• East Asian mathematical journal
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• 제15권2호
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• pp.337-344
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• 1999

If any geodesic on $F^n$ is also a geodesic on $\={F}^n$ and the inverse is true, the change $\sigma:L{\rightarrow}\={L}$ of the metric is called projective. In this paper, we will find the condition that a recurrent Finsler space remains to be a recurrent one under the projective change.

• Kyungpook Mathematical Journal
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• 제52권1호
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• pp.81-89
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• 2012

In the present paper, we nd the conditions to characterize projective change between two (${\alpha}$, ${\beta}$)-metrics, such as Matsumoto metric $L=\frac{{\alpha}^2}{{\alpha}-{\beta}}$ and Randers metric $\bar{L}=\bar{\alpha}+\bar{\beta}$ on a manifold with dim $n$ > 2, where ${\alpha}$ and $\bar{\alpha}$ are two Riemannian metrics, ${\beta}$ and $\bar{\beta}$ are two non-zero 1-formas.

• 대한수학회보
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• 제58권2호
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• pp.497-505
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• 2021

Let R → S be a ring homomorphism. The relations of Gorenstein projective dimension with respect to a semidualizing module of homologically bounded complexes between U ⊗LR X and X are considered, where X is an R-complex and U is an S-complex. Some sufficient conditions are given under which the equality ${\mathcal{GP}}_{\tilde{C}}-pd_S(S{\otimes}{L \atop R}X)={\mathcal{GP}}_C-pd_R(X)$ holds. As an application it is shown that the Auslander-Buchsbaum formula holds for GC-projective dimension.

• 대한수학회보
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• 제58권4호
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• pp.939-958
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• 2021

Some properties of strongly Gorenstein C-projective, C-injective and C-flat modules are studied, mainly considering these properties under change of rings. Specifically, the completions of rings, the localizations and the polynomial rings are considered.

• 대한수학회논문집
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• 제15권2호
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• pp.331-338
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• 2000

In the present paper, we investigate a problem in a sym-metric Finsler space, which is a special space. First we prove that if a symmetric space remains to be a symmetric one under the Z-projective change, then the space is of zero curvature. Further we will study W-recurrent space and D-recurrent space under the pro-jective change.

• 대한수학회보
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• 제53권3호
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• pp.779-791
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• 2016

Transfer of homological properties under base change is a classical field of study. Let $R{\rightarrow}S$ be a ring homomorphism. The relations of Gorenstein projective (or Gorenstein injective) dimensions of unbounded complexes between $U{\otimes}^L_RX$(or $RHom_R(X,U)$) and X are considered, where X is an R-complex and U is an S-complex. In addition, some sufficient conditions are given under which the equalities $G-dim_S(U{\otimes}^L_RX)=G-dim_RX+pd_SU$ and $Gid_S(RHom_R(X,U))=G-dim_RX+id_SU$ hold.

• 대한수학회지
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• 제10권2호
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• pp.89-91
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• 1973

• 대한수학회보
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• 제16권1호
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• pp.31-35
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• 1979

• 방송공학회논문지
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• 제4권2호
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• pp.87-102
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• 1999

가상의 삼 차원 컴퓨터 그래픽 영상을 실제 비디오 영상과 합성하는 증강현실을 구현하기 위해서는 카메라의 초점거리 같은 내부변수와 카메라가 어떻게 움직였는지를 나타내는 회전 및 직선 운동에 대한 이동정보가 반드시 필요하다. 따라서, 기존의 방법들은 미리 카메라의 내부변수를 계산해 둔 다음, 실제 영상에서 얻어지는 정보를 이용하여 카메라의 이동정보를 계산하거나, 실제 영상에 카메라 보정을 위한 삼 차원 보정 패턴이 보이도록 한다음 영상에서 그 패턴의 형태를 분석하여 카메라의 내부변수와 운동정보를 동시에 계산하는 방법을 사용하였다. 이 논문에서는 실제 영상에서 얻어지는 정합점들로부터 카메라 조정없이 구할 수 있는 투영기하공간 카메라 이동정보를 이용하여 증강현실을 구현하는 방법을 제안한다. 실제 카메라의 내부변수와 유클리드공간 이동정보를 대신하기 위하여 가상카메라를 정의하며, 가상카메라는 실제공간과 가상 그래픽 공간의 연결을 위하여 두 장의 영상에 사용자가 삽입하는 가상공간 좌표계의 기준점들의 영상좌표로부터 구해진다. 제안하는 방법은 카메라의 내부변수에 대한 정보를 따로 구할 필요가 없으며 컴퓨터 그래픽이 지원하는 모든 기능을 비유클리드공간의 정보로도 구현이 가능하다는 것을 보여준다.

• 한국CDE학회논문집
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• 제9권4호
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• pp.397-405
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• 2004

Texture mapping is the process of covering 3D models with texture images in order to increase the visual realism of the models. For proper mapping the coordinates of texture images need to coincide with those of the 3D models. When projective images from the camera are used as texture images, the texture image coordinates are defined by a camera calibration method. The texture image coordinates are determined by the relation between the coordinate systems of the camera image and the 3D object. With the projective camera images, the distortion effect caused by the camera lenses should be compensated in order to get accurate texture coordinates. The distortion effect problem has been dealt with iterative methods, where the camera calibration coefficients are computed first without considering the distortion effect and then modified properly. The methods not only cause to change the position of the camera perspective line in the image plane, but also require more control points. In this paper, a new iterative method is suggested for reducing the error by fixing the principal points in the image plane. The method considers the image distortion effect independently and fixes the values of correction coefficients, with which the distortion coefficients can be computed with fewer control points. It is shown that the camera distortion effects are compensated with fewer numbers of control points than the previous methods and the projective texture mapping results in more realistic image.