• The Mathematical Education
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• v.29 no.1
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• pp.63-68
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• 1990

Let M be a differentiable manifold, TM its tangent bundle and FM its frame bundle. The theory of complete lifts and Horizontal lifts to FM of vector fields on M ahs been studied by many authors. Tn this paper, vertical lifts of functions vector fields md 1-forms on M to FM are studied.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.791-803
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• 2021

Earlier investigators have made detailed studies of geometric properties such as integrability, partial integrability, and invariants, such as the fundamental 2-form, of some canonical f-structures, such as f³ ± f = 0, on the frame bundle FM. Our aim is to study metallic structures on the frame bundle: polynomial structures of degree 2 satisfying F² = pF +qI where p, q are positive integers. We introduce a tensor field F_α, α = 1, 2…, n on FM show that it is a metallic structure. Theorems on Nijenhuis tensor and integrability of metallic structure F_α on FM are also proved. Furthermore, the diagonal lifts g^D and the fundamental 2-form Ω_α of a metallic structure F_α on FM are established. Moreover, the integrability condition for horizontal lift F_α^H of a metallic structure F_α on FM is determined as an application. Finally, the golden structure that is a particular case of a metallic structure on FM is discussed as an example.

• Honam Mathematical Journal
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• v.37 no.1
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• pp.53-63
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• 2015

We get a necessary and sufficient condition for a generalized affine connection in the affine orthonormal frame bundle over a smooth manifold (M, g) to be a Yang-Mills connection.

• East Asian mathematical journal
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• v.14 no.2
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• pp.317-320
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• 1998

The main result is that the connection form in the orthonormal frame bundle by the Levi-Civita connection over a Riemannian symmetric space is a Yang-Mills connection

• The Journal of the Convergence on Culture Technology
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• v.10 no.2
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• pp.181-185
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• 2024

The purpose of this research is to investigate how purchase cycle of a product and bundle frame influence consumers' responses to the bundle promotion. In order to test hypotheses of this study, we conducted an experimental study that was a 2(Purchase cyle: Long vs. Short) X 2(Bundle frame: 1+1 vs. Buy2 and 50% off) between-subjects design. The reseults of this study showed the interaction effects of purchase cycle of product and bundle frame on perceived level of discount and product attitude. Based on the results, we provide theoretical implcations to extent the existing research regarding bundling promotion. Moreover, the results of this study suggest some practical implications and a new aspect about bunle promotions.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.971-986
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• 2001

Equations. See Full-text.

• International Journal of Internet, Broadcasting and Communication
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• v.15 no.4
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• pp.100-106
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• 2023

Bundling has become a general promotion strategy in mobile shopping context. Previous research on bundling has mostly focused on bundle frame or price frame. Even though consumers are searching and purchasing the product in mobile channels, little research has investigated the effects of bundling in mobile shopping. The objectives of this study is to examine how different product image of bundle affects consumer's perception and purchase intention differently, and how brand familiarity moderate this influence. A sample of 140 subjects participated in a within-subjects experiment. A bundling composed of two different product image (a single product vs. bundled products) was evaluated by individuals. Brand familiarity (familiar brand vs. unfamiliar brand) were manipulated to test a set of hypotheses. We found that the effectiveness of bundling does not depend on the type of product image and brand familiarity. The findings of our study provide some implications for researchers and marketers. Although there have been studies on the effects of bundle framing on consumer behavior, we suggest new insights regarding bundling based on product image and mobile shopping context.

• Journal of Korea Multimedia Society
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• v.16 no.2
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• pp.160-168
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• 2013

In this paper an algorithm that represents shape sequences with moving frames parallel along the sequences are developed. According to Levi-Civita connection, it is not easy to measure the variation of the vector fields on non-Euclidean spaces without tools to parallel transport them. Thus, parallel transport of the vector fields along the shape sequences is implemented using the theories of principal frame bundle and analyzed via extensive simulation.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.40 no.5
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• pp.347-356
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• 2003

Camera pose and scene geometry estimation from video sequences is widely used in various areas such as image composition. Structure and motion recovery based on the auto calibration algorithm can insert synthetic 3D objects in real but un modeled scenes and create their views from the camera positions. However, most previous methods require bundle adjustment or non linear minimization process [or more precise results. This paper presents a new auto' calibration algorithm for video sequence based on two steps: the one is key frame selection, and the other removes the key frame with inaccurate camera matrix based on an absolute quadric estimation by LMedS. In the experimental results, we have demonstrated that the proposed method can achieve a precise camera pose estimation and scene geometry recovery without bundle adjustment. In addition, virtual objects have been inserted in the real images by using the camera trajectories.

• Journal of the Korean Mathematical Society
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• v.21 no.2
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• pp.183-206
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• 1984