A, K and L the second fundamental forms with respect to the unit normal vector C, D and E respectively, where C is the distinguished normal vector, and by R_𝜉 = R(𝜉, ·)𝜉 the structure Jacobi operator. 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 , and at the same time R_𝜉K = KR_𝜉 and ∇_{𝜙∇𝜉𝜉}R_𝜉 = 0. In this paper, we prove that if it satisfies ∇_𝜉R_𝜉 = 0 on M, then M is a real hypersurface of type (A) in M_n(c) provided that the scalar curvature $\bar{r}$ of M holds $\bar{r}-2(n-1)c{\leq}0$.

• 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.

• Journal of the Korea Society of Computer and Information
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• v.19 no.9
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• pp.21-31
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• 2014

Singular value decomposition (SVD) has been widely used to identify unique features from a data set in various fields. However, a complex matrix calculation of SVD requires tremendous computation time. This paper improves the performance of a representative one-sided block Jacoby algorithm using a two-dimensional (2D) multi-core system. In addition, this paper explores an optimal multi-core system by varying the number of processing elements in the 2D multi-core system with the same 400MHz clock frequency and TSMC 28nm technology for each matrix-based one-sided block Jacoby algorithm ($128{\times}128$, $64{\times}64$, $32{\times}32$, $16{\times}16$). Moreover, this paper demonstrates the potential of the 2D multi-core system for the one-sided block Jacoby algorithm by comparing the performance of the multi-core system with a commercial high-performance graphics processing unit (GPU).

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.951-962
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• 2003

In this paper we address focal points and treat manifolds (M, g) whose Lorentzian metric tensors g have a spacelike $C^{0}$-hypersurface $\Sigma$ [10]. We apply Jacobi fields for such manifolds, and check the local length maximizing properties of $C^1$-geodesics. The condition of maximality of timelike curves(geodesics) passing $C^{0}$-hypersurface is studied.ied.

• Journal of the Korean Mathematical Society
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• v.40 no.1
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• pp.61-72
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• 2003

Let N be the quaternionic Heisenberg group equipped with a left-invariant metric. We characterize all the conjugate points along the geodesics on N.