• Nonlinear Functional Analysis and Applications
• /
• v.26 no.5
• /
• pp.985-994
• /
• 2021

The object of this paper is to study non-invariant hypersurface of a (𝜖, 𝛿)-trans Sasakian manifolds equipped with (f, g, u, v, λ)-structure. Some properties obeyed by this structure are obtained. The necessary and sufficient conditions also have been obtained for totally umbilical non-invariant hypersurface with (f, g, u, v, λ)-structure of a (𝜖, 𝛿)-trans Sasakian manifolds to be totally geodesic. The second fundamental form of a non-invariant hypersurface of a (𝜖, 𝛿)-trans Sasakian manifolds with (f, g, u, v, λ)-structure has been traced under the condition when f is parallel.

• International Journal of Computer Science & Network Security
• /
• v.21 no.12
• /
• pp.149-156
• /
• 2021

This study intended to test the structure of the latent factor of an effectiveness scale and the stability of invariance across groups of students' classifications (gender and levels of education). In the large, non-clinical sample (850), students completed the effectiveness scale. The (CFA) confirmatory factor analysis was used to investigate the factor-structure of the measure, and multiple-group confirmatory factor analysis (MGCFA) model was used to test the stability of invariance across groups of students' classifications. The findings of the CFA indicated support for the original four-factor model. Additional analyses of the MGCFA method support the measurement (configural, metric and strong) invariant and practical invariant components of this model. There was an invariant across gender. There was partially invariant across groups of levels of education. The scale exists in groups of levels of education assess the same concepts of, excluding Items 15 and 10. Given that this study is the first investigation for the structure of the effectiveness scale.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.867-873
• /
• 2024

A pseudo-Riemannian solvmanifold is a solvable Lie group endowed with a left invariant pseudo-Riemannian metric. In this short note, we investigate the nilpotency of the Ricci operator of pseudo-Riemannian solvmanifolds. We focus on a special class of solvable Lie groups whose Lie algebras can be expressed as a one-dimensional extension of a nilpotent Lie algebra ℝD⋉n, where D is a derivation of n whose restriction to the center of n has at least one real eigenvalue. The main result asserts that every solvable Lie group belonging to this special class admits a left invariant pseudo-Riemannian metric with nilpotent Ricci operator. As an application, we obtain a complete classification of three-dimensional solvable Lie groups which admit a left invariant pseudo-Riemannian metric with nilpotent Ricci operator.

• Journal of applied mathematics & informatics
• /
• v.2 no.1
• /
• pp.11-16
• /
• 1995

Scale Invariant Transforms are defined for both one- and two- dimensioned input functions. These have the desirable properties of linearity and invariance to scale change of the input.

• Korean Journal of Mathematics
• /
• v.20 no.4
• /
• pp.485-491
• /
• 2012

In this paper, we show the norm attaining paranormal operators have a nontrivial invariant subspace. Also, we show the norm attaining quadratically hyponormal weighted shift is subnormal.

• The Journal of the Korea institute of electronic communication sciences
• /
• v.15 no.2
• /
• pp.237-244
• /
• 2020

This paper describes an implement of Simultaneous Localization and Mapping(SLAM) in two dimensional space. The method uses Invariant Extended Kalman Filter(IEKF), which transforms the state variables and measurement variables so that the transformed variables constitute a linear space when variables called the invariant quantities are kept constant. Therefore, the IEKF guarantees convergence provided in the invariant quantities are kept constant. The proposed IEKF approach uses Lie group matrix for the transformation. The method is tested through simulation, and the results show that the Kalman gain is constant as it is the case for the linear Kalman filter. The coherence between the estimated locations of the vehicle and the detected objects verifies the estimation performance of the method.

• KIPS Transactions on Software and Data Engineering
• /
• v.3 no.9
• /
• pp.375-380
• /
• 2014

Under controlled environment, such as fixed viewpoints or consistent illumination, the performance of face recognition is usually high enough to be acceptable nowadays. Face recognition is, however, a still challenging task in real world. SIFT(Scale Invariant Feature Transformation) algorithm is scale and rotation invariant, which is powerful only in the case of small viewpoint changes. However, it often fails when viewpoint of faces changes in wide range. In this paper, we use Affine SIFT (Scale Invariant Feature Transformation; ASIFT) to detect affine invariant local descriptors for face recognition under wide viewpoint changes. The ASIFT is an extension of SIFT algorithm to solve this weakness. In our scheme, ASIFT is applied only to gallery face, while SIFT algorithm is applied to probe face. ASIFT generates a series of different viewpoints using affine transformation. Therefore, the ASIFT allows viewpoint differences between gallery face and probe face. Experiment results showed our framework achieved higher recognition accuracy than the original SIFT algorithm on FERET database.

• Journal of the Institute of Electronics Engineers of Korea CI
• /
• v.39 no.1
• /
• pp.60-66
• /
• 2002

In this paper, an efficient content-based rotation-invariant retrieval of the trademarks is proposed using the edge-direction histogram for a principal symmetry axis and the moment invariants. Rotation invariant retrieval of trademarks is difficult for the conventional retrieval systems because their feature vectors are not rotation-invariant. In this paper, to obtain rotation invariant feature vectors, in addition to invariant moments, the edge-direction histogram for a principal symmetry axis is introduced and is used to solve the bin shift problem of the histogram resulted from the rotated trademark. Performance evaluation has been carried out for a database of 300 kinds of trademarks including 20 kinds of typical trademarks which are reported to be difficult to retrieve when rotated, and the proposed scheme is proved to retrieve trademarks more efficiently, especially for the rotated trademarks, than the conventional methods.

• Bulletin of the Korean Mathematical Society
• /
• v.26 no.1
• /
• pp.47-52
• /
• 1989

Methods of Riemannian geometry has played an important role in the study of compact transformation groups. Every effective action of a compact Lie group on a differential manifold leaves a Riemannian metric invariant and the study of such actions reduces to the one involving the group of isometries of a Riemannian metric on the manifold which is, a priori, a Lie group under the compact open topology. Once an action of a compact Lie group is given an invariant metric is easily constructed by the averaging method and the Lie group is naturally imbedded in the group of isometries as a Lie subgroup. But usually this invariant metric has more symmetries than those given by the original action. Therefore the first question one may ask is when one can find a Riemannian metric so that the given action coincides with the action of the full group of isometries. This seems to be a difficult question to answer which depends very much on the orbit structure and the group itself. In this paper we give a sufficient condition that a subgroup action of a compact Lie group has an invariant metric which is not invariant under the full action of the group and figure out some aspects of the action and the orbit structure regarding the invariant Riemannian metric. In fact, according to our results, this is possible if there is a larger transformation group, containing the oringnal action and either having larger orbit somewhere or having exactly the same orbit structure but with an orbit on which a Riemannian metric is ivariant under the orginal action of the group and not under that of the larger one. Recently R. Saerens and W. Zame showed that every compact Lie group can be realized as the full group of isometries of Riemannian metric. [SZ] This answers a question closely related to ours but the situation turns out to be quite different in the two problems.

• The Journal of Korean Institute of Information Technology
• /
• v.17 no.5
• /
• pp.13-20
• /
• 2019

Recently, object detection technology based on CNN has been actively studied. Object detection technology is used as an important technology in autonomous vehicles, intelligent image analysis, and so on. In this paper, we propose a rotation change robust object detection system by applying MI-FL (Moment Invariant-Feature Layer) to SSD (Single Shot Multibox Detector) which is one of CNN-based object detectors. First, the features of the input image are extracted based on the VGG network. Then, a total of six feature layers are applied to generate bounding boxes by predicting the location and type of object. We then use the NMS algorithm to get the bounding box that is the most likely object. Once an object bounding box has been determined, the invariant moment feature of the corresponding region is extracted using MI-FL, and stored and learned in advance. In the detection process, it is possible to detect the rotated image more robust than the conventional method by using the previously stored moment invariant feature information. The performance improvement of about 4 ~ 5% was confirmed by comparing SSD with existing SSD and MI-FL.