• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.523-537
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• 2020

In this work we consider the Sol₃ Lie group, equipped with the left-invariant metric, Lorentzian or Riemannian. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.73-80
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• 1992

We discuss transverse harmonic fields on compact foliated Riemannian manifolds, and give a necessary and sufficient condition for a transverse field to be a transverse harmonic one and the non-existence of transverse harmonic fields. 1. On a foliated Riemannian manifold, geometric transverse fields, that is, transverse Killing, affine, projective, conformal fields were discussed by Kamber and Tondeur([3]), Molino ([5], [6]), Pak and Yorozu ([7]) and others. If the foliation is one by points, then transverse fields are usual fields on Riemannian manifolds. Thus it is natural to extend well known results concerning those fields on Riemannian manifolds to foliated cases. On the other hand, the following theorem is well known ([1], [10]): If the Ricci operator in a compact Riemannian manifold M is non-negative everywhere, then a harmonic vector field in M has a vanishing covariant derivative. If the Ricci operator in M is positive-definite, then a harmonic vector field other than zero does not exist in M.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.817-823
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• 1998

In the present paper, we study conformal and projective Killing vector fields and infinitesimal Q-transformations on a quaternionic Kahlerian manifold, and prove that an infinitesimal conformal or projective automorphism in a compact quaternionic Kahlerian manifold is necessarily infinitesimal automorphism.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.70.3-70.3
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• 2019

We present a method to estimate 3-component plasma velocity (Vx, Vy and Vz) at solar photosphere near solar disk center, using the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) called Space-weather HMI Active Region Patch (SHARP). In Heliocentric-Cartesian Coordinates, the component of Vz is obtained from Dopplergram while the components of Vx and Vy are derived from the relation of $B_z{\overrightarrow{u}}=B_z{\overrightarrow{{\nu}_t}}-{\nu}_z{\overrightarrow{B_t}}$ (Demoulin & Berger 2003) using a series of vector magnetograms by an optical flow technique NAVE (Nonlinear Affine Velocity Estimator). This velocity measurement method is applied to AR 12158 producing an X1.6 flare along with a coronal mass ejection. We find noticeable upflow motions at both ends of flux ropes which become a major eruption part, and strong transverse motions nearby them before the eruption. We will discuss the change of plasma motions and magnetic fields before and after the eruption.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.989-999
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• 2023

The aim of this paper is to study the projective curvature tensor field of the Curvature tensor Rⁱ_jkh on a recurrent non Riemannian space admitting recurrent affine motion, which is also decomposable in the form Rⁱ_jkh=Xⁱ Y_jkh, where Xⁱ and Y_jkh are non-null vector and tensor respectively. In this paper we decompose Special Pseudo Projective Curvature Tensor Field. In the sequal of decomposition we established several properties of such decomposed tensor fields. We have considered the curvature tensor field Rⁱ_jkh in a Finsler space equipped with non symmetric connection and we study the decomposition of such field. In a special Pseudo recurrent Finsler Space, if the arbitrary tensor field 𝜓ⁱ_j is assumed to be a covariant constant then, in view of the decomposition rule, 𝜙_kh behaves as a recurrent tensor field. In the last, we have considered the decomposition of curvature tensor fields in Kaehlerian recurrent spaces and have obtained several related theorems.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.2
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• pp.79-88
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• 2004

Gaze detection is to locate the position on a monitor screen where a user is looking by computer vision. Gaze detection systems have numerous fields of application. They are applicable to the man-machine interface for helping the handicapped to use computers and the view control in three dimensional simulation programs. In our work, we implement it with a computer vision system setting a IR-LED based single camera. To detect the gaze position, we locate facial features, which is effectively performed with IR-LED based camera and SVM(Support Vector Machine). When a user gazes at a position of monitor, we can compute the 3D positions of those features based on 3D rotation and translation estimation and affine transform. Finally, the gaze position by the facial movements is computed from the normal vector of the plane determined by those computed 3D positions of features. In addition, we use a trained neural network to detect the gaze position by eye's movement. As experimental results, we can obtain the facial and eye gaze position on a monitor and the gaze position accuracy between the computed positions and the real ones is about 4.8 cm of RMS error.