• 호남수학학술지
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• 제44권1호
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• pp.1-16
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• 2022

In this paper, we define and study warped product skew semi-invariant submanifolds of a locally golden Riemannian manifold. We investigate a necessary and sufficient condition for a skew semi-invariant submanifold of a locally golden Riemannian manifold to be a locally warped product. An equality between warping function and the squared normed second fundamental form of such submanifolds is established. We also construct an example of warped product skew semi-invariant submanifolds.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권1호
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• pp.1-8
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• 2001

Semi-invariant submanifolds of Lorentzian almost paracontact mani-folds are studied. Integrability of certain distributions on the submanifold are in vestigated. It has been proved that a LP-Sasakian manifold does not admit a proper semi-invariant submanifold.

• 호남수학학술지
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• 제42권4호
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• pp.829-841
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• 2020

The object of the present paper is to study the invariant submanifolds of (LCS)n-manifolds. We study generalized quasi-conformally semi-parallel and 2-semiparallel invariant submanifolds of (LCS)n-manifolds and showed their existence by a non-trivial example. Among other it is shown that an invariant submanifold of a (LCS)n-manifold is totally geodesic if the second fundamental form is any one of (i) symmetric, (ii) recurrent, (iii) pseudo symmetric, (iv) almost pseudo symmetric and (v) weakly pseudo symmetric.

• 호남수학학술지
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• 제43권1호
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• pp.35-46
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• 2021

The purpose of this paper is to study invariant pseudoparallel, Ricci generalized pseudoparallel and 2-Ricci generalized pseudoparallel submanifold of a para-Kenmotsu manifold and I obtained some equivalent conditions of invariant submanifolds of para-Kenmotsu manifolds under some conditions which the submanifolds are totally geodesic. Finally, a non-trivial example of invariant submanifold of paracontact metric manifold is constructed in order to illustrate our results.

• Bulletin of the Korean Chemical Society
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• 제35권3호
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• pp.805-810
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• 2014

The shape invariant potentials are proved to be exactly solvable, i.e. the wave functions and energies of a particle moving under the influence of the shape invariant potentials can be algebraically determined without any approximations. It is well known that the SWKB quantization is exact for all shape invariant potentials though the SWKB quantization itself is approximate. This mystery has not been mathematically resolved yet and may not be solved in a concrete fashion even in the future. Therefore, in the present work, to understand (not prove) the mystery an attempt of deriving exactly solvable potentials directly from the SWKB quantization has been made. And it turns out that all the derived potentials are shape invariant. It implicitly explains why the SWKB quantization is exact for all known shape invariant potentials. Though any new potential has not been found in this study, this brute-force derivation of potentials helps one understand the characteristics of shape invariant potentials.

• 한국통신학회논문지
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• 제19권1호
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• pp.1-9
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• 1994

In general, when IIR digital filter are designed from analog filters, the bilinera transformation and the impluse invariant tramsformation are commonly used. It is known, however, that high frequency response of digital filters designed by these transformations can not be well approximated to the sampled analog signals. In this paper, the symbol pulse invariant transformation is analyzed theoretically so that the symbol pulse invariant transformation which was originally application to a rectangular pulse is newly applied to double rate pulse signals and generic shape pulse signals. Also, the relation of spectra between a transfer function of digital filter and one of analog filter is considered. Further, we apply to design the digital high pass filters using the symbol pulse invariant transformation method.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
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• pp.517-519
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• 2004

This paper describes an approach to estimate a robot pose with an image. The algorithm of pose estimation with an image can be broken down into three stages : extracting scale-invariant features, matching these features and calculating affine invariant. In the first step, the robot mounted mono camera captures environment image. Then feature extraction is executed in a captured image. These extracted features are recorded in a database. In the matching stage, a Random Sample Consensus(RANSAC) method is employed to match these features. After matching these features, the robot pose is estimated with positions of features by calculating affine invariant. This algorithm is implemented and demonstrated by Matlab program.

• 대한수학회지
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• 제53권5호
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• pp.1149-1165
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• 2016

In this paper, we show that there exists no left invariant Riemannian metric h on the Heisenberg group H such that (H, h) is a symmetric Riemannian manifold, and there does not exist any H-invariant metric $\bar{h}$ on the Heisenberg manifold $H/{\Gamma}$ such that the Riemannian connection on ($H/{\Gamma},\bar{h}$) is a Yang-Mills connection. Moreover, we get necessary and sufficient conditions for a group homomorphism of (SU(2), g) with an arbitrarily given left invariant metric g into (H, h) with an arbitrarily given left invariant metric h to be a harmonic and an affine map, and get the totality of harmonic maps of (SU(2), g) into H with a left invariant metric, and then show the fact that any affine map of (SU(2), g) into H, equipped with a properly given left invariant metric on H, does not exist.

• 대한수학회보
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• 제36권2호
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• pp.239-246
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• 1999

We extend the Ding's vanishing theorem of $\delta$-invariant slightly on a Cohen-Macaulay local ring using the concept of Golod paris. we also investigate the relation between the vanishing of $\delta$-invariant and Hochster's Monomial Conjecture.

• 호남수학학술지
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• 제32권4호
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• pp.651-661
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• 2010

In this paper, we obtain a necessary and sufficient condition for a left invariant connection in the tangent bundle over a closed Lie group with a left invariant metric to be a Yang-Mills connection. Moreover, we have a necessary and sufficient condition for a left invariant connection with a torsion-free Weyl structure in the tangent bundle over SU(2) with a left invariant Riemannian metric g to be a Yang-Mills connection.